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We provide theoretical investigations and empirical evidence that the effective stresses in computational homogenization of inelastic materials converge with a higher rate than the local solution fields. Due to the complexity of industrial-scale microstructures, computational homogenization methods often utilize a rather crude approximation of the microstructure, favoring regular grids over accurate boundary representations. As the accuracy of such an approach has been under continuous verification for decades, it appears astonishing that this strategy is successful in homogenization, but is seldom used on component scale. A part of the puzzle has been solved recently, as it was shown that the effective elastic properties converge with twice the rate of the local strain and stress fields. Thus, although the local mechanical fields may be inaccurate, the averaging process leads to a cancellation of errors and improves the accuracy of the effective properties significantly. Unfortunately, the original argument is based on energetic considerations. The straightforward extension to the inelastic setting provides superconvergence of (pseudoelastic) potentials, but does not cover the primary quantity of interest: the effective stress tensor. The purpose of the work at hand is twofold. On the one hand, we provide extensive numerical experiments on the convergence rate of local and effective quantities for computational homogenization methods based on the fast Fourier transform. These indicate the superconvergence effect to be valid for effective stresses, as well. Moreover, we provide theoretical justification for such a superconvergence based on an argument that avoids energetic reasoning.

Porous materials are defined as materials that contain holes, voids, or spaces in their structures, which can be interconnected or isolated. In the most complex forms of these materials, the holes can have irregular shapes with a random distribution in size, location, and direction, making studying their properties a challenging problem. Additive manufacturing techniques offer opportunities to create complex structures, and in this paper, we investigate the effective mechanical properties of porous material produced by the Fused Displacement Modeling (FDM) technique. We also propose an algorithm for generating a porous body containing irregularly shaped holes with arbitrary distributions in size and location while maintaining specific porosity. Due to the orthotropic properties of bodies created by the FDM technique, Reinforced Isotropic Solid Modeling (RISM) is combined with existing theories that calculate the effective properties of isotropic materials. For the experiments, some modified standard specimen with a porosity of 0.05 to 0.40 has been fabricated, and the elastic modulus and ultimate stress have been calculated using the tensile test. Finally, the results are compared with experimental data.

Polymer electrolyte fuel cells (PEFCs) are key elements in governments' plans to create a future hydrogen economy, providing clean, affordable electrical power for vehicles and portable electronic devices, among other applications. However, excessive cost and limited performance and durability still limit PEFC commercialization. At this stage of technological development, reducing Pt loading while improving performance and durability requires a tailored design of effective properties (e.g., thermal conductivity and diffusivity) and electrochemical activity (e.g., electrochemical surface area) of porous transport layers. Multifunctional thin, porous layers must be optimized by a combination of modeling and experimental work at different scales, ranging from a single layer up to cell (and stack) level(s). Even though this challenging task has already motivated a large body of work, further research on effective properties through the multiscale pore structure of PEFCs is needed to meet PEFC targets in the coming years.

Symmetry 15(3), 646 (2023). doi:10.3390/sym15030646, Published by MDPI, Basel

An optimization problem is proposed for inferring physical properties of polycrystals given ultrasonic (elastic) wave velocity measurements, made across multiple sample orientations. The feasibility of the method is demonstrated by inferring both the effective grain elastic parameters and the grain c -axis orientation distribution function (ODF) of ice-core samples from Priestley glacier, Antarctica. The method relies on expanding the ODF in terms of a spherical harmonic series, which allows for a non-parametric estimation of the sample ODF. Moreover, any linear combination of the Voigt (strain) and Reuss (stress) homogenization scheme is allowed, although for glacier ice, the exact choice is found to matter little for bulk elastic behaviour, and thus for inferred physical properties, too. Finally, the accuracy of the inferred grain elastic parameters is discussed, including the well-posedness and shortcomings of the inverse problem, relevant for future adoptions in glaciology, geology and elsewhere.

In this paper we present a semi-multiscale methodology, where a micrograph is split into multiple independent numerical model subdomains. The purpose of this approach is to enable a controlled reduction in model fidelity at the microscale, while providing more detailed material data for component level- or more advanced finite element models. The effective anisotropic elastic properties of each subdomain are computed using periodic boundary conditions, and are subsequently mapped back to a reduced mesh of the original micrograph. Alternatively, effective isotropic properties are generated using a semi-analytical method, based on averaged Hashin–Shtrikman bounds with fractions determined via pixel summation. The chosen discretization strategy (pixelwise or partially smoothed) is shown to introduce an uncertainty in effective properties lower than 2% for the edge-case of a finite plate containing a circular hole. The methodology is applied to a aluminium alloy micrograph. It is shown that the number of elements in the aluminium model can be reduced by $$99.89\%$$ 99.89 % while not deviating from the reference model effective material properties by more than $$0.65\%$$ 0.65 % , while also retaining some of the characteristics of the stress-field. The computational time of the semi-analytical method is shown to be several orders of magnitude lower than the numerical one.

The study is aimed at the development of finite element models for the analysis of numerical physical systems, applying them to the simulation of heat and mass transfer processes occurring between human skin and textile structures. The proposed methodology and numerical analysis of textile structures can be applied to predict the physical properties and performance of future products at the design stage. For example, the finite element models can be used in the development of protective clothing, outdoor clothing, passive and active cooling systems. In this work, finite element analysis (FEA) was done by using Comsol Multiphysics and Matlab software.

In this work, a general mathematical model for functionally graded heterogeneous equilibrium boundary value problems is considered. A methodology to find the local problems and the effective properties of functionally graded materials (FGMs) with generalized periodicity is presented, using the asymptotic homogenization method (AHM). The present models consist of the matrix metal Mo and the reinforced phase ceramic ZrC, the constituent ratios and the property gradation profiles of which can be described by the designed volume fraction. Firstly, a new threshold segmentation method is proposed to construct the gradient structure of the FGMs, which lays the groundwork for the subsequent research on the properties of materials. Further, a study of FGMs varied along a certain direction and the influence of the varied constituents and graded structures in the behavior of heterogeneous structures are investigated by the AHM. Consequently, the closed–form formulas for the effective thermo–mechanical coupling tensors are obtained, based on the solutions of local problems of FGMs with the periodic boundary conditions. These formulas provide information for the understanding of the traditional homogenized structure, and the results also be verified the correctness by the Mori–Tanaka method and AHM numerical solution. The results show that the designed structure profiles have great influence on the effective properties of the present inhomogeneous heterogeneous models. This research will be of great reference significance for the future material optimization design.

The use of 3D printing in modular building connections is a novel and promising technique. However, the performance of 3D printed steel modular building connections has not been investigated adequately to date. Therefore, this paper presents a three-dimensional finite element model (FEM), using the multi-purpose software Abaqus, to study the effect of different geometrical and material parameters on the ultimate behaviour of modular building connections (herein named 3DMBC) using a wire and arc additive manufacturing (WAAM) method, as part of the UK’s 3DMBC (3D Modular Building Connections) project. The proposed model considers material and geometrical non-linearities, initial imperfections, and the contact between adjacent surfaces. The finite element results are compared with the currently available experimental results and validated to ensure developed FEM can be used to analyse the behaviour of 3DMBC with some adjustments. Case studies were investigated using the validated model to analyse the ultimate behaviour with different nominal and WAAM-produced materials under various loading arrangements. Based on the results, it is recommended to conservatively use the treated or untreated WAAM material properties obtained in θ = 90° print orientation in the finite element modelling of 3DMBCs considering the complex component arrangements and multi-directional loading in the modular connections. It is also noted that the thickness of beams and columns of fully 3D printed connections can be increased to achieve the same level of performance as traditional modular connections. For the 3DMBCs printed using untreated WAAM, the thickness increment was found to be 50% in this study.

In this article, an investigation was carried out to verify hybrid models capabilities to predict the effective properties of heterogeneous materials. A hybrid model (Formula presented.) is developed by combining artificial neural networks and micromechanical modeling. The homogenization approach used in this study is mainly based on Eshelby's inclusion problem. The (Formula presented.) model, once trained on an Eshelby's tensors database, showed an excellent predictive capabilities of the effective mechanical behavior and local stresses in heterogeneous materials. The obtained results with (Formula presented.) are compared to numerical estimations which are often costly in terms of computational time. The results presented in this work show that the developed hybrid model can provide a significant computational time saving by a factor up to 2000 for (Formula presented.) phases while maintaining its accuracy and reliability.

Polymer electrolyte coated carbon fibres embedded in polymeric matrix materials represent a multifunctional material with several application scenarios. Structural batteries, thermal management materials as well as stiffness adaptive composites, made from this material, are exposed to significant joule heat, when electrical energy is transferred via the carbon fibres. This leads to a temperature increase of up to 100 K. The thermal behaviour of this composite material is characterized in this numerical study based on a RVE representation for the first time. Compared to classical fibre reinforced plastics, this material comprises a third material phase, the polymer electrolyte coating, covering each individual fibre. This material has not been evaluated for effective thermal conductivity, specific heat and thermal behaviour on the microscale before. Therefore, boundary conditions, motivated from applications, are applied and joule heating by the carbon fibres is included as heat source by an electro-thermal coupling. The resulting temperature field is discussed towards its effect on the mechanical behaviour of the material. Especially the temperature gradient is pronounced in thickness direction, leading to a temperature drop of 1 °Cmm, which needs to be included in thermal stress analysis in future thermo-mechanically coupled models. Another important emphasis is the identification of suitable homogenization and model reduction strategies in order to reduce the numerical effort spent on the thermal problem. Therefore, traditional analytical homogenization methods as well as a newly proposed “Two-Level Lewis-Nielsen” approach are discussed in comparison to virtually measured effective quantities. This extensive comparison of analytical and numerical methods is original compared to earlier works dealing with PeCCF composites. In addition, the accuracy of the new Two-Level Lewis-Nielsen method is found to fit best compared to classical methods. Finally, a first efficient and accurate 2D representation of the thermal behaviour of the PeCCF composite is shown, which reduces computational cost by up to 97%. This benefit comes with a different Temperature drop prediction in thickness direction of 1.5 °Cmm. In the context of future modelling of multifunctional PeCCF composite materials with multiphysical couplings, this deviation is acceptable with respect to the huge benefit for computational cost.

This paper studies a mechanical metamaterial with tetrachiral topology by mathematical modeling. Chirality is the property of an object that makes the object distinguishable from its mirror image; chirality can be left- or right-handed. The mechanical response of two metamaterial unit cells with different configurations (patterns A and B) is investigated. It is found that the cubic cell with a regular pattern A exhibits orthotropic mechanical behavior under loading along three coordinate axes. An irregular pattern B differs from pattern A in that the upper face of the unit cell has an opposite chirality. This architectural transformation is considered as a topological defect, which enhances the twisting effect in the loaded metamaterial. Analysis of displacements and stresses shows that the mechanical behavior of the pattern B cell is described by the model of a transversely isotropic material. The orthotropic and transversely isotropic behavior of the cells of given configurations is also confirmed by the values of the effective elastic constants. Microstructural geometry and mechanical deformation of metamaterials are shown to be closely related. It is shown that a topological defect in a unit cell of a tetrachiral metamaterial strongly determines its twisting behavior.

In this paper, a novel auxetic structure with rotating squares with holes is investigated. The unit cell of the structure consists of four units in the shape of a square with cut corners and holes. Finally, the structure represents a kind of modified auxetic structure made of rotating squares with holes or sheets of material with regularly arranged diamond and square cuts. Effective and dynamic properties of these structures depend on geometrical properties of the structure. The structures are characterized by an effective Poisson’s ratio from negative to positive values (from about minus one to about plus one). Numerical analysis is made for different geometrical features of the unit cells. The simulations enabled the determination of the dynamic characteristic of the analyzed structures using vibration transmission loss, transmissibility, and mechanical impedance. Numerical calculations were conducted using the finite element method. In the analyzed cases of cellular auxetic structures, a linear elasticity model of the material is assumed. The dynamic characteristic of modified rotating square structures is strongly dependent not only on frequency. The dynamic behavior could also be enhanced by adjusting the geometric parameter of the structure. Auxetic and non-auxetic structures show different static and dynamic properties. The dynamic properties of the analyzed structures were examined in order to determine the frequency ranges of dynamic loads for which the values of mechanical impedance and transmissibility are appropriate.

Estimating porous media properties is a vital component of geosciences and the physics of porous media. Until now, imaging techniques have focused on methodologies to match image-derived flows or geomechanical parameters with experimentally identified values. Less emphasis has been placed on the compromise between image processing techniques and the consequences on topological and morphological characteristics and on computed properties such as permeability. The effects of some of the most popular image processing techniques (filtering and segmentation) available in open source on 3D X-ray Microscopy (micro-XRM) images are qualitatively and quantitatively discussed. We observe the impacts of various filters such as erosion-dilation and compare the efficiency of Otsu’s method of thresholding and the machine-learning-based software Ilastik for segmentation.

International audience; An image-based effective medium approximation (EMA) is developed so as to permit very fast transport properties evaluations of 3D porous media. From an image-based porous network (IBPN) built upon digital image processing of 3D binary images, we focus on throat’s local geometrical properties at the pore scale, for being the most sensible structural units which build up the local pressure. This approach is a 3D image–based extension of the critical point approach proposed in 2D fractures. We show, from analyzing various core rock samples available in the literature, that the asymptotic assumptions associated with the preeminence of critical points in throats are indeed geometrically relevant. We then describe how the image-based EMA evaluated from the conductances computed from the discrete IBPN can be reliably evaluated. The proposed method is evaluated upon the estimation of core sample permeability from binarized image obtained using X-ray tomography. Since it combines digital image treatments with statistical data post-processing without the need of computational fluid dynamics (CFD) computation, it is extremely cost efficient. The results are compared with a micro-scale Stokes flow computation in various rock samples. The sensitivity to the pore discretization also is discussed and illustrated.

International audience; Microcracks are known to affect the behaviour of the materials and several modelling studies are devoted to finding their effective elasticity. This paper aims to extend such investigation to thermal properties, concerning both the steady-state conduction and the thermoelasticity. Accounting simultaneously for the anisotropy induced by microcracks orientation and for their unilateral effect (different behaviour whether they are open or closed) remains a difficult task. In this work, 3D homogenization-based approaches are developed to derive closed-form estimations of the effective thermal properties of a microcracked media with arbitrarily oriented microcracks, either open or closed.

This paper reviews the analytical, numerical as well as the computational homogenization multiscale modelling schemes for determining the effective material properties for heterogeneous medium at the macroscopic level. It also looked at the limitations of the analytical homogenization techniques in simulating the effective non linear heterogeneous material behaviours (for example the rapid localization of damage and so on) as well as the advancements of the computational techniques in addressing these limitations. In addition, the possible future trends for the computational technique such as the development of a fully coupled micro-macro computational scheme were also discussed. It was concluded that although, the analytical technique was quite popular and straight forward, its inability to capture rapid localization of damage limited its application and that numerical and computational schemes were able to address these limitations as they relied on the establishment of constitutive relations for the macroscopic problems in a numerical form through which the macroscopic problems were constructed and solved in a nested manner.

The objective of this paper is to critically evaluate the accuracy and efficiency of a general-purpose micromechanics approach based on the Mechanics of Structure Genome (MSG), when it is applied to the constitutive modeling of 3D structures. The Generalized Method of Cell (GMC) is chosen as a reference method during efficiency evaluation. The predictions by Three-Dimensional Finite Element Analysis (3D FEA) are chosen as benchmarks during accuracy evaluation. Composites such as a continuous fiber-reinforced composite, a particle-reinforced composite, two discontinuous fiber-reinforced composites, and a woven composite are analyzed using MSG, GMC, and 3D FEA. During homogenization, MSG is found to be as accurate but much more efficient than 3D FEA, and despite high efficiency, GMC is found to sacrifice accuracy for efficiency. During dehomogenization, MSG is found to be as accurate as 3D FEA, but GMC is found not to be so accurate. The fidelity of MSG, when it is applied to the modeling of other structures (e.g., beams, plates, and shells), can be similarly evaluated.

Ultra-high temperature ceramics (UHTCs) are a class of materials that maintain their structural integrity at high temperatures, e.g. 2000 °C. They have been limited in their aerospace applications because of their relatively high density and the difficulty involved in forming them into complex shapes, like leading edges and inlets. Recent advanced processing techniques have made significant headway in addressing these challenges, where the introduction of multiscale porosity has resulted in lightweight UHTCs dubbed multiscale porous UHTCs. The effect of multiscale porosity on material properties must be characterized to enable design, but doing so experimentally can be costly, especially when attempting to replicate hypersonic flight conditions for relevant testing of selected candidate samples. As such, this dissertation seeks to computationally characterize the thermomechanical properties of multiscale porous UHTCs, specifically titanium diboride, and validate those results against experimental results so as to build confidence in the model. An implicit quasi-static variant of the Material Point Method (MPM) is developed, whose capabilities include intrinsic treatment of large deformations and contact which are needed to capture the complex material behavior of the as-simulated porous UHTC microstructures. It is found that the MPM can successfully obtain the elastic thermomechanical properties of multiscale porous UHTCs over a wide range of temperatures. Furthermore, characterizations of post-elastic behavior are found to be qualitatively consistent with data obtained from uniaxial compression experiments and Brazilian disk experiments. Doctor of Philosophy This dissertation explores a class of materials called ultra-high temperature ceramics (UHTCs). These materials can sustain very high temperatures without degrading, and thus have the potential to be used on hypersonic aircraft which routinely experience high temperatures during flight. In lieu of performing experiments on physical UHTC specimens, one can perform a series of computer simulations to figure out how UHTCs behave under various conditions. This is done here, with a particular focus what happens when pores are introduced into UHTCs, thus rendering them more like a sponge than a solid block of material. Doing computer simulations instead of physical experiments is attractive because of the flexibility one has in a computational environment, as well as the significantly decreased cost associated with running a simulation vs. setting up and performing an experiment. This is especially true when considering challenging operating environments like those experienced by high-speed aircraft. The ultimate goal with this research is to develop a computational tool than can be used to design the ideal distribution of pores in UHTCs so that they can best perform their intended functions.

Article number 730 Porosity is a characteristic present in most sintered materials, full densification only being achieved in special cases. For some sintered materials, porosity is indeed a desired characteristic, serving for the intended application of the material. In any case, the porosity present in materials can have a strong effect on some of their properties, both structural and functional. In this paper, some of the expressions proposed to describe the influence of the total porosity on the effective properties of sintered materials are examined. Moreover, a universal expression (with two fitting parameters) valid to satisfactorily represent all the analysed behaviours is proposed. One of these parameters can be assimilated to the tap porosity of the powders used to manufacture the material. The properties examined were elastic moduli, ultimate strength, thermal and electrical conductivities, magnetic characteristics, and other properties directly related to these ones. The study is valid for sintered materials, both metallic and ceramic, with a homogeneous and non-texturised microstructure. Ministerio de Economía y Competitividad (España) DPI2015-69550-C2-1-P Feder DPI2015-69550-C2-2-P Fundación Portuguesa para la Ciencia y la Tecnología (FCT) UIDB / 50022/2020

A comprehensive micromechanical model for the analysis of structurally periodic and fully coupled magneto-electric and thermoelastic smart composite and reinforced thin shells is developed on the basis of Asymptotic Homogenization. Starting with the quasi-static approximation of Maxwell’s equations as well as force and thermal balance the model is decomposed into a macroscopic and a microscopic problem which are treated separately and sequentially even though the two scales are inherently coupled and co-existent in the original structure. The microscopic problem allows the computation of the effective coefficients and the macroscopic problem determines an asymptotic approximation of the field variables (stress, electric displacement, heat flux etc.). It is shown that in the limiting case of a thin elastic shell whereby any magnetoelectric and thermal behavior is suppressed, the derived model converges to the familiar classical shell model. As illustrated, the results of the model constitute an important refinement over previously established work.

Homogenization theories provide models that simplify the constitutive description of heterogeneous media while retaining their macroscopic features. These theories have shown how the governing fields can be macroscopically coupled, even if they are microscopically independent. A prominent example is the Willis theory which predicted the strain–momentum coupling in elastodynamic metamaterials. Recently, a theory that is based on the Green’s function method predicted analogous electro–momentum coupling in piezoelectric metamaterials. Here, we develop a simpler scheme for fibrous piezoelectric composites undergoing antiplane shear waves. We employ a source-driven approach that delivers a unique set of effective properties for arbitrary frequency–wavevector pairs. We numerically show how the resultant homogenized model recovers exactly the dispersion of free waves in the composite. We also compute the effective properties in the long-wavelength limit and off the dispersion curves, and show that the resultant model satisfy causality, reciprocity and energy conservation. By contrast, we show how equivalent models that neglect the electromomentum coupling violate these physical laws.

International audience; The effective piezoelectric properties of heterogeneous materials are evaluated in the context of periodic homogenization, whereby a variational formulation is developed, articulated with the extended Hill macrohomogeneity condition. The entire set of homogenized piezoelectric moduli is obtained as the volumetric averages of the microscopic properties of the individual constituents weighted by the displacement and polarization localization operators. This framework is extended in a second part of the paper to the computation of the flexoelectric effective properties, thereby accounting for higher gradient effects that may be induced by a strong contrast of properties of the composite constituents. The effective properties of inclusion-based composites are evaluated numerically as an illustration of the general homogenization theory and the respective effect of the volume fraction and relative tensile modulus of the reinforcement is assessed numerically.

Porous materials are of interest because of their applications in many areas of everyday life. Nevertheless, the relation between their effective properties and porous microstructures which are complex and dependent on the production process remains poorly resolved. In addition, the current need to decrease the dependence on petroleum justifies the current demand for the development of more environmentally friendly polymeric materials. In order to respond to these issues, this research work is devoted to the study of the microstructures-properties relation through the development of new porous materials based on bio-sourced epoxy resins for acoustic and thermal insulation in construction. The first part of the thesis concerns the elaboration and experimental characterization of porous materials synthesized by cationic polymerization under irradiation of resorcinol diglycidyl ether. Model macroporous materials obtained using a sintered salt template have allowed correlation with the modeling aspect. The optimization of UV polymerization of an opaque formulation has resulted in resorcinol-diatomite composites with attractive mechanical, acoustic and thermal characteristics and significant flame retardancy properties. The second part focuses on the development of multiscale methods for the numerical characterization of effective properties of elaborated macroporous resins. Based on the asymptotic homogenization method, this multiscale framework has permitted to show the effect of diverse microstructural characteristics on the macroscopic behaviour of the studied materials., Les matériaux poreux sont d’intérêts en raison de leurs utilisations dans de nombreux domaines du quotidien. Néanmoins, la relation entre leurs propriétés effectives et leurs microstructures poreuses lesquelles sont complexes et dépendantes du processus d’élaboration reste encore mal résolue. De plus, la nécessité actuelle de diminuer la dépendance vis-à-vis du pétrole justifie la demande actuelle pour le développement de matériaux polymériques plus respectueux de l’environnement. Afin de répondre à ces problématiques, cette étude est consacrée à l’étude de la relation microstructures-propriétés à travers le développement de nouveaux matériaux poreux à base de résines époxydes biosourcées pour l’isolation acoustique et thermique dans la construction. La première partie de la thèse concerne l’élaboration et la caractérisation expérimentale de matériaux poreux synthétisés par polymérisation cationique sous irradiation de l’éther diglycidique de résorcinol. Des matériaux macroporeux modèles obtenus à l’aide d’un gabarit de sels frittés ont permis la corrélation au volet modélisation. L’optimisation de la polymérisation sous UV d’une formulation opaque a conduit à des composites résorcinol-terre de diatomée dont les caractéristiques mécaniques, acoustiques et thermiques sont attrayantes et les propriétés de retard au feu significatives. La deuxième partie se concentre sur le développement de méthodes multi-échelles pour la caractérisation numérique des propriétés effectives des résines macroporeuses élaborées. Basée sur la méthode d’homogénéisation asymptotique, ce cadre multi-échelle a permis de montrer l'effet de diverses caractéristiques microstructurales sur le comportement macroscopique des matériaux étudiés.

The mechanical properties of heterogeneous geomaterials are evaluated by simultaneously taking into account the microstructural anisotropy as well as the one of matrix. To this end, the microstructural anisotropy is represented by the complexity of porous shape which is considered in the present work as concave or convex by particular attention to the superspherical and the axisymmetrical superspheroidal pores. The concentration and contribution tensors are numerically computed using Finite Element Method (FEM), which are next approximated by analytical expressions for the case of the concavity parameter being p, Les propriétés mécaniques des géomatériaux hétérogènes sont évaluées en prenant simultanément en compte l'anisotropie microstructurale ainsi que celle du matériau matriciel. A cet effet, l'anisotropie de la microstructure est représentée par la complexité de forme poreuse et/ou d'inclusion qui est considérée dans le présent travail comme concave ou convexe en portant nos attentions particulières aux pores supersphériques et supersphéroïdaux axisymétriques. Les tenseurs de concentration et de contribution sont calculés numériquement à l'aide de la méthode des élément finis (FEM), qui est ensuite utilisés au niveau de la modélisation semi-analytique pour l'objectif d'évaluer des propriétés effectives associées, telles que des réponses effectives élastiques et celles de conductivité. Plus précisément, afin de résoudre le 2ème problème d'Eshelby (Eshelby (1961)) dans le cas d'inhomogénéités 3D et non ellipsoïdales, nous utilisons conditions aux limites adaptées récemment développées par Adessina et al. (2017) basé sur une solution en champ lointain (Sevostianov and Kachanov (2011)) pour intégrer l'anisotropie matricielle et la correction du biais induit par le caractère borné du domaine du maillage, ce qui permet d'accélérer la convergence du calcul sans sacrifier sa précision. En adoptant la technique d'homogénéisation numérique, les tenseurs de contribution compliance/résistivité sont calculés pour différentes formes de pores (attention particulière des pores supersphéroïdaux et supersphériques) noyés dans une matrice isotrope transverse. La méthode numérique proposée s'avère efficace et précise après un grand nombre d'estimations et leurs validations. Dans certains cas particuliers, ces validations s'effectuent avec des comparaisons entre les résultats analytiques et numériques disponibles dans littérature. En prenant en compte les résultats numériques obtenus pour des microstructures tridimensionnelles (3D) considérées, les tenseurs de contribution dans les deux cas d'inclusions/pores concaves indiqués ci-dessus, supersphère et supersphéroïde axisymétrique, sont développées dans les contextes des problèmes élastiques et thermiques. Notons ici que la forme d'inclusion/pore sphérique (i.e. paramètre de concavité p=1) ainsi que celle de fissure circulaire (i.e. rapport d'aspect γ → 0), qui peuvent être considérés comme deux cas particuliers, sont également étudiés. Cela permet d'évaluer et de valider la méthode proposée dans le présent travail. De plus, dans le cadre de l'homogénéisation, une application aux géomatériaux poreux à matrice isotrope transverse, tels que les roches argileuses, est présentée pour illustrer l'impact du paramètre de concavité et celui de l'anisotropie de la matrice sur les propriétés globales à travers plusieurs schémas d'homogénéisation micromécanique, tels que l'approche basée sur l'approximation de non-interaction (i.e. NIA: Non-Interaction Approximation), schéma de Mori-Tanaka-Benveniste et celui de Maxwell. Les propriétés effectives des composites à pores réguliers sont également estimées à l'aide de l'approche dite champ complet par simulations numériques, puis comparées à la modélisation micromécanique. L'effet de microstructure complexes est étudié en considérant des Volumes Elémentaires Représentatifs (VERs) périodiques contenant des arrangements aléatoires des pores noyés dans des matrices isotropes transverses.

International audience; The aim of this paper is to investigate the effective properties of Fe–TiB2 composites obtained after hot or cold rolling. The elastic moduli of both hot and cold rolled composites are measured experimentally using several methods. Microstructure analyses based on SEM observations are performed to characterize the distribution of particles and cracks, and are then used to generate 3D representative microstructures using the RSA method. This allows the numerical determination of the overall elastic behavior of Fe–TiB2 composites using full-field FFT-based simulations. In addition, Young’s moduli of the hot rolled Fe–TiB2 composites are also determined analytically using the mean-field homogenization scheme of Mori–Tanaka. The elastic properties determined experimentally, analytically and numerically are in a good agreement. Overall, a significant improvement of the specific stiffness in comparison to standard steels is achieved irrespective of the processing conditions

This study identified the governing variables affecting the effective properties of the representative volume element (RVE) of nanocomposites consisting of unidirectionally aligned carbon nanotubes (CNTs) and determined the mechanism through which they act. For this purpose, multi-walled nanotubes (MWNTs) and polyvinylidene fluoride (PVDF) were selected as the components of the nanocomposites, and Monte Carlo simulations were conducted to examine the variability of the effective properties according to the CNT length. The governing variables affecting the effective properties were identified considering the conditions under which the selected CNTs can be arranged inside the RVE. Using the geometrical relationship between the RVE and CNTs, a simplified two-parameter equation that can calculate the effective properties of the RVE was derived. Using this equation and Monte Carlo simulations, this study confirmed that the characteristics of the effective properties vary with changes in the length of the RVE and the length fraction of the CNTs, and the mechanism of these changes was determined. In addition, the variation in the characteristics of the effective properties according to the coefficient of variation of the CNT length was also determined.

This paper presents a verification and validation analysis of Finite Element (FE) models predicting the mechanical response of linearly elastic honeycomb structures. We have studied three main models, namely: analytical models based on beam theories, explicit FE models where the cell geometry is explicitly meshed with 3D elements, and numerical homogenized FE models where a plate made of a honeycomb structure is meshed with 2D elements whose mechanical properties were predicted from numerical homogenization. We compared the predictions of these simulations against experimental uni-axial tensile tests where we mechanically tested 3D printed honeycomb specimens having a relative density of 40% and made of 13 and 37 cells, respectively. Comparison of the experimentally measured axial stiffness to the numerical predictions revealed that the numerical homogenization models can predict the apparent in-plane stiffness in structures made of 37 cells within 4%, while the discrepancy increases to 70% when 13 cells are considered. To quantify this discrepancy, we also provided a relationship between the number of represented cells and the discrepancy of the numerical homogenized model against the explicit FE models to predict the in-plane stiffness. We believe that these results could be important for the application of the homogenized models in optimization of honeycomb lattice structures whose relative density varies with space.

The gas diffusion layer (GDL) typically consists of a thin layer of carbon fiber paper, carbon cloth or nonwoven and has numerous pores. The GDL plays an important role that determines the performance of the fuel cell. It is a medium through which hydrogen and oxygen are transferred and serves as a passage through which water, generated by the electrochemical reaction, is discharged. The GDL tissue undergoes a compressive loading during the stacking process. This leads to changes in fiber content, porosity and resin content due to compressive load, which affects the mechanical, chemical and electrical properties of the GDL and ultimately determines fuel cell performance. In this study, the geometry of a GDL was modeled according to the compression ratios (10%, 20%, 30%, 40% and 50%), which simulated the compression during the stacking process and predicted the equivalent properties according to the change of GDL carbon fiber content, matrix content and pore porosity, etc. The proposed method to predict the equivalent material properties can not only consider the stacking direction of the material during stack assembling process, but can also provide a manufacturing standard for fastening compressive load for GDL.

As at the nanoscale the surface-to-volume ratio may be comparable with any characteristic length, while the material properties may essentially depend on surface/interface energy properties. In order to get effective material properties at the nanoscale, one can use various generalized models of continuum. In particular, within the framework of continuum mechanics, the surface elasticity is applied to the modelling of surface-related phenomena. In this paper, we derive an expression for the effective bending stiffness of a laminate plate, considering the Steigmann&ndash, Ogden surface elasticity. To this end, we consider plane bending deformations and utilize the through-the-thickness integration procedure. As a result, the calculated elastic bending stiffness depends on lamina thickness and on bulk and surface elastic moduli. The obtained expression could be useful for the description of the bending of multilayered thin films.

International audience; Recent works demonstrated the abilities of magneto rheological elastomers (MREs) for mechanical to electrical energy conversion. This class of materials consists of composites composed of a soft elastic matrix filled by ferromagnetic particles. In this work we focus primarily on anisotropic MREs featuring particles that are non-homogenously dispersed in the matrix but form of chains of particles. Such anisotropic MRE are good candidates for energy conversion and harvesting purpose because of the coupling between high magnetization of the soft ferromagnetic particles and low elastic modulus of the matrix; thus, the anisotropic MREs can convert a mechanical cyclic deformation into electric signal. In the framework of magnifying the conversion capabilities of such materials, this study reports the investigation of different filling factors of particles, submitted to various magnetic excitations and amplitudes of mechanical deformation. The multiscale analysis provided by this work, from local effect to global characterization, shows that optimal conditions depend on intrinsic material parameters (e.g., filling factor) as well as external conditions (mainly bias magnetic flux density and applied mechanical solicitation).

Актуальність теми: Магнітоактивні еластомери відносяться до класу «розумних» матеріалів, що змінюють власні властивості при зміні зовнішніх умов. Своєю приналежністю до цього класу вони зобов'язані ряду цікавих особливостей поведінки в магнітному полі. Еластомери здатні виявляти магнітну пам'ять форми, магнітодеформаціонний і магнітореологічний ефекти і т.д., що робить їх вкрай цікавими матеріалами для фундаментального дослідження і практичних застосувань. Зв’язок роботи з науковими програмами, планами, темами: тема роботи відповідає пріорітетному науковому напрямку кафедри загальної фізики та фізики твердого тіла – «Фундаментальні наукові дослідження з найбільш важливих проблем розвитку науково-технічного, соціальноекономічного, людського потенціалу для забезпечення конкурентоспроможності України у світі та сталого розвитку суспільства і держави». Робота виконана в межах держбюджетних тем та тематичних планів науководослідних робіт Міністерства освіти і науки України. Об’єкт дослідження: ефективні властивості магнітоактивних еластомерів. Предмет дослідження: теорія середнього поля та її модифікації для дослідження ефективних властивостей магнітоактивних еластомерів. Мета роботи: дослідити модифікації теорії середнього поля для опису поведінки магнітоактивних еластомерів в зовнішньому магнітному полі. Методи дослідження: основні результати роботи одержано за допомогою теоретичного дослідження та чисельних обчислень. Задачі дослідження: 1. дослідити модифікацію для описання пружних властивостей композитів; 2. дослідити модифікацію для описання термоелектричних властивостей композитів; 3. дослідити модифікацію для описання поведінки магнітоактивних еластомерів у зовнішньому магнітому полі ; Наукова новизна одержаних результатів: вперше теоретично отримано порядок магнітореологічного ефекту, який видно на експерименті, і передбачено новий ефект впливу магнітного поля на модуль Пуассона. Практичне значення одержаних результатів: модифікована теорія, що досліджена в магістерській роботі дозволяє усунути деякі недоліки старих теорій та розширює сферу використання теорії. Апробація результатів дисертації: під час роботи над дисертацією було написано чотири статті, дві з яких, на данний момент, вже опубліковано в наукових журналах. Публікації: стаття на тему «Effective Medium Theory for the Elastic Properties of Composite Materials with Various Percolation Thresholds» в журналі “MDPI Materials” , стаття на тему «Теорія середнього поля для термоелектричних властивостей композитних матеріалів з різними порогами протікання» в журналі “Термоэлектричество”. Actuality of theme: magnetoactive elastomers support a class of "smart" materials that change their own properties under external influence. By belonging to this class, they associate a variety of behaviors in a magnetic field. Elastomers are capable of magnetic memory form effect, magnetodeformation and magnetorheological effects, etc. Relationship of work with scientific programs, plans, themes: the theme of the work corresponds to the priority scientific direction of the Department of General Physics and Solid State Physics - "Fundamental scientific researches on the most important problems of development of scientific and technical, socioeconomic, human potential for ensuring the competitiveness of Ukraine in the world and sustainable development of society and the state." The work was carried out within the limits of the state budget topics and thematic plans of research works of the Ministry of Education and Science of Ukraine. Object of research: effective properties of magnetoactive elastomers. Subject of research modification and extension of the effective medium theory to study the effective properties of magnetoactive elastomers. Purpose of work: the purpose of the individual task is to study the modification of the effective medium theory with a movable percolation threshold. Research methods: the main results of the work were obtained with the help of theoretical research and numerical calculations. Tasks of research: 1. Make two types of thermal film based on mixtures of liquid crystals, soot and polymer. 2. Investigate spectra of optical reflection at different temperatures in the range of cholesterol phase. 3. Investigate the effect of mixtures of cholesterol liquid crystals on the dielectric properties of their dispersions in polyvinyl alcohol. Scientific novelty of the results: for the first time, the order of the magnetorheological effect observed in the experiment is theoretically obtained, and it creates a new action of the magnetic field on the Poisson modulus. The practical significance of the results: modified theory, studied in the master's thesis allows to eliminate some shortcomings of the old theories and expands the scope of the theory. Approbation of dissertation results: during the work on the dissertation four articles were written, two of which, at the moment, have already been published in scientific journals. Publications: article "Effective Medium Theory for the Elastic Properties of Composite Materials with Various Percolation Thresholds" in the journal "MDPI Materials", article "Medium field theory for thermoelectric properties of composite materials with different percolation thresholds" in the journal "Thermoelectricity".

International audience; We discuss a homogenized model of a pantographic bar considering flexoelectricity. A pantographic bar consists of relatively stiff small bars connected by small soft flexoelectric pivots. As a result, an elongation of the bar relates almost to the torsion of pivots. Taking into account their flexoelectric properties we find the corresponding electric polarization. As a results, the homogenized pantographic bar demonstrates piezoelectric properties inherited from the flexoelectric properties of pivots. The effective stiffness properties of the homogenized bars are determined by the geometry of the structural elements and shear stiffness whereas the piezoelectric properties follow from the flexoelectric moduli of the pivots.

International audience; Like most sarcomas with complex genomics,or more generally bone tissues, osteosarcoma isa type of tumors exhibiting a strong spatialheterogeneity of the micro-environment. Thisheterogeneity makes the diagnostic complex andcan induce strong spatial variability in theresponse to treatments. New researchstrategies are consequently needed tounderstand the impact of spatial heterogeneity onthe diagnostic accuracy and on the treatmentefficiency, and more generally to understand thelinks between tissue scale bone matrix structuresand underlying biology occurring at the cell scale.The aim of this interdisciplinary work is to obtain the quantification of correlations between clinicaldata, heterogeneity of bone tissues and mechanobiological parameters. To this purpose, original numerical developments were initiated in our group to study the intratumoral and healthy bone tissue heterogeneity from histological and immunohistological sections. The code aimed at obtaining quantitative metrics of the cell population distribution, of the bone matrix micro-architecture (porosity) and of the transport properties (such as effective diffusivity). Because tissues exhibit naturally a complex spatial scales cascade, it can be modeled, at the tissue scale, as a three phases porous medium (fluid, solid, cell populations). Using methodologies related to porous media analysis, characteristic lengths were extracted and correlations of phenomena occurring cell and tissue scale examined. Further developments permitted the calculation of effective mechanical properties. The methodology used successive algorithms of machine learning for the histological image segmentation and a combination of iterative algorithms and filters for the correlation calculations. Results put forward the strength of this approach for the identification of new markers in the study of pathological bone tissues.

Real-time decision making needs evaluating quantities of interest (QoI) in almost real time. When these QoI are related to models based on physics, the use of Model Order Reduction techniques allows speeding-up calculations, enabling fast and accurate evaluations. To accommodate real-time constraints, a valuable route consists of computing parametric solutions&mdash, the so-called computational vademecums&mdash, that constructed off-line, can be inspected on-line. However, when dealing with shapes and topologies (complex or rich microstructures) their parametric description constitutes a major difficulty. In this paper, we propose using Topological Data Analysis for describing those rich topologies and morphologies in a concise way, and then using the associated topological descriptions for generating accurate supervised classification and nonlinear regression, enabling an almost real-time evaluation of QoI and the associated decision making.

Understanding and optimizing effective properties of porous functional materials, such as permeability or conductivity, is one of the main goals of materials science research with numerous applications. For this purpose, understanding the underlying 3D microstructure is crucial since it is well known that the materials' morphology has a significant impact on their effective properties. Because tomographic imaging is expensive in time and costs, stochastic microstructure modeling is a valuable tool for virtual materials testing, where a large number of realistic 3D microstructures can be generated and used as geometry input for spatially-resolved numerical simulations. Since the vast majority of numerical simulations is based on solving differential equations, it is essential to have fast and robust methods for generating high-quality volume meshes for the geometrically complex microstructure domains. The present paper introduces a novel method for generating volume-meshes with periodic boundary conditions based on an analytical representation of the 3D microstructure using spherical harmonics. Due to its generality, the present method is applicable to many scientific areas. In particular, we present some numerical examples with applications to battery research by making use of an already existing stochastic 3D microstructure model that has been calibrated to eight differently compacted cathodes.

International audience; Sound absorbing porous materials are widely used for protection and insulation applications. In recent years, the development of recyclable bio-based porous materials have aroused a great interest to replace petroleum-based traditional materials. This work aims for studying, in particular, acoustic properties of a novel bio-based porous epoxy resin obtained by an adapted combination of cationic photopolymerization and porogen leaching technique. A multiscale framework was proposed for studying the acoustic absorption performances of a plate-like panel made of this kind of material. To do so, the asymptotic homogenization method was first used to estimate the effective properties of the elaborated material, which has fillet-edge cubic pore shapes according to the SEM (Scanning electron microscope) images. The finite element method was used to solve the cell problems and compute the effective properties. The sound absorption of a plate made by the equivalent poroelastic material with rigid impervious backing under a normal incidence was then studied. The validation was done by comparing the numerical estimation of equivalent dynamic density and bulk modulus to corresponding experimental results obtained by using the three-microphone impedance tube testing on several elaborated samples. A parametric study was carried out to investigate influence of the porosity, the pore arrangement, and the pore size on effective properties and sound absorption performances of the material. The obtained results should be very useful for improve the elaboration process of these materials in order to optimize, in particular, the sound absorption performances of isolation structures.

International audience; The propagation of elastic waves in materials containing randomly distributed particles is a fundamental topic that has been treated by many authors for several decades. In particular, the advent of metamaterials has highlighted the need to determine the effective properties of samples and in particular the effective density. In this context, we are interested in the propagation of elastic waves in an epoxy resin containing a monodisperse distribution of spherical dense particles. This kind of scatterer has two sub-wavelength resonances: the dipolar resonances in translation and in rotation. The influence of the dipolar resonance in translation on coherent longitudinal waves has already been studied previously in the team [1]. In the continuity of this work, we present here coherent transverse wave measurements and we highlight the influence of the two dipolar resonances on these coherent waves. For this, we use a new and original technique of characterization of the samples, called the technique "Sandwich" [2]. This technique, which has already shown its potential to characterize very attenuating homogeneous samples, is based on the study of Fabry-Perot interferences in the sample. The use of this technique allows us to determine not only the effective transverse wavenumber, but also the effective density and the effective shear modulus. [1] :Duranteau et al., Random acoustic metamaterial with a subwavelength dipolar resonance, Journal of Acoustical Society of America, 139, 2016 [2] :Simon et al., Viscoelatic shear modulus measurement of thin materials by interferometry at ultrasonic frequencies. Journal of Acoustical Society of America, 146, 2019

International audience; This paper proposes a micromechanical approach aimed at identifying the response of unidirectional fuzzy fiber composites undergoing inelastic fields. Fuzzy fibers are reinforcement fibers coated with radially aligned straight or wavy carbon nanotubes grown through chemical deposition process (PVD or CVD). Due to this nature, the composite with fuzzy fibers is describedby three scales: i) the microscale consisting of carbon nanotubes and their surrounding matrix, ii) the mesoscale containing the fiber, the nanocomposite and the matrix, and iii) the macroscale related to the overall fuzzy fiber composite. The developed framework considers for the mesoscopic scale an analytical formulation, based on the composite cylinders assemblage (CCA) method, combining the principles of the Transformation Field Analysis (TFA) technique. A numerical example that includes comparisons with full field homogenization strategies confirms the accuracy of the framework to predict the overall response, as well as the average local fields of the constituents.

The asymptotic homogenization method is applied to complex dielectric periodic composites. An equivalence to coupled dielectric problems with real coefficients is shown. This is similar to a piezoe...

The acoustic modelling of fibrous materials is fundamental for the design of a sound-absorbing acoustic treatment. Several analytical formulas have been proposed to calculate the acoustic performance of materials made of fibres with a homogeneous diameter and a mono, bi, or three-dimensional distribution, while only a few studies have been carried out on materials made up of a mixture of fibres with non–homogeneous diameter. Fibrous materials for automotive applications, developed both for acoustic and thermal applications, are commonly obtained by moulding mixtures of recycled fibres of different nature, bonded together and compacted with a wide range of variability in density and thickness. The acoustic modelling of the mixtures is thus relevant for the simulation of the performance of the final component. The main goal of the study was to determine the physical properties of a given mixture of fibres to compute its acoustic performance, based on the knowledge of the characteristic of each kind of fibre in the blend composition. A homogenisation process is proposed to determine the effective density and radius of a given mixture according to its composition and the characteristics of each kind of fibre. The normal incidence sound absorption coefficient of the investigated mixtures was computed according to the Johnson-Champoux-Allard-Lafarge (JCAL) model, by using the physical parameters, analytically computed from the effective properties of the mixture, as input data. The reliability of the approach was validated by comparing the computed results with the experimental airflow resistivity and the normal incidence sound absorption coefficient measured for five different fibre mixtures, at different compression rates.

We develop in this paper a general asymptotic homogenization model pertaining to magnetoelectric shells and sandwich shells composed of an arbitrary distribution of reinforcements or actuators attached to the surface of a thin shell or sandwiched between two shells. The constituents of the reinforced shells are orthotropic and may exhibit piezoelectric and/or piezomagnetic behavior. A set of twenty unit cell problems are solved for a basic reinforced shell that acts as a building block from which other, more comprehensive structures, can be designed and analyzed. The unit cell problems permit the computation of the so-called effective coefficients of the homogenized shell structure. Of particular interest among the effective coefficients are the product properties which manifest themselves in piezoelectric/piezomagnetic composites but not (usually) in the individual constituents. The work highlights the strong influence of the curvature of the shell’s middle surface on the effective properties; thus, after homogenization the effective shell may be characterized by structural inhomogeneity even if the original structure was homogeneous. The model is illustrated via a number of interesting and practically important examples which include spherical, paraboloidal, ellipsoidal and cylindrical shells reinforced with ribs, wafers, or triangularly arranged reinforcements. It is shown in this paper that in the case of a purely elastic shell the results of the model converge to those of previously published works; in the more comprehensive case however pertaining to a shell reinforced with piezoelectric and piezomagnetic constituents, it is shown that the effective elastic (and most other) coefficients are functions of not only the elastic properties (as predicted by some other models) but also of the remaining properties (such as electric and magnetic properties) of the constituents. In this sense therefore, the model developed represents an important refinement over other works.

This paper presents a numerical homogenization analysis of a porous piezoelectric composite with a partially metalized pore surface. The metal layers can be added to the pore surfaces to improve the mechanical and electromechanical properties of ordinary porous piezocomposites. Physically, constructing that composite with completely metalized pore surfaces is a challenging process, and imperfect metallization is more expected. Here, we investigate the effects of possible incomplete metallization of pore surfaces on the composite’s equivalent properties. We applied the effective moduli theory, which was developed for the piezoelectric medium based on the Hill–Mandel principle, and the finite element method to compute the effective moduli of the considered composites. Using specific algorithms and programs in the ANSYS APDL programming language, we constructed the representative unit cell element models and performed various computational experiments. Due to the presence of metal inclusion, we found that the dielectric and piezoelectric properties of the considered composites differ dramatically from the corresponding properties of the ordinary porous piezocomposites. The results of this work showed that piezocomposites with partially metallized pore surfaces can have a higher anisotropy, compared to the pure piezoceramic matrix, due to the defects in metal coatings.

A comprehensive asymptotic homogenization model for the analysis of composite and reinforced magnetoelectric plates is developed. The model culminates in a set of unit cell problems via which the relevant expressions for the effective coefficients are derived. The micromechanical and geometrical platform pertinent to the desired model is set up in this paper which also obtains the effective elastic, piezoelectric and piezomagnetic coefficients; the remaining properties, including product properties, are calculated in another work. Examples of structures that can be examined include diagonally- and triangularly-reinforced plates, hexagonal honeycomb sandwich plates and others. The developed model can be used to customize the effective properties of a reinforced plate to the requirements of a particular engineering application by changing some geometric, structural or material parameter of interest. It is shown that in the limiting case of a thin composite plate of uniform thickness whereby electrical conductivity is ignored and all pertinent quantities are time-averaged the presented model converges to the familiar classical plate model. Overall, this paper represents an important addition to the existing literature in terms of the complex geometries that can be designed and analyzed and at the same time constitutes an important refinement over previously published work.

Maxwell's equations and the equations of dynamic force and thermal balance are used to develop an asymptotic homogenization model for the analysis and design of magnetoelectric composite and reinforced plates. The developed model generates a set of unit cell problems the solution of which enables the determination of the effective coefficients of the homogenized structure. Of particular importance among the effective coefficients are the product properties which are manifested in the macroscopic structure but are not usually exhibited by the individual constituents. Examples of effective properties are the magnetoelectric, pyroelectric and pyromagnetic coefficients. The model is illustrated by means of several examples such as diagonally restrained magnetoelectric plates, plates reinforced with a triangular arrangement of ribs, wafer reinforced magnetoelectric plates and three-layered sandwich plates. From the nature of the structures considered, it is shown that it is more practical if a basic unit cell consisting of only a single arbitrarily oriented rib and a base plate is analyzed first. Then, the effective properties of magnetoelectric structures with more families of ribs can be obtained by superposition. It is shown in this paper that the effective coefficients as well as the field variables are functions of time and are not constants as predicted by other models. In fact, it is shown that other models are special cases of the model derived here when electrical conductivity is ignored and the aforementioned temporal functions are time-averaged by integrating them over the entire time spectrum. Thus, overall, this paper represents an important addition to the existing literature in terms of the complex geometries that can be designed and analyzed and at the same time constitutes an important refinement over previously established work. In fact, the present work permits the design and analysis of a fully-coupled magnetoelectric plate or sandwich plate with any desired arrangement of the actuators/reinforcements.

Li-ion batteries are interesting for applications such as electric vehicles. They have indeed a high energy and power density, which makes them good substitutes for internal combustion engines. However, even if they are now quite widely used in many fields, there is still a need to optimize their performance. This requires a better understanding of the impact of the electrodes microstructure on their effective properties to narrow the gap between ideal and practical performance. Three-dimensional characteristics such as the carbon additive percolation or the tortuosity of the porosity have a strong impact on the electrode charge transport properties and power performance. The use of 3D imaging techniques such as X-ray tomography and serial focused ion beam and SEM tomography (FIB/SEM) is very powerful to quantify the electrode microstructures and interpret their charge transport properties. Furthermore, by processing the reconstructed volumes, one can use them as a basis for numerical simulations. We have chosen the FFT (Fast Fourrier Transform) method with "discrete" Green operator for numerical computations. These simulations can either be used to back calculate the phase (active material or conducting additive/binder) conduction properties from macroscopic electrical measurements by inverse method, or to predict the electrode effective conductivity from the phase conductivities. The 3D numerical microstructures obtained can also be modified in order to predict the influence of compositional changes in the electrode formulation on its properties. This study sets new tools to understand better the relationships between microstructure, effective electrical properties and the performance of Li-ion battery composite electrodes.; Cette étude porte sur la compréhension du lien existant entre l’architecture microstructurelle et les propriétés effectives de conductivité dans les électrodes des batteries Li-ion. Les batteries Li-ion sont très intéressantes pour des domaines tels que le transport électrique. En effet, elles présentent une grande densité d’énergie et de puissance ce qui en fait de bons substituts pour les moteurs thermiques. Cependant, même si elles sont maintenant assez largement utilisées dans beaucoup de domaines, il y a toujours besoin d’en optimiser les performances. Ceci passe par une meilleure compréhension de l’impact de la microstructure sur les propriétés effectives pour réduire l’écart entre théorie et pratique. L’attention est portée ici sur les électrodes positives des batteries lithium-ion. Les caractéristiques tridimensionnelles telles que la percolation des phases, leur tortuosité ou encore leurs dimensions caractéristiques ont un fort impact sur les propriétés à l'échelle macroscopique. Leur étude nécessite l’utilisation de techniques d’imagerie 3D comme la tomographie aux rayons X et la tomographie sériée par faisceau d’ions focalisés et MEB (FIB/SEM) pour obtenir des données quantitatives et en interpréter les propriétés de transport de charge. Ces volumes sont alors traités (segmentation et analyses morphologiques) et utilisés comme base pour des simulations numériques. La méthode FFT (Fast Fourrier Transform) avec opérateur de Green « discret » est choisie. Ces simulations permettent, soit de remonter aux propriétés de conduction électrique des phases, à partir de la mesure de la conductivité de l’électrode, par méthode inverse, soit de prédire la conductivité effective de l’électrode, en utilisant des propriétés mesurées expérimentalement sur les phases prises séparément. Les microstructures 3D numériques peuvent également être altérées afin de prédire l’impact, sur ses propriétés effectives, de changements de composition dans la formulation de l’électrode. De nouveaux outils consacrés à la meilleure compréhension de la relation entre microstructure, propriétés effectives et performance des batteries lithium-ion sont développés.

Li-ion batteries are interesting for applications such as electric vehicles. They have indeed a high energy and power density, which makes them good substitutes for internal combustion engines. However, even if they are now quite widely used in many fields, there is still a need to optimize their performance. This requires a better understanding of the impact of the electrodes microstructure on their effective properties to narrow the gap between ideal and practical performance. Three-dimensional characteristics such as the carbon additive percolation or the tortuosity of the porosity have a strong impact on the electrode charge transport properties and power performance. The use of 3D imaging techniques such as X-ray tomography and serial focused ion beam and SEM tomography (FIB/SEM) is very powerful to quantify the electrode microstructures and interpret their charge transport properties. Furthermore, by processing the reconstructed volumes, one can use them as a basis for numerical simulations. We have chosen the FFT (Fast Fourrier Transform) method with "discrete" Green operator for numerical computations. These simulations can either be used to back calculate the phase (active material or conducting additive/binder) conduction properties from macroscopic electrical measurements by inverse method, or to predict the electrode effective conductivity from the phase conductivities. The 3D numerical microstructures obtained can also be modified in order to predict the influence of compositional changes in the electrode formulation on its properties. This study sets new tools to understand better the relationships between microstructure, effective electrical properties and the performance of Li-ion battery composite electrodes.; Cette étude porte sur la compréhension du lien existant entre l’architecture microstructurelle et les propriétés effectives de conductivité dans les électrodes des batteries Li-ion. Les batteries Li-ion sont très intéressantes pour des domaines tels que le transport électrique. En effet, elles présentent une grande densité d’énergie et de puissance ce qui en fait de bons substituts pour les moteurs thermiques. Cependant, même si elles sont maintenant assez largement utilisées dans beaucoup de domaines, il y a toujours besoin d’en optimiser les performances. Ceci passe par une meilleure compréhension de l’impact de la microstructure sur les propriétés effectives pour réduire l’écart entre théorie et pratique. L’attention est portée ici sur les électrodes positives des batteries lithium-ion. Les caractéristiques tridimensionnelles telles que la percolation des phases, leur tortuosité ou encore leurs dimensions caractéristiques ont un fort impact sur les propriétés à l'échelle macroscopique. Leur étude nécessite l’utilisation de techniques d’imagerie 3D comme la tomographie aux rayons X et la tomographie sériée par faisceau d’ions focalisés et MEB (FIB/SEM) pour obtenir des données quantitatives et en interpréter les propriétés de transport de charge. Ces volumes sont alors traités (segmentation et analyses morphologiques) et utilisés comme base pour des simulations numériques. La méthode FFT (Fast Fourrier Transform) avec opérateur de Green « discret » est choisie. Ces simulations permettent, soit de remonter aux propriétés de conduction électrique des phases, à partir de la mesure de la conductivité de l’électrode, par méthode inverse, soit de prédire la conductivité effective de l’électrode, en utilisant des propriétés mesurées expérimentalement sur les phases prises séparément. Les microstructures 3D numériques peuvent également être altérées afin de prédire l’impact, sur ses propriétés effectives, de changements de composition dans la formulation de l’électrode. De nouveaux outils consacrés à la meilleure compréhension de la relation entre microstructure, propriétés effectives et performance des batteries lithium-ion sont développés.

This thesis deals with the 3D-printing, numerical simulation and experimental testing of porous materials with random isotropic microstructures. In particular, we attempt to assess by means of well-chosen examples the effect of partial statistical descriptors (i.e., porous volume fraction or porosity, two-point correlation functions and chord-length distribution) upon the linear effective elastic response of random porous materials and propose (nearly) optimal microstructures by direct comparison with available theoretical mathematical bounds. To achieve this, in the first part of this work, we design ab initio porous materials comprising single-size (i.e. monodisperse) and multiple-size (polydisperse) spherical and ellipsoidal non-overlapping voids. The microstructures are generated using a random sequential adsorption (RSA) algorithm that allows to reach very high porosities (e.g. greater than 80%). The created microstructures are then numerically simulated using finite element (FE) and Fast Fourier Tranform (FFT) methods to obtain representative isotropic volume elements in terms of both periodic and kinematic boundary conditions. This then allows for the 3D-printing of the porous microstructures in appropriately designed dog-bone specimens. An experimental setup for uniaxial tension loading conditions is then developed and the 3D-printed porous specimens are tested to retrieve their purely linear elastic properties. This process allows, for the first time experimentally, to show that such polydisperse (multiscale) microstructures can lead to nearly optimal effective elastic properties when compared with the theoretical Hashin-Shtrikman upper bounds for a very large range of porosities spanning values between 0-82%. To understand further the underlying mechanisms that lead to such a nearly optimal response, we assess the influence of several statistical descriptors (such as the one- and two-point correlation functions, the chord-length distribution function) of the microstructure upon the effective elastic properties of the porous material. We first investigate the ability of the two-point correlation function to predict accurately the effective response of random porous materials by choosing two different types of microstructures, which have exactly the same first (i.e., porosity) and second-order statistics. The first type consists of non-overlapping spherical and ellipsoidal pores generated by the RSA process. The second type, which uses the thresholded Gaussian Random Field (GRF) method, is directly reconstructed by matching the one- and two-point correlation functions from the corresponding RSA microstructure. The FFT-simulated effective elastic properties of these two microstructures reveal very significant differences that are in the order of 100% in the computed bulk and shear moduli. This analysis by example directly implies that the two-point statistics can be highly insufficient to predict the effective elastic properties of random porous materials. We seek to rationalize further this observation by introducing controlled connectivity in the original non-overlapping RSA microstructures. The computed effective elastic properties of these microstructures show that the pore connectivity does not change neither the two-point correlation functions nor the chord-length distribution but leads to a significant decrease in the effective elastic properties. In order to quantify better the differences between those three microstructures, we analyze the link between the local geometry of the porous phase and the corresponding computed elastic fields by computing the first (average) and second moments of the elastic strain fluctuations. This last analysis suggests that partial statistical information of the microstructure (without any input from the corresponding elasticity problem) might be highly insufficient even for the qualitative analysis of a porous material and by extension of any random composite material.; Dans le cadre de cette thèse, la combinaison de plusieurs outils numériques et expérimentaux a permis la génération de différents modèles de microstructures aléatoires afin d'étudier l'influence des descripteurs statistiques sur les propriétés élastiques effectives des matériaux poreux.Dans un premier temps, nous avons développé une procédure qui associe impression 3D, caractérisation expérimentale et numérique ainsi que les résultats théoriques sur les propriétés effectives de matériaux poreux désordonnée. Cette méthodologie est appliquée à la fabrication de microstructures constituées de pores sphériques, de taille unique ou avec une distribution de plusieurs tailles, qui sont disposés dans une volume cubique par un procédé d'ajout séquentiel et aléatoire (RSA). Un protocole expérimental est développé en commençant par la détermination du volume élémentaire représentatif (VER) afin d'obtenir des propriétés macroscopiques indépendantes des conditions aux limites imposées à l'échantillon numérique ou expérimental. A partir de ces résultats, une éprouvette standard est réalisée pour des essais multi-étapes de traction-relaxation sur matériaux polymères. Les résultats numériques et expérimentaux concernant les propriétés élastiques effectives de ces microstructures sont proches de la borne supérieure de Hashin-Shtrikman pour les matériaux isotropes pour une large gamme de porosité.Dans la seconde partie de cette thèse, on cherche à évaluer l'influence de certains descripteurs statistiques de la microstructure sur les propriétés élastiques macroscopiques pour les relier à l'espace poreux aléatoire et multi-échelle dans les carbonates. Pour cela, nous commençons par tester la pertinence des fonctions de corrélation à deux points en considérant deux familles différentes de microstructures poreuses qui ont les mêmes statistiques de second ordre. La première famille est générée par le code RSA avec différents élancements des pores ellipsoïdaux. La deuxième famille est, quant à elle, obtenue par seuillage de champs gaussiens générés à partir des fonctions de corrélations mesurées sur la première. Les propriétés élastiques effectives de ces deux familles sont obtenues par simulations numériques basées sur la transformée de Fourier rapide (FFT). Les résultats montrent que la fonction de corrélation est insuffisante pour prédire les propriétés effectives de matériaux poreux aléatoires. Nous proposons ensuite une manière d'évaluer l'influence de la connectivité sur les propriétés élastiques en considérant un réseau connecté de pores ellipsoïdaux reliés par des canaux cylindriques. Les propriétés effectives de ces microstructures montrent qu'une faible porosité additionnelle pour relier les pores ne change pas de manière significative la fonction de corrélation ou la distribution de cordes entre les microstructures mais peut engendrer d'important changement dans les modules élastiques des microstructures.Par la suite, une analyse du lien entre la géométrie locale dans l'espace poreux et les champs élastiques du matériaux est proposée. Cela consiste à étudier la distribution des fluctuations locales du champ de déformation par rapport à la distance euclidienne séparant un point de la phase solide de l'interface avec la phase poreuse. La moyenne et l'écart type des fluctuations de la composante hydrostatique du champ de déformation pour un chargement hydrostatique concordent qualitativement avec les modules de compressibilité effectives obtenus. Des observations similaires sont obtenues en analysant la composante de cisaillement pour un chargement en cisaillement. Compte tenu de ces résultats, il semble que les propriétés élastiques effectives des différentes microstructures étudiées sont fortement sensibles à l'information géométrique locale contenus dans la forme des pores et leur connectivité.

This thesis deals with the 3D-printing, numerical simulation and experimental testing of porous materials with random isotropic microstructures. In particular, we attempt to assess by means of well-chosen examples the effect of partial statistical descriptors (i.e., porous volume fraction or porosity, two-point correlation functions and chord-length distribution) upon the linear effective elastic response of random porous materials and propose (nearly) optimal microstructures by direct comparison with available theoretical mathematical bounds. To achieve this, in the first part of this work, we design ab initio porous materials comprising single-size (i.e. monodisperse) and multiple-size (polydisperse) spherical and ellipsoidal non-overlapping voids. The microstructures are generated using a random sequential adsorption (RSA) algorithm that allows to reach very high porosities (e.g. greater than 80%). The created microstructures are then numerically simulated using finite element (FE) and Fast Fourier Tranform (FFT) methods to obtain representative isotropic volume elements in terms of both periodic and kinematic boundary conditions. This then allows for the 3D-printing of the porous microstructures in appropriately designed dog-bone specimens. An experimental setup for uniaxial tension loading conditions is then developed and the 3D-printed porous specimens are tested to retrieve their purely linear elastic properties. This process allows, for the first time experimentally, to show that such polydisperse (multiscale) microstructures can lead to nearly optimal effective elastic properties when compared with the theoretical Hashin-Shtrikman upper bounds for a very large range of porosities spanning values between 0-82%. To understand further the underlying mechanisms that lead to such a nearly optimal response, we assess the influence of several statistical descriptors (such as the one- and two-point correlation functions, the chord-length distribution function) of the microstructure upon the effective elastic properties of the porous material. We first investigate the ability of the two-point correlation function to predict accurately the effective response of random porous materials by choosing two different types of microstructures, which have exactly the same first (i.e., porosity) and second-order statistics. The first type consists of non-overlapping spherical and ellipsoidal pores generated by the RSA process. The second type, which uses the thresholded Gaussian Random Field (GRF) method, is directly reconstructed by matching the one- and two-point correlation functions from the corresponding RSA microstructure. The FFT-simulated effective elastic properties of these two microstructures reveal very significant differences that are in the order of 100% in the computed bulk and shear moduli. This analysis by example directly implies that the two-point statistics can be highly insufficient to predict the effective elastic properties of random porous materials. We seek to rationalize further this observation by introducing controlled connectivity in the original non-overlapping RSA microstructures. The computed effective elastic properties of these microstructures show that the pore connectivity does not change neither the two-point correlation functions nor the chord-length distribution but leads to a significant decrease in the effective elastic properties. In order to quantify better the differences between those three microstructures, we analyze the link between the local geometry of the porous phase and the corresponding computed elastic fields by computing the first (average) and second moments of the elastic strain fluctuations. This last analysis suggests that partial statistical information of the microstructure (without any input from the corresponding elasticity problem) might be highly insufficient even for the qualitative analysis of a porous material and by extension of any random composite material.; Dans le cadre de cette thèse, la combinaison de plusieurs outils numériques et expérimentaux a permis la génération de différents modèles de microstructures aléatoires afin d'étudier l'influence des descripteurs statistiques sur les propriétés élastiques effectives des matériaux poreux.Dans un premier temps, nous avons développé une procédure qui associe impression 3D, caractérisation expérimentale et numérique ainsi que les résultats théoriques sur les propriétés effectives de matériaux poreux désordonnée. Cette méthodologie est appliquée à la fabrication de microstructures constituées de pores sphériques, de taille unique ou avec une distribution de plusieurs tailles, qui sont disposés dans une volume cubique par un procédé d'ajout séquentiel et aléatoire (RSA). Un protocole expérimental est développé en commençant par la détermination du volume élémentaire représentatif (VER) afin d'obtenir des propriétés macroscopiques indépendantes des conditions aux limites imposées à l'échantillon numérique ou expérimental. A partir de ces résultats, une éprouvette standard est réalisée pour des essais multi-étapes de traction-relaxation sur matériaux polymères. Les résultats numériques et expérimentaux concernant les propriétés élastiques effectives de ces microstructures sont proches de la borne supérieure de Hashin-Shtrikman pour les matériaux isotropes pour une large gamme de porosité.Dans la seconde partie de cette thèse, on cherche à évaluer l'influence de certains descripteurs statistiques de la microstructure sur les propriétés élastiques macroscopiques pour les relier à l'espace poreux aléatoire et multi-échelle dans les carbonates. Pour cela, nous commençons par tester la pertinence des fonctions de corrélation à deux points en considérant deux familles différentes de microstructures poreuses qui ont les mêmes statistiques de second ordre. La première famille est générée par le code RSA avec différents élancements des pores ellipsoïdaux. La deuxième famille est, quant à elle, obtenue par seuillage de champs gaussiens générés à partir des fonctions de corrélations mesurées sur la première. Les propriétés élastiques effectives de ces deux familles sont obtenues par simulations numériques basées sur la transformée de Fourier rapide (FFT). Les résultats montrent que la fonction de corrélation est insuffisante pour prédire les propriétés effectives de matériaux poreux aléatoires. Nous proposons ensuite une manière d'évaluer l'influence de la connectivité sur les propriétés élastiques en considérant un réseau connecté de pores ellipsoïdaux reliés par des canaux cylindriques. Les propriétés effectives de ces microstructures montrent qu'une faible porosité additionnelle pour relier les pores ne change pas de manière significative la fonction de corrélation ou la distribution de cordes entre les microstructures mais peut engendrer d'important changement dans les modules élastiques des microstructures.Par la suite, une analyse du lien entre la géométrie locale dans l'espace poreux et les champs élastiques du matériaux est proposée. Cela consiste à étudier la distribution des fluctuations locales du champ de déformation par rapport à la distance euclidienne séparant un point de la phase solide de l'interface avec la phase poreuse. La moyenne et l'écart type des fluctuations de la composante hydrostatique du champ de déformation pour un chargement hydrostatique concordent qualitativement avec les modules de compressibilité effectives obtenus. Des observations similaires sont obtenues en analysant la composante de cisaillement pour un chargement en cisaillement. Compte tenu de ces résultats, il semble que les propriétés élastiques effectives des différentes microstructures étudiées sont fortement sensibles à l'information géométrique locale contenus dans la forme des pores et leur connectivité.

A random dispersion of identical elastic solid particles in a viscous fluid is considered and effective properties, appropriate to the propagation through the medium of an ultrasonic compressional wave of large wavelength compared to the radius of the particles, is investigated.The scattering coefficients of a single spherical particle in a viscous medium are investigated for all combinations of incident and scattered wave types for use in multiple scattering models. Approximate formulae are obtained for the coefficients at n’th partial wave order in the Rayleigh limit. For spherical particles, a core-shell self-consistent model is used, in which the medium is modelled by an elastic core of the same material and radius as the particles, surrounded by a shell of the host fluid, and placed in the effective medium. The radius of the shell is such that the ratio of the core/shell volume is equal to the particle concentration. The dynamic properties of the effective medium are sought by minimising the scattering of the shell for different incident compressional partial wave orders (n).The effective bulk modulus is found from the monopole mode n=0 and the effective mass density from the dipole mode n=1. When compared to Ament’s formula based on local force balance at the particles (assumed rigid), the effective mass density obtained from the core-shell model shows a frequency-dependent effect of concentration similar to that observed in multiple scattering models and experimentally. Ament’s method is then applied to obtain the effective mass density in case of aligned rigid spheroids.; La propagation d’une onde ultrasonore de compression au travers d’une distribution de particules solides identiques localisées aléatoirement dans un liquide visqueux est étudiée. La longueur d’onde de l’onde de compression est supposée grande devant le rayon des particules, et les propriétés effectives dynamiques du milieu sont recherchées.Les coefficients de diffusion d’une sphère solide isolée sont étudiés pour différentes polarisations des ondes partielles de mode n incidentes et diffusées. Des expressions approchées en sont données pour tout n dans le régime de diffusion de Rayleigh.Dans le cas de particules sphériques, le milieu est modélisé par un noyau élastique, de même matériau et rayon que les particules, et entouré d’une coque emplie du fluide hôte. L’ensemble est insoné, dans le milieu effectif, par une onde de compression partielle de mode n. Les propriétés effectives sont recherchées par minimisation de la diffusion pour différentes valeurs de n. Le module d’élasticité volumique effectif et la masse volumique effective sont obtenus respectivement à partir des modes n=0 et n=1. Comparée à la formule d’Ament, fondée sur l’équilibre des forces hydrodynamiques et inertielle au niveau de chaque particule supposée rigide, celle obtenue ici fait apparaître un effet de la concentration sur la dépendance fréquentielle de la masse volumique similaire à celui observé, expérimentalement et dans des modèles de diffusion multiple, sur les propriétés effectives des ondes de compression. La méthode d’Ament est ensuite appliquée pour obtenir la masse volumique effective dans le cas de sphéroïdes rigides alignés.