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A micromechanical model for the analysis of structurally periodic flexoelectric plates with periodically varying thickness is developed on the basis of asymptotic homogenization. The period of thickness variation is small and comparable to the plate thickness; accordingly, the plate is usually referred to as having a "rapidly varying thickness." The stipulation for rapidly varying thickness is important because it is envisioned that the developed model can be applied to a broad range of thin plates, both stratified as well as plates endowed with an arbitrary distribution of reinforcements attached to the surface or embedded within the plate. The microscopic problem is implemented in two steps pertaining, respectively, to first- and second-gradient asymptotic homogenization. Each level of homogenization culminates in its own set of unit cell problems from which the effective coefficients of the homogenized structure can eventually be obtained. These effective coefficients couple the force and moment resultants as well as the averaged electric displacement with the first and second gradients of the macroscopic displacement and electric potential. Once the effective coefficients are obtained, the macroscopic problem is invoked, which provides a set of four differential equations from which the macroscopic variables of mechanical displacement and electric potential can be obtained. The model is illustrated by means of laminated flexoelectric composites as well as simple rib-reinforced plates. It is shown that in the limiting case of a thin, purely elastic plate, the derived model converges to the familiar classical plate model. [ABSTRACT FROM AUTHOR]

One of the key difficulties in applications of the effective media theories to real materials is the complex and "irregular" character of microstructures. However, in cases of moderate contrast between properties of the constituents, the sensitivity of the effective properties to microgeometries is much lower; it vanishes in the first approximation. The latter actually remains applicable at substantial (up to 70%–100%) contrast in properties. The effective elastic and conductive properties are considered as functions of property contrast between constituents. Whereas in the isotropic cases the Voigt–Reuss bounds provide guidance, in anisotropic cases these issues are less obvious. Two origins of effective anisotropies are discussed: (A) anisotropy of material constants and (B) geometric factors: non-random orientations of non-spherical inclusions. To the first order in contrast, the factor (A) is dominant, and factor (B) can be ignored (effective properties are independent of microgeometries, such as inhomogeneity shapes); the importance of factor (B) increases sharply with increasing contrast. For matrix composites (continuous matrices containing inhomogeneities), an interesting interplay takes place between the moderate contrast assumption and the non-interaction assumption (NIA). It shows that, in cases of moderate contrast, the NIA remains accurate at substantial concentrations. An application to monitoring fatigue of austenitic steel, whereby property contrast between the martensite and austenite phases is moderate, is discussed. Results of the second order in contrast, that are limited to the ellipsoidal inhomogeneities, are also given. [ABSTRACT FROM AUTHOR]

This paper presents a new method of dynamic homogenization of periodic elastic media under harmonic antiplane deformation based on energy equivalence. The dynamic homogenization is based on two main steps, (1) determining the dispersion relation and the detailed local response in a representative volume element (RVE) by analyzing the propagation of Bloch waves and (2) using energy equivalence between the periodic and effective media to determine the effective properties. The method is first applied to a one-dimensional periodic medium, from which the analytical solutions of the effective material properties are obtained. The results are compared with that from the original periodic medium and an excellent agreement is observed. The dynamic homogenization method is then applied to general two-dimensional periodic media to determine the effective properties and to predict wave fields under typical loading conditions. Illustrative examples are presented and compared with the results from the multiple scattering model. The method has also been applied to multiscale modeling of complicated inhomogeneous media containing multiple groups of periodic inhomogeneities. By treating each group as a homogeneous material with effective properties determined by the current homogenization method, the wave field is obtained using the boundary element method. The resulting wave fields from the current method show an excellent agreement with that from the multiple scattering model with matching local response details. [ABSTRACT FROM AUTHOR]

Metamaterials, characterized by unique structures, exhibit exceptional properties applicable across various domains. Traditional methods like experiments and finite-element methods (FEM) have been extensively utilized to characterize these properties. However, exploring an extensive range of structures using these methods for designing desired structures with excellent properties can be time-intensive. This paper formulates a machine-learning-based approach to expedite predicting effective metamaterial properties, leading to the discovery of microstructures with diverse and outstanding characteristics. The process involves constructing 2D and 3D microstructures, encompassing porous materials, solid–solid-based materials, and fluid–solid-based materials. Finite-element methods are then employed to determine the effective properties of metamaterials. Subsequently, the Random Forest (RF) algorithm is applied for training and predicting effective properties. Additionally, the Aquila Optimizer (AO) method is employed for a multiple optimization task in inverse design. The regression model generates accurate estimation with a coefficient of determination higher than 0.98, a mean absolute percentage error lower than 0.088, and a root mean square error lower than 0.03, indicating that the machine-learning-based method can accurately characterize the metamaterial properties. An optimized structure with a high Young's modulus and low thermal conductivity is designed by AO within the first 30 iterations. This approach accelerates simulating the effective properties of metamaterials and can design microstructures with multiple excellent performances. The work offers guidance to design microstructures in various practical applications such as vibration energy absorbers. [ABSTRACT FROM AUTHOR]

AbstractThe growing global demand for sustainability has led bio-sourced fibers to be identified as an alternative to synthetic fibers. In this paper, micromechanics and multiscale modeling approaches are used to predict the thermomechanical behavior of thermoplastic (polypropylene PP matrix) composites reinforced with four different natural fibers: flax, vegetal-technic, woodforce and a hybrid of flax and vegetal-technic, for random and aligned fiber orientations. Different microstructural orientations (0°, 45°, 90° and random) are generated and computed using the finite element method. Besides, an analytical modeling based on the Mori-Tanaka homogenization scheme is used to validate numerical results. The thermomechanical results showed a good agreement between the numerical computation and analytical approach for the aligned fiber orientations. In addition, the mechanical results obtained for the random fiber orientation remain in agreement with the experimental and analytical results reported in the literature. Besides, a user-defined material (UMAT) is implemented on tensile, compression and shear specimens. Through a virtual characterization, a material card for a 50% volume fraction of fiber is established for a flax-PP composite. Finally, an application made on a quadcopter frame, gives the failure indicators under thermomechanical loads at −20 °C and 55 °C, demonstrating the capability of plant fibers composites to withstand extreme conditions. [ABSTRACT FROM AUTHOR]

We analyze small amplitude shearing motions superimposed onto a harmonic extension of a string made of an isotropic rate-type viscoelastic material. In particular, we consider also the case in which the harmonic extension is perturbed by adding stochastic noise. We study the onset of resonance as a function of the characteristic parameters both in the absence and in the presence of noise. In the first case, we use the renormalization group (RG) method, while in the second case, we make use of a " deterministic" approach that implies replacing the noise by high-frequency excitations. The main conclusion of our investigation is that the substitution of a classical elastic rope with a viscoelastic stress–relaxing string allows us to reproduce the parametric resonance phenomena observed by Melde. The presence of noise can change the well-known 2:1 resonance. In particular, the 2:1 resonance is reduced proportionally to the square of the amplitude ratio, frequency of the noise, and to the ratio between the characteristic viscous stress and the elastic stress. [ABSTRACT FROM AUTHOR]

Relative permeability and capillary pressure are key parameters in multiphase flow modelling. In heterogeneous porous media, flow direction- and flow-rate dependence result from non-uniform saturation distributions that vary with the balance between viscous, gravitational, and capillary forces. Typically, relative permeability is measured using constant inlet fractional-flow—constant outlet fluid pressure conditions on samples mounted between permeable porous plates to avoid capillary end-effects. This setup is replicated in numeric experiments but ignores the extended geologic context beyond the sample size, impacting the saturation distribution and, consequently, the upscaled parameters. Here, we introduce a new workflow for measuring effective relative permeability and capillary pressure at the bedform scale while considering heterogeneities at the lamina scale. We harness the flexibility of numeric modelling to simulate continuum-REV-scale saturation distributions in heterogeneous rocks eliminating boundary artefacts. Periodic fluid flux boundary conditions are applied in combination with arbitrarily oriented, variable-strength pressure gradient fields. The approach is illustrated on a periodic model of cross-bedded sandstone. Stepping saturation while applying variable-strength pressure-gradient fields with different orientations, we cover the capillary-viscous force balance spectrum of interest. The obtained relative permeability and capillary pressure curves differ from ones obtained with traditional approaches highlighting that the definition of force balances needs consideration of flow direction as an additional degree of freedom. In addition, we discuss when the common viscous and the capillary limits are applicable and how they vary with flow direction in the presence of capillary interfaces. [ABSTRACT FROM AUTHOR]

This study aims to critically assess different micromechanical analysis models applied to carbon-fiber-reinforced plastic (CFRP) composites, employing micromechanics-based homogenization to accurately predict their effective properties. The paper begins with the simplest Voigt and Reuss models and progresses to more sophisticated micromechanics-based models, including the Mori–Tanaka and Method of Cells (MOC) models. It provides a critical review of the areas in which these micromechanics-based models are effective and analyses of their limitations. The numerical analysis results were confirmed through finite element simulations of the periodic representative volume element (RVE). Furthermore, the effective properties predicted by these micromechanics-based models were validated via experiments conducted on IM7/5320-1 composite material with a fiber volume fraction of 0.62. [ABSTRACT FROM AUTHOR]

Additive manufacturing (AM) significantly provides opportunities to design and produce components with complex shapes and geometries without a demand for many conventional manufacturing steps. The AM technique has been also used for accomplishing such customized, multi-cell lattice structures for lightweight applications. However, an eligible design approach for integrating lattice structures is challenging so that desired mechanical properties in various advanced engineering structures can be achieved. Therefore, multi-cell lattice structures and graded design approaches for improving load-bearing capacities of additively manufactured parts were studied in this work. C-clip structures infilled with different lattice configurations were investigated under tension load. It was found that uniform BCC-Shell and SC-BCC-Shell lattice samples exhibited considerably higher overall stiffness values than the others due to their large normalized shear moduli. By both stress- and topology optimization-based tailored density methods, lattice structures with suitable effective properties, anisotropic characteristics, and relative densities could be employed, especially for highly loaded regions. The proposed strategies provided the structural performance which was just less than 3% from the benchmark. [ABSTRACT FROM AUTHOR]

AbstractIn the present study, a smart laminated composite beam with auxetic configurations is considered to improve its energy harvesting capabilities. For this purpose, three different cases of auxetic geometries are considered on the cantilever laminated composite beam near the fixed end, and the piezoelectric patches are attached in bimorph configuration over this auxetic region. The coupled structural and piezoelectric equations are developed based on beam element theory. The principle of minimum potential energy is implemented to solve the equations of motion. Effective Young’s modulus and Poisson’s ratio of the auxetic geometric region are utilized in the beam model, and the results are validated with three-dimensional finite element solution. An experimental study is carried out to validate the finite element studies. The energy harvesting capability of laminated composite beam has significantly improved by using reentrant auxetic geometry. In addition to auxetic geometry, auxetic cubical inclusions are also considered to study their effect on energy harvesting potential. On validating the results obtained from auxetic geometry and auxetic cubical inclusion cases, some parametric studies are conducted to know the influence of auxetic inclusion dimensions, ply orientations, and thickness ratio on the voltage energy output. It is found that with an increase in the length and thickness of the auxetic geometry, the cross-ply oriented auxetic energy harvester’s output potential raised considerably. To obtain the optimum parameters required to enhance average output power and minimize the energy loss factor, grey-relational analysis tool, and artificial neural network-based optimization schemes are implemented. The energy harvesting system with the optimized parameters has shown about 60% improvement in the average power output and conversion efficiency. [ABSTRACT FROM AUTHOR]

The article considers the problems in the numerical stress-strain analysis of heterogeneous models of rock samples and biological tissues. The information about the geometric structure of such models is usually obtained using computed tomography (CT). The construction of the unstructured hexahedral meshes (based on CT scan data) is used to reduce the problem dimension. Examples of estimating the effective properties of a core sample and modeling a human lower jaw are given in the article. [ABSTRACT FROM AUTHOR]

A numerical-analytical solution to the "effective modulus problem" of transversally isotropic porous ceramics is obtained, taking into account its initial stressed state and the ellipsoidal shape of oriented pores of various connectivity based on the solution of the associated stochastic boundary value problem of electroelasticity of composite mechanics using the Green's function method. A numerical calculation of the initial and resulting values of the effective piezoelectric modulus of porous piezoceramics (PZT-4) was carried out depending on the values of the volume fraction, shape parameter and connectivity of ellipsoidal, in particular: spherical, disk or tunnel pores, taking into account the initial stressed state of the porous piezoceramics due to its initial axisymmetric deformation. Characteristic values of the volume fraction of spherical and disk pores are identified, taking into account their connections, at which the sign of the numerical values of the initial effective piezoelectric modulus changes with respect to the corresponding module of PZT-4 monolithic ceramics. The values of the volume fraction, shape parameter and type of pore connectivity at which the maximum gradients of the linear dependence of the values of the resulting piezoelectric modulus of porous piezoceramics on its initial macrodeformations are realized are determined. An analysis of graphs of continuous dependences of the initial and resulting values of the effective piezoelectric modulus on the pore shape parameter is given for various cases of their volumetric content, connectivity and axisymmetric initial deformations of porous piezoceramics. [ABSTRACT FROM AUTHOR]

This paper aims to explore the potential of carbon nanotubes (CNTs) in enhancing the structural capability and multifunctionality of carbon fiber composites in aerospace applications, primarily by focusing on interfacial applications. The conventional method of dispersing CNTs in a matrix is not fully efficient in exploiting the mechanical and multifunctional performance of CNTs. Hence, the use of CNTs at the interface or as a coating on the surface of carbon fibers has been suggested as a means of achieving multifunctionality, in addition to enhanced mechanical performance. The paper presents an overview of the various processes for growing CNTs on carbon fiber surfaces and examines the effects of CNT geometry and growth parameters on the properties of grafted fibers and their composites. Furthermore, it discusses the potential improvements in thermal and electrical conductivity achievable by incorporating CNTs at the interface, as well as the benefits of using CNTs as a sizing layer for carbon fibers, including enhanced fracture toughness and resistance to delamination. Highlights: Comprehensive study of interface engineering in carbon fibers and Carbon Fibre Reinforced Plastic (CFRPs) using carbon nanotubes (CNTs).Improved transverse mechanical properties and overall thermal and electrical properties.Multifunctional applications possible with the use of CNT.Both experimental and numerical studies reviewed. [ABSTRACT FROM AUTHOR]

This article proposes a modeling method for C/C-ZrC composite materials. According to the superposition of Gaussian random field, the original gray model is obtained, and the threshold segmentation method is used to generate the C-ZrC inclusion model. Finally, the fiber structure is added to construct the microstructure of the three-phase plain weave composite. The reconstructed inclusions can meet the randomness of the shape and have a uniform distribution. Using an algorithm based on asymptotic homogenization and finite element method, the equivalent thermal conductivity prediction of the microstructure finite element model was carried out, and the influence of component volume fraction on material thermal properties was explored. The sensitivity of model parameters was studied, including the size, mesh sensitivity, Gaussian complexity, and correlation length of the RVE model, and the optimal calculation model was selected. The results indicate that the volume fraction of the inclusion phase has a significant impact on the equivalent thermal conductivity of the material. As the volume fraction of carbon fiber and ZrC increases, the equivalent thermal conductivity tensor gradually decreases. This model can be used to explore the impact of material microstructure on the results, and numerical simulations have studied the relationship between structure and performance, providing the possibility of designing microstructure based on performance. [ABSTRACT FROM AUTHOR]

The aim of this study was to investigate the hair coat characteristics of sows raised in a free-range system in a tropical climate and assess associations with effective radiative properties and thermal conductivity. Bristles were collected from December 2017 to April 2018 and evaluated for diameter (mm), length (mm), and density (bristles per cm2). From these data, the effective thermal conductivity, absorptivity, transmissivity, and reflectivity of the hair coat were determined. Sows were separated into four groups according to skin pigmentation and color parameters. The environment was characterized with regard to average air temperature (°C), relative humidity (%), and shortwave radiation (W m-2). The data were analyzed by repeated measures analysis. Bristle length (33 mm) and density (10 bristles cm-2) were lower in summer than in colder months (48 mm and 20 bristles cm-2, respectively). Effective absorptivity was higher and transmittance was lower in more pigmented sows, demonstrating a connection with protection against solar radiation. Therefore, the combination of a pigmented and dense coat seems to be ideal for pigs reared in free-range systems.

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

The effective design of metallic metamaterials, characterized by interconnected struts or 'lattices,' hinges on the ability to predict strut and strut intersection ('node') responses. This is critical for predicting the macroscopic properties of structures comprised of thousands of struts. Computationally efficient beam descriptions, defined by strut properties like cross-sectional area, modulus, and yield stress, can significantly expedite the prediction of lattice structures and ultimately enable topology optimization. This paper provides a comprehensive examination of the properties of electron-beam melted three-dimensional printed struts and their 'nodes'—four intersecting struts. The findings elucidate the efficacy of various strategies for defining effective properties that accurately capture mechanical response. The study reveals that using a single set of effective properties can introduce inconsistencies between strut stiffness, peak load, and critical displacement. Stiffness correlates with averaged cross-sectional areas, while the peak load capacity correlates more closely with minimum inscribed cross-sectional areas. Analysis of nodes indicates that the interaction of surface defects and heterogeneity within the node strongly influences multi-strut response. Data from CT scans, EBSD scans, and nanoindentation maps highlight spatial variations comparable to the strut diameter, posing a significant challenge in defining effective homogenized properties. This study emphasizes the need for future efforts to integrate statistical property distributions with high throughput simulations to overcome the difficulty in defining a representative volume element (RVE) at the strut scale.

In this paper, a novel microscopic method is presented to investigate the effective mechanical properties and local stress distribution of the composites with respect to some specific interfacial cracks. To this end, a subdomain boundary element method (SBEM) is combined with the asymptotic homogenization theory to calculate their effective mechanical properties. In order to accurately capture the stress distribution on the boundary and inside points (Gaussian integral points) of representative volume element (RVE), the parametric sub-cell is firstly constructed to discretize the RVE. On this basis, a node-pair decoupling method is introduced with consideration of unilateral and bilateral damage. The influence on mechanical properties of composites is revealed, which provides a solid foundation for the design and manufacture of the composite interface. [ABSTRACT FROM AUTHOR]

The paper develops a complex approach to accounting for imperfect contacts (IC) when determining effective properties of various nature. The IC are assumed to be caused by various factors (microstructure features, process’s specifity and so on). To obtain macroscopic properties, we seek a solution of the homogenization problem for the material containing isolated ellipsoidal inhomogeneities when fields are discontinuous at the interphase boundaries. The paper considers, generalizes and compares two existing approaches to accounting for the IC, namely, an approach where IC is modeled by means of a field jump specified in terms of a ratio of field values on the outer and inner sides of the inhomogeneity boundary, and approach, which introduces inhomogeneity with a surface effect. To take into account IC, we have considered an equivalent inhomogeneity with ideal contacts at the boundary. Working the problem on determining the effective diffusional permeability of material provided an example.

The use of nanoparticles to improve the thermal efficiency of PTCs has become a popular area of research. In this study, we present a comparative analysis of the effects of nanoparticles on the thermal performance of PTCs using water and thermal oil as heat transfer fluids. To obtain accurate temperature estimates, we developed a mathematical model that considers heat transfer in both axial and radial directions. The model includes a two-phase flow homogenous model for the liquid phase, as well as nanoparticle concentration, to achieve the best temperature estimation. We validated our model using experimental data and found that the maximum relative error was 2.3% for water and a lower error of 1.5% for thermal oil. Our analysis of thermal efficiency and exergetic efficiency showed that the addition of Al2O3 nanoparticles led to greater improvements in the thermal efficiency for water, even at the same range of nanoparticle concentration. Furthermore, our results demonstrated that exergetic efficiency was generally higher for water than for thermal oil. Overall, this study highlights the potential benefits of using nanoparticles to enhance the thermal efficiency of PTCs. Our findings could help guide the design and optimization of PTC systems in various applications.

We develop a computational framework for the semi-analytic representation of the effective transport properties of two-component composite materials, in the spirit of Bergman's spectral representation. The components of the effective permittivity (or conductivity) tensor are expanded as power series in a contrast parameter between the two phases. The coefficients (the moments of a spectral measure) of these expansions are determined recursively through the numerical evaluations of integrals defined solely on the boundary between the constituent phases, and discretized by high-order (possibly exponentially converging) quadrature schemes. The high precision reached by these coefficients allows the series representation to be recast into Padé approximants (or continued fractions) to provide analytical expressions valid over large (possibly infinite) regions of the parameter complex plane. Examples, thus far limited to two-dimensional rhombic unit cells, demonstrate that the method is reliable for microgeometries and material parameters for which other methods are far less dependable. The analytical representations are particularly useful to study the optical or electrostatic resonant behaviour of some composite materials. [ABSTRACT FROM AUTHOR]

Eshelby tensors serve as the basis of micromechanics which should be explored first to study the effective mechanical behavior of heterogeneous materials. In this paper, Eshelby tensors are extended from isotropic materials to quasicrystals. By utilizing Green's functions and Cauchy's residue theorem, simple and unified expressions of Eshelby tensors for one-dimensional (1D) orthorhombic quasicrystal are derived. Specifically, the closed-form Eshelby tensors are given when the shapes of the inclusions are spheroid, elliptic cylinder, rod-shaped, penny-shaped, and ribbon-like, respectively. Furthermore, the effective stiffnesses of 1D orthorhombic quasicrystal are obtained in view of the received Eshelby tensors and the Mori–Tanaka mean theory. Finally, parameter studies are carried out, and the effect of material properties and volume fraction on the effective overall material properties are investigated. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This work reports on a theoretical and experimental study on the role of fire retardant treatments on the discontinuous ignition of wildland fuels. The effect of the concentration of fire retardant in the solution applied to the vegetation is as expected to increase the ignition delay time. We found that the fire retardant modifies the fuel bed effective thermophysical properties, delaying the thermal response of the specimen when subjected to an incident heat flux. Nevertheless, the critical heat flux remains unaltered within the experimental error. We followed a proven approach based on the thermal ignition theory and testing which however has not been previously employed to study fire retardants on wildland fuels. To carry this out, we performed experiments on the I-FIT apparatus, which yields repeatable results and controlled boundary conditions. The theoretical model shows a good agreement with the experimental results, delivering simple expressions for pencil-and-paper calculations of the ignition delay time and analytical tools to evaluate effective fuel properties. These results will help CONAF and other forest services around the world to gain insight on the optimal concentrations and delivery methods for these types of products during wildfire response. [ABSTRACT FROM AUTHOR]

A microscale modelling framework to compute effective properties related to flow, heat and mass transfer during vacuum cooling (VC) of porous foods was developed. A heterogeneous computational domain reconstructed from steamed bread (SB) was used for modelling, while the cellular water transport in SB investigated using nuclear magnetic resonance was applied for model validation. The computed porosity (63.47 ± 1.05%), effective permeability (1.91 ± 0.39 × 10−11 m2), effective thermal conductivity, (0.33 ± 0.08 W m−1 K−1), and effective diffusivity (5.56 × ± 0.24 10−8 m2 s−1) were in the same range as those measured from the experiment/literature. Also, the analysis revealed that microstructural variability significantly affected the estimated effective properties. The microscale model yielded results similar to the lumped formulation but provided details not visible in the latter. Therefore, the developed model provides a framework for multiscale modelling, which could lead to a better understanding of the underlying moisture loss mechanisms during VC. [ABSTRACT FROM AUTHOR]

This work presents a computational study on the impact of carbon nanotube (CNT) enriched matrix on the performance of 1–3 lead-free piezoelectric periodic composites. Specifically, we investigate a piezoelectric composite system consisting of x 3 parallel aligned fibers of polycrystalline barium titanate (BaTiO3) embedded in a polydimethylsiloxane (PDMS) matrix doped with multiwalled CNT. The effective properties and several figures of merit have been obtained to evaluate the performance of this composite system as is typically done for these materials used for sensing, actuating, or harvesting applications. The results reveal that, in lead-free BaTiO3/PDMS piezocomposites, the addition of CNTs in the PDMS matrix should be f CNT ≈ 0. 5 f c "being f c the percolation threshold", but not higher. In another case, we will only improve the performance of the lead-free piezocomposite for sensing or actuating, but not for energy harvesting applications. This study provides insights into the use of multiwalled CNTs in lead-free piezocomposites and suggests the optimal concentration of CNTs to enhance their performance. The findings have potential implications for the development of new piezoelectric materials and devices for sensing and harvesting applications. [ABSTRACT FROM AUTHOR]

High-frequency excitation (HFE) can be used to change the effective stiffness of an elastic structure, and related quantities such as resonance frequencies, wave speeds, buckling loads, and equilibrium states. There are two ways to do this: by using parametric HFE (with or without nonlinearity) or by using external HFE along with strong nonlinearity. The first way, parametric stiffening, has been examined for many different systems, and analytical predictions exist that have been repeatedly confirmed against numerical simulation and laboratory experiments. The current work presents results using the other way, external stiffening: Combining the method of direct separation of motions with results of a modified multiple-scale approach, valid also for strong or even essential nonlinearity, quantitative measures of the stiffening effect are predicted for a generic 1-DOF system and tested with generally good agreement against numerical simulation and laboratory experiments. [ABSTRACT FROM AUTHOR]

Nanocomposites are heterogeneous media with two or more micro‐structural levels. For instance, a nano‐level is characterized by isolated nano‐inclusions, and a micro‐level is represented by the clusters resulting from aggregation processes. Based on the reiterated homogenization method, we present a procedure to study the influence of this aggregation process and interfacial thermal resistance on the effective thermal conductivity for 2‐D square arrays of circular cylinders. First, an effective intermediate thermal property is obtained by taking into account only the influence of the individual nano‐inclusions in the matrix. Second, the final effective thermal coefficient (k^RH$$ {\hat{k}}_{RH} $$) is calculated considering the clusters immersed in the intermediate effective medium derived in the first step. The conductivity gain (kgain$$ {k}_{gain} $$) is defined as the quotient (k^RH/k^CH$$ {\hat{k}}_{RH}/{\hat{k}}_{CH} $$) where k^CH$$ {\hat{k}}_{CH} $$ is the effective thermal coefficient computed considering only one microstructural level with the same volumetric fraction of inclusions. We apply the theory of complex variable functions deriving in an infinite system of equations solvable by truncation method. The analytical formulas of the effective coefficient used in the calculations generalize other well‐known formulas reported in the literature. We also provide formulas for several truncation orders. The main novel contribution is in the reiterative application of the obtained formulas to illustrate the gain effect in nanocomposites, expressed as a function of the Biot number, thermal conductivities, volumetric fibers fraction, and an aggregation parameter. Furthermore, this result can be used to assess numerical computations and for nano‐reinforced fibers and nanofluids applications. An appendix is included showing similarities and differences with a three‐phase model. [ABSTRACT FROM AUTHOR]

The design of engineering projects in fractured rockmasses requires the determination of the effective elastic properties of a rockmass at a large scale. Theoretical upscaling methods provide accurate estimates of elastic parameters for limited cases of rockmasses containing several sets of infinite size fractures (Amadei and Goodman 1981) or non-persistent fractures with low densities (Kachanov 1980; Kachanov 1992; Yang et al. 2018). Geomechanical classification methods (Bieniawski 1973, Bieniawski 1989; Barton et al. 1974; Hoek and Brown 1997) are based on empirical approaches. They do not provide an accurate estimation of the elastic parameters. In the present study, an improved version of a numerical homogenization method based on Joint Enriched Finite Elements (Pouya and Ghoreychi 2001) is applied to calculate the effective mechanical parameters of two typical patterns of fractured rockmasses. The first type contains a set of non-persistent fractures with various lengths and densities. The second type includes one set of non-persistent fractures perpendicular to bedding planes. A parametric study has been carried out to determine the homogenized elastic parameters according to the mechanical and geometrical properties of the rock and joints. The tabulated numerical output is of interest to be used by patricians for the design of projects in rockmasses, especially for high density of fractures. Analytical expressions of the Representative Volume Element (RVE) size, the homogenized Young's and shear modulus were developed. The elaborated expressions allow extending the results to a wide range of rockmasses with non-persistent fractures. They constitute a generalized form of Amadei and Goodman 1981 analytical expressions widely used in rock mechanics. [ABSTRACT FROM AUTHOR]

In Switzerland, the Opalinus Clay unit was chosen as host rock for a repository for nuclear waste and has recently been investigated in a deep drilling campaign at possible repository construction sites. X-ray images of drill cores were compiled into virtual rock columns and were statistically analyzed with respect to layered compositional variations. This provides insight into scale-dependent homogenization and improves sampling strategy. To predict the repository behavior, using continuum-based models of Opalinus Clay, requires the knowledge of effective properties related to a minimum volume at which Opalinus Clay behaves homogeneously. It turned out that with respect to rock composition, such a volume does not exist in the sense that a single sample of manageable size provides a reliable mean composition. This is because the variation of the cm to dm thick layers, which differ in composition, does not sufficiently homogenize even at the 10-m scale. Thus, effective properties must be obtained by averaging several handleable samples. Regarding the composition of Opalinus Clay at a particular location, about 30 samples, distributed over the whole thickness, with a length of about 30 cm should be measured so that the relative error of the mean value is not higher than 5%–10%. For the statistical analyses computed tomography (CT) values of X-ray data were calibrated with respect to rock composition based on laboratory measurements. The CT values are largely controlled by the respective volume fraction of calcite, quartz, and porous clay matrix. These three components form >80 vol% of the sedimentary rocks studied (also above and below Opalinus Clay). The relationship between CT value and component contents depends on the rock type. The use of data from different rock types to calibrate CT values with respect to composition can lead to erroneous results.

The microencapsulated self-healing composite (SHC) has received much attention for their ability to automatically detect and repair cracks. However, the general micromechanical models relating to SHC did not adequately consider the complex interaction between components and the interfacial transition zone. To address these problems, the four-phase micromechanical model containing core-wall-interface-matrix is proposed based on the composite-sphere theory and the Mori–Tanaka method in this study, and the effective properties of SHC are investigated by regarding the parameter of microscopic component as variables. The results showed that the predictive effective properties of SHC lie between the upper and lower limits obtained from the investigations of Walpole, indicating that the proposed micromechanical model is feasible, and the effect of interfacial strength and interfacial thickness on the properties of SHC is significant, indicating that it is necessary to build the micromechanical model consisting of the interfacial phase in this study, the core-to-wall ratio, size, and the strength of capsule wall have high sensitivity to the effective properties of SHC. These results can help investigate the influence of individual components on the properties of SHC, which are useful to guide the selection of individual components for functional materials. [ABSTRACT FROM AUTHOR]

One of the most common approximations in the theory of composite materials is the homogenization theory. The main difficulty in its application lies in solving the cell problem, i.e., the boundary value problem on a periodically repeating element of composite material. For the case of inclusions of large size and with characteristics far superior to those of the matrix, the lubrication approach gives good results. However, the use of such an asymptotic approach is unnatural for the case when the characteristics of the matrix exceed the characteristics of the inclusion. In the presented work, the problem of conductivity for a 2D composite with rhombic voids is considered. The solution of the cell problem is carried out by two methods. First, the lubrication approach is used for this purpose. In addition, a modification of the Schwarz alternating method is proposed. This new approach has been called an "inhomogeneous cell model". Both methods made it possible to obtain analytical expressions for the effective conductivity. A comparison of the indicated approximate models is carried out, and it is shown that the obtained solutions exactly satisfy Keller's theorem. The physical foundations of the proposed inhomogeneous cell model are discussed. Its advantage in solving the considered problem is shown. [ABSTRACT FROM AUTHOR]

Silicon has a large impact on today's world economy, also known as Silicon Age. For instance, it is an extremely important material for renewable energy systems like photovoltaics. Thereby, the use of polycrystalline silicon has a very wide range of application. For a safe and economic operation with this material, the most accurate prediction or measurement of the elastic properties possible is of interest in the first place even if the focus is on the analysis of the inelastic behavior and related reliability and service life predictions. The problem of effective elastic parameters of polycrystals is also a question of material symmetry. The silicon single crystals obey cubic symmetry while for the aggregate, at random orientation of its constituents, isotropy results. We here give a synopsis on established analytical approaches used to predict effective values as well as a review on experimental outcomes at crystal and aggregate level. In context of present material, the methods are applied and effective properties are predicted analytically while results are compared in terms of the different approaches applied and the material data sets accessed. The results are also contrasted to the measured findings. The resulting deviations are discussed whereby the reasons for these discrepancies are identified. For the application of the effective properties in practicable calculations, this implies that special emphasis must be placed on the origin of these data. The results of mono- and polycrystal properties for both, experimental and analytical findings, are tabulated in clear and concise form, so that they are readily accessible to design engineers. [ABSTRACT FROM AUTHOR]

Three-dimensional (3D) printable lead-free piezocomposites offer scalable and environmentally friendly solutions in many engineering applications. Typically, the composite system consists of polymeric matrices reinforced with active polycrystalline particles, and possibly nanoadditives. The presence of interfacial inclusion/matrix damage could not only compromise the structural integrity of the component but also significantly alter its ability to act as functional smart materials. In addition, both the agglomeration of the nanoadditives, such as carbon nanotubes (CNTs), and the degree of polarization could also affect the electromechanical behavior of the composite. In this paper, we develop a computational micromechanical model for the study of the influence of three types of internal defects on the piezoelectric performance of such composites. We investigate the influence of (a) the texture of the active phase, which is linked to the degree of polarization; (b) the effect of agglomerations of the CNTs; and (c) the presence of damage in the inclusion/matrix interphase region. Performance is assessed through the macroscopic response in various figures of merit. This work provides numerical evidence that the effective piezoelectric constants related to normal strain modes are strongly affected by the presence of damage in the interphase. Instead, the piezoelectric constant related to the shear strain remains unchanged by interfacial damage. Near the percolation threshold of the CNTs, piezocomposites exhibit a notable improvement in the piezoelectric response compared to the composite without nanomodification, as noted in previous works. Interestingly, this trend also applies in the presence of interfacial damage, and it is described in this work. The piezoelectric performance also depends on the texture of the active particles. We find, under some simplifications, the optimal orientation for the crystallites, and we find how the texture changes the performance in the presence of damage. Regarding energy harvesting applications, optimal energy conversion efficiency has been observed for polycrystalline inclusions that resembles a highly oriented single crystal and CNT volume fraction of 60 % of percolation threshold. This is a quite surprising result since the optimal is usually expected for volume fractions very close to percolation and active inclusions with some orientational dispersion. The optimal CNT volume fraction depends on the presence of interfacial damage. Under perfect interface conditions, the energy conversion efficiency is improved with the presence of CNT agglomerations. Under imperfect interface conditions, there is no enhancement due to the addition of CNT. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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We have considered the most general from the point of view of coupled processes a linear model of reversible thermomechanical processes, in which gradient thermoelasticity and stationary thermal conductivity are coupled processes. Mathematical statements for the model including the gradient equilibrium equations of the fourth order, generalized thermal gradient conductivity equation, and the boundary value problems as a whole are considered, the structure of the fundamental solutions is studied, and the general solution is established in analytical form for the one-dimensional problems. We study the influence of both couple effects and scale effects on the deformation process, temperature distribution, and effective mechanical properties of the periodic inhomogeneous structures. Thermal resistance is also taken into account. We show that an analytical solution predicts the possible abnormal effects due to couple and scale effects for diapason of the parameters allowed by the positive definition constraints. Certainly the possible realization of these effects for the inhomogeneous structures is dependent on the real diapason parameters, which must be determined from the experimental data. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Knowing the effective of both mechanical and thermal properties of composite materials allows researchers to improve their behavior and increasing its reliability. In this study, a simplified micromechanical approach is used to modelling and analysis the unidirectional carbon-fiber/epoxy composite performances. The principle objective of this work is to evaluate the effect of the fiber geometrical configurations on the effective mechanical properties and the thermal expansion's coefficients considering three different geometrical configuration of the fiber. Hence, the unidirectional composite with ellipsoidal fiber is stiffer than others with cylindrical or parallelepipedal fibers. Moreover, the considered configuration wherein the fiber has an ellipsoidal shape leads to lower effective coefficients of thermal expansion corresponding to more cohesion between particles. [ABSTRACT FROM AUTHOR]

This work investigates a developed porous piezoelectric composite with metal layers introduced at the interfaces between the piezoelectric and vacuum phases. These metal layers can be added to improve the mechanical and electromechanical properties of the composite. The ordinary porous piezocomposite, which contains only vacuum pores, and the piezocomposite with metal inclusions, whose pores are filled with metal, were explored as specific cases. We constructed the finite element model for all composites understudy and determined their macro properties using the effective moduli theory, which depends on the well-known Hill-Mandel principle. We considered a simple representative unit cell cubic volume, which consists of a piezoelectric matrix with a spherical pore at its center. We compared the properties of all systems and explored the effects of the metal fraction increase on the effective moduli. There are drastic effects on the dielectric permittivity and piezoelectric properties of the considered composite due to the presence of metal inclusion. With an appropriate design of the porous piezocomposite with a metalized pore surface, better effective piezoelectric strain coefficients d i j eff and transverse transduction coefficient ( d 31 eff ) 2 / ε 33 T eff can be achieved. As a result, it is expected that piezoelectric transducers made from this piezocomposite would perform well in piezoelectric motors, transverse piezoelectric sensors, and transverse piezoelectric energy harvesters. [ABSTRACT FROM AUTHOR]