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A computationally efficient method to study the in-plane and out-of-plane dimensional instability of thin paper sheets under the influence of moisture changes is presented. The method explicitly resolves the bonded and the free segments of fibers in the sheet, capturing the effect of anisotropic hygroexpansion at the fiber level. The method is verified against a volumetric model. The importance of longitudinal fiber hygroexpansion is demonstrated in spite of the absolute value of longitudinal hygroexpansion being an order of magnitude lower than the transverse hygroexpansion component. Finally, the method is used to demonstrate the formation of macroscopic sheet curl due to a moisture gradient in structurally uniform sheets in the absence of viscoelastic or plastic constitutive behavior and through-thickness residual stress profiles. [ABSTRACT FROM AUTHOR]

In fibrous paper materials, an exposure to a variation in moisture content causes changes in the geometrical and mechanical properties. Such changes are strongly affected by the inter-fibre bonds, which are responsible for the transfer of the hygro-mechanical response from one fibre to its neighbours in the network, resulting in sheet-scale deformation. Most models developed in literature assume perfect bonding between fibres. In the 3D reality, there is some flexibility in the bond region, even for the perfectly bonded fibres, because of the possibility of deformation gradients through the fibre thickness. In earlier 2D idealizations, perfectly bonded fibres were assumed, implying full kinematic constraint through the entire thickness of the sheet. The purpose of the present study is to assess the effect of this assumption. Using a homogenization approach, a random network of fibres is generated with different coverages and modelled using finite elements. In order to understand the role of bonding between fibres on the hygro-expansive behaviour of a network, a bond model is developed. In this model, the fibres are modelled using 2D regular bulk finite elements and the bonds are represented by interfacial elements of finite stiffness, which are introduced between each pair of fibres bonded in the network. These embedded interfacial elements form a connection between two respective fibres, allowing relative displacements between their mid-planes. The hygro-elastic response of networks obtained with this bond model is investigated by varying the bond stiffness and the network coverage under the application of mechanical loading and changes in moisture content. Furthermore, the bond model is used to analyse the influence of inter-fibre bonds on the anisotropic response of the paper fibre network. [ABSTRACT FROM AUTHOR]

Abstract: Continuum damage mechanics (CDM) is used to describe the post-elastic behavior of low-basis-weight paper. The relevance of undertaking studies of the mechanical behavior of low-basis-weight paper is that it enables characterization, optimization and quality control. In accordance with a CDM theory, an internal variable is introduced that represent the degree to which the material has degraded in a continuum sense and details inherent in a damage evolution law contain information about the rupture mechanism. To account for long ranging micro-structural effects, because of the fiber structure in the paper material, a non-local formulation of the constitutive law is considered. Of particular interest is the fracture toughness of the material, i.e. the ability to resist further crack propagation, as it is often a good measure of flaw tolerance and durability in the context of paper. The constitutive model discussed is verified against tensile tests on rectangular paper specimens containing pre-fabricated cracks. Acoustic emission was used to study the damage evolution in paper specimens during tensile loading. An orthotropic material description has been utilized. The model is contrasted with a purely isotropic formulation. It seems that for the type of problem analyzed in this work, an orthotropic material description does not significantly improve the predictive capability as compared to an isotropic formulation. It is concluded that the model can be used to evaluate the influence of arbitrary defect geometries, defect size and loading conditions and can easily be incorporated into a finite element code. [Copyright &y& Elsevier]

The mechanical behavior of two packaging paper materials subjected to tensile loading up to complete breakage has been investigated. A model for isotropic strain hardening elastic anisotropic plasticity, coupled to anisotropic damage, is discussed. The constitutive relations, including a gradient enhanced damage model, are developed within a thermodynamical framework. The Helmholtz free energy in the continuum is assumed to depend not only on the strain and stress components but also on the damage in the material.The model has been analyzed in a non-linear finite element procedure. The capability of the model to properly capture and simulate the failure of a paper material subjected to tensile loading is demonstrated by means of several numerical examples that are compared to, and verified with, experiments on packaging paper specimens of varying geometry. [Copyright &y& Elsevier]

Abstract: This paper presents a method to predict the through-thickness moisture content distribution and associated induced deformations of paper and cardboard sheets as they are subjected to relative humidity changes. The transient moisture diffusion problem is solved using a “natural” analytic approach that has previously been applied for solving transient heat conduction in multi-layer solids. The deformation behaviour of the sheet during the moisture diffusion process is predicted using a semi-analytical approach based on a Rayleigh–Ritz minimization of the total potential energy. Geometrically nonlinear effects are taken into account. Curvatures of the originally flat sheet are predicted as a function of time, as are the shapes of the sheet for steady-state condition. As multiple solutions exist, stability is studied. The developed model was used to study the deformation behaviour of one paper and two cardboard sheets. Comparisons with finite-element results demonstrate that the developed model provides accurate results. The displacements obtained for steady-state conditions are within +6%. Comparisons with previous steady-state analyses reveal important differences in the shape of one cardboard sheet. This suggests that the moisture diffusion process may influence the configuration assumed by the sheet at steady-state equilibrium. Hence, it may be necessary to take the moisture diffusion into account in the analysis to accurately predict the hygro-mechanical behaviour of paper or cardboard sheets. [Copyright &y& Elsevier]

Abstract: An anisotropic elasto-plastic constitutive model of paper material is presented. It is formulated in a spatial setting in which anisotropic properties are accounted for by use of structural variables. A multiplicative split of the deformation gradient is employed to introduce plasticity. A similar approach is used to model the plastic deformation of the substructure. The yield surface adopted is based on the Tsai–Wu failure criterion, used previously to model failure of paper material. A non-associated plasticity theory is employed to calibrate the model to experimental data. It turns out that a multi-axial loading situation is needed to calibrate the model and here a biaxial tension test is audited. The model was implemented into a finite element environment and the creasing process of a corrugated board panel is investigated. [Copyright &y& Elsevier]

Abstract: Strains, computed by the finite element method, are evaluated and compared to an experimentally determined strain field. The analyzed low-density paper has been designed to ensure bond–breakage as the dominating damage mechanism and the paper material is approximately in-plane isotropic. An optical non-contact displacement measuring system has been used in fracture tests to determine the strain field in the crack-tip region of a pre-fabricated crack. Additionally, acoustic emission monitored tensile tests have been conducted to determine onset and evolution of damage processes and thereby enabling calibration of required constitutive parameters. The results suggest that the investigated paper material can tolerate significantly higher strains than what is predicted by a classic elastic–plastic J 2-flow theory. Immediately before onset of the final fracture (i.e., localization), the experimental measured normal strain in the near-tip region is around 60% higher than the computed strain when using exclusively an elastic–plastic theory for the corresponding load while the strain computed utilizing a non-local damage theory is of the same order of magnitude as the experimentally measured strain. Hence, it seems essential to include a non-local continuum theory to describe strains in the near-tip region quantitatively correct for paper materials. It is demonstrated that path independence of the well-known J-integral does not prevail for this class of material models. Only for the special situation of a homogenous damage field in the crack-tip region may the stress and strain fields be described by the well-known HRR-solutions. [Copyright &y& Elsevier]

Paper is a complex material consisting of a network of cellulose fibres at the micro-level. During manufacturing, the network is dried under restraint conditions due to tension in the paper web in machine direction. This gives rise to internal strains that are stored in the produced sheet. Upon exposure to a moisture cycle, these strains may be released. This results in permanent shrinkage that may cause instabilities such as curl or waviness of the sheet. The prime objective of this paper is to model this irreversible shrinkage and to link its magnitude to the properties of the fibres and of the network. For this purpose, randomly generated fibrous networks of different coverages (i.e. ratio of the area occupied by fibres and that of the sheet) are modeled by means of a periodic representative volume element (RVE). Within such RVEs, a finite element method combined with a kinematic hardening plasticity model at the scale of the fibres is used to capture the irreversible response. The computational results obtained demonstrate that the magnitude of the irreversible strains increases with coverage until a certain coverage and beyond that coverage decreases in magnitude. This phenomenon is explained by considering the area fraction of free-standing fibre segments relative to bonded fibre segments in the network. A structure–property dependency of irreversible strains at the sheet-level on the micro-structural parameters of the network is thereby established. [ABSTRACT FROM AUTHOR]

Abstract: The creep of paper is accelerated by moisture cycling. This effect is known as mechano-sorptive creep. It is assumed that this is an effect of transient stresses produced during moisture content changes in combination with non-linear creep behaviour of the fibres. The stresses produced by the moisture content changes are often much larger than the applied mechanical loads. If this is the case, the mechanical loads are only a perturbation to the internal stress state, and it will appear as if the mechano-sorptive creep is linear in stress. It is possible to take advantage of this feature. In the present report the pure moisture problem is first solved. The mechanical load is then treated as a perturbation of the solution to the moisture problem. Using this strategy, it is possible to linearize a non-linear network model for mechano-sorptive creep and to formulate a continuum model. As a result, the number of variables in the model is reduced. This is a significant improvement as it will be possible to use the linearized model to describe the material in a finite element program and solve problems with complicated geometries. [Copyright &y& Elsevier]

• The non-uniform wrapping process is studied in theoretical analysis, numerical simulation and experiments. • A tape spring can be rolled around a hub, and localized folds are formed. • A theoretical model is presented to predict the shape of the tape spring during the non-uniform wrapping process. • The shape of a tape spring after non-uniform wrapped is a polygon or a continuous curve. • The shapes of four tape springs stay the same as that of single tape spring. A tape spring, which has a high ratio of retraction and deployment, is a type of basic deployable member that plays an important role in deployable structures. This paper is focused on the non-uniform wrapping process of a tape spring that the fixed end section preserves the initial shape. A theoretical method is presented to predict the non-uniform wrapping process of a metallic tape spring based on classical theories about the bending behavior of this type of tape spring. There are two possible shapes for a tape spring after the non-uniform wrapping process, namely a polygon or a continuous curve. The boundary lines of the two possible shapes are studied, and it is shown that the shape depends on the radius of the central cylindrical hub. A finite element model is built using the commercial software ABAQUS to verify the reliability of the theoretical model. Experimental measurement is also conducted to record the shape change process of a tape spring. The comparisons of the results of the three different methods show that they are in good agreement with each other, which means that the theoretical model can be used to predict the non-uniform wrapping behavior of the tape spring. Additionally, the behavior of four tape springs during the non-uniform wrapping process is studied, and the results show that the shapes of multiple tape springs in a coiled state correspond to that of a single tape spring. [ABSTRACT FROM AUTHOR]

• A finite element model to simulate the lined pipe wrinkles is developed. • The manufacturing process of the lined pipe is considered in the paper. • The different effects of friction on two types of wrinkles are investigated. • The effect of friction on maximum amplitude of wrinkles is investigated. Transporting corrosive hydrocarbons using lined pipe is an economical method and has been widely applied in inshore and offshore pipelines. However, when the lined pipe is subjected to bending, wrinkling behavior will occur. Wrinkle can pose a serious threat to the service life and structural integrity of the lined pipe. In this paper, the effect of the friction coefficient between the liner and carrier on the wrinkling behavior of liner under bending is studied. First, a finite element model of lined pipe is established. Second, the influence of friction coefficient on the starting time and amplitude of first type of wrinkles is studied. In the end, the influence of friction coefficient on the amplitude and shape of the second type of wrinkles is examined. The results show that the friction coefficient can affect both the first and the second type of wrinkles, but their effects are different. The friction coefficient can contribute to the first type of wrinkles. Friction coefficient will facilitate the appearance of the first type of wrinkles. While, the friction coefficient showed a strong inhibitory effect on the second type of wrinkles, which inhibited the maximum amplitude and shape of the wrinkles. [ABSTRACT FROM AUTHOR]

This paper addresses the effect of wire slipping on the mechanical properties of structural cables. Based on parameter calibration with experimental data, the paper proposes a Finite Element modelling framework aimed at enhancing the prediction accuracy of the stick/slip behaviour of semi-parallel wire (SPW) cables. The model considers the specific arrangement of the SPW cable composition, interwire friction, and residual interlock between wires. Gaussian Process regression is employed as a surrogate model to reduce the model's computational cost, optimise parameters and quantify uncertainty. The results show high prediction accuracy when compared with experimental data for different pretension forces. The study finds that wire slip varies considerably between wire layers and is significantly influenced by residual interlock between wires. Additionally, cyclic loading under high bending curvatures reveals that the hysteresis behaviour is dependent on wire slip and loading history. The proposed model accurately predicts the stick/slip behaviour of SPW cables, emphasising the importance of accounting for wire slipping in cable analysis models for various applications. • A proposed FEM framework for accurate prediction of stick/slip behaviour of large diameter semi-parallel wire cables. • Gaussian Processes used to reduce computational cost and quantify uncertainty. • Significant influence of residual interlock between wires on stick/slip and hysteresis. • Residual cohesion interlock is significantly higher in the inner wire layers. • Wire slip is dependent on bending curvature and loading history. [ABSTRACT FROM AUTHOR]

• Snap-folding mechanics of differently shaped ring structures (circular, elliptical, rounded rectangular, and rounded triangular rings) under twisting loads is studied. • Various folding modes in terms of foldability, stability and snapping type are identified. • Phase diagrams of the folding modes with respect to geometric parameters are constructed. • Diagrams of the areal packing ratios are constructed using the reduced planar rod model. • The results provide mechanics insights into the ring snap-folding and can guide the design of ring-origami assembly. Ring origami is a new strategy to design bistable foldable/deployable structures by assembling multiple rings with the same geometry. The successful folding of ring origami assembly leverages the snap-folding capability of single rings. It is thus important to model the snap-folding of ring-shaped structures for the rational design of ring origami with good foldability, stability and high areal packing ratio. This paper studies the folding mechanics of differently shaped rings (circular, elliptical, rounded rectangular and rounded triangular rings) under twisting loads by developing theoretical and three-dimensional finite element analysis (FEA) models. The rod model is re-formulated for different ring geometries as two-point boundary value problem systems, which are then solved through numerical continuation, allowing one to capture complex equilibrium paths with multiple fold points. The rod model, verified by FEA simulations and experiments, can accurately, quantitatively capture the snap-folding behaviors for rings of different geometries. Using the rod model, we analyze the folding modes in terms of foldability, stability and snapping type. Phase diagrams of folding modes are then constructed with respect to geometric parameters for the ring profile and cross-section for differently shaped rings. Diagrams of areal packing ratios are obtained using the reduced planar rod model. This work provides comprehensive mechanics insights into the ring folding through twisting and can guide future ring origami design. [ABSTRACT FROM AUTHOR]

• Novel zero-macrospin co-rotational approach for 3D continuum finite elements. • Formulation simplicity via deformation gradient defined at macro element level. • Full derivation with symmetric geometric stiffness matrix arising naturally. • Exposition of misconceptions and errors in Crisfield's seminal asymmetric formulation. • Demonstration of computational superiority of proposed symmetric formulation. The seminal work of Crisfield on co-rotational finite elements came to a profound conclusion that the geometric stiffness matrix of 3D continuum finite elements is inherently asymmetric, though it becomes symmetric under equilibrium conditions. Contending that these outcomes are misconceptions, this paper presents a novel zero-macrospin co-rotational approach for 3D continuum elements in which the geometric stiffness matrix is always symmetric for work-conjugate conservative loads, suggesting that Crisfield's geometric stiffness is erroneously asymmetric and inconsistent. This contention is subsequently upheld by identifying crucial terms omitted in Crisfield's formulation which are responsible for the erroneous asymmetry, and the notion that symmetry is eventually recovered at equilibrium is shown to be a further misconception. Importantly, this critical appraisal of Crisfield's formulation, which has been adopted by numerous researchers, and the delineation of its underlying misconceptions exceed academic interest to real practical relevance. Several numerical examples are presented in the paper which highlight the superiority of the proposed approach, lending incontrovertible practical evidence that the consistent geometric stiffness matrix for co-rotational 3D continuum elements is always symmetric for work-conjugate conservative loads. [ABSTRACT FROM AUTHOR]

In this paper, a novel nonlinear viscoelastic constitutive model is proposed to describe the mechanical behavior of a polymer matrix composite (HTPB propellant). The model is built upon two stress-dependent nonlinear functions within the hereditary integral formulation of viscoelasticity. After implementation into a finite element code, the proposed model is utilized to simulate the stress-strain responses of cyclically loaded HTPB propellant. The results show that the model is capable of capturing the main characteristics of the hysteresis loops during fatigue process and good quantitative agreement is found under circumstances that self-heating effect is not evident. This paper deepens the understanding of the nonlinear behaviors of composite propellant under cyclic loading. [ABSTRACT FROM AUTHOR]

• MSG is applied for the first time to the homogenization of masonry. • The results agree with numerical or theoretical methods, including a 3D FEA. • MSG considerably reduces the computational cost. • 3D properties are obtained from the solution of 2D problems. • Absence of necessity of applying boundary conditions. Masonry is a composite material formed by units and joints, highly anisotropic and difficult to characterize. This paper presents the application of Mechanics of Structure Gene (MSG) to the homogenization of masonry. Since it is a semi-analytical technique, MSG considerably reduces the computational cost and maintains the same precision of three-dimensional (3D) analyses, for example, by the Finite Element Method. Other interesting features are the possibility of obtaining 3D properties from the solution of 1D or 2D problems and the absence of necessity of applying boundary conditions. In the analyzed examples, the 3D elastic constants of the masonry, considered as an anisotropic material, are calculated from Young's modulus and Poisson's ratio of the blocks (or units) and the mortar joints, considered as isotropic. The results obtained are compared with numerical or theoretical methods by different authors, including a 3D finite element analysis, and present agreement, even for large ratios between Young's moduli of blocks and mortar. Thus, the results presented in the paper show that the MSG method can be successfully applied in the homogenization of masonry and presents advantages over other methods for the same purpose. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamic modeling and analysis of rotating pretwisted structures with varying speed, considering complex geometries and setting angles. For thin structures with large curvature and pretwist, a modeling approach with high accuracy and efficiency is needed to capture their highly coupled vibratory behaviors. Therefore, there exists a clear demand for refining beam models with only few additional parameters to describe the shell-like performance. In this paper, we propose a novel three dimensional (3D) pretwisted beam element formulation based on the Carrera unified formulation (CUF) theory. The formulation is implemented to the coupled vibration studies of varying speed rotating pretwisted structures by describing the displacement field in rotating coordinate systems. Using nonlinear strain-displacement relations and Hamilton's principle, a 3D pretwisted beam model is derived on the basis of refined beam theories. Also the inertial, centrifugal and Coriolis effects are taken into account, so that the established model is able to reveal coupled dynamic responses, including in-plane, out-ofplane and torsional deformations. Numerical simulation is performed to study the dynamic characteristics and time responses of a fan blade and a space boom. Results show that this method accurately captures the periodic motions and unstable motions of rotating structures. Compared with traditional theories and finite element analysis (FEA) software, the proposed method significantly reduces the computational cost by using self-adaptive model order and element number. In summary, the proposed method can be used to study dynamics of varying speed rotating pretwisted structures in a precise, flexible and numerically economical fashion. [ABSTRACT FROM AUTHOR]

• A prediction model of grain strain variations due to a specific neighborhood is proposed based on FE simulation observations. • A Cellular Automaton (CA) model is developed using this model and the approximations proposed in Part 1. The methodology to identify the model parameters and the model algorithm are fully described. • Studied polycrystals are represented by a regular structure (Kelvin structure) where all grains are of identical shape and size. • Both CA and FE polycrystalline aggregate stress fields predictions show very close results, but with a really shorter amount of CPU time for the CA model. • Using the quickness of the CA model, orientations causing stress concentrations were easily identified and have shown in the worst scenario to generate in a grain a resolved shear stress concentration twice more significant than for any other grains of the aggregate, without showing any different macroscopic behavior nor crystallographic texture. This paper presents the development of a Cellular Automaton (CA) capable of describing polycrystalline structures heterogeneous behavior in the elastic domain. Based on Eshelby's inclusion problem, this model is the first step to a better consideration of heterogeneities in polycrystals by including the neighborhood effect in grain's behavior. Neighborhood effects have been defined, quantified, and approximated from observations made in the first of this two-part paper, using finite element method (FEM). Considering these approximations, and based on FEM simulations results, an analytical model of the neighborhood effect was proposed in the present paper on which the CA model was built. As a first step in the model development, a regular aggregate structure (Kelvin structure) is used where grains are considered spherical and having identical size. The stress field predictions obtained with the FEM for a polycrystalline aggregate submitted to an elastic loading were compared with the CA predictions, grain by grain, for two different crystal structures (Fe and Ti). Considering the FEM as a reference tool, CA model predictions show an excellent propensity at predicting the local stress fields in polycrystals by capturing the neighborhood effect induced by grain orientations for a low computation time cost. The CA model has also shown its facility to evaluate quickly a grain influence on another grain stress level, and therefore, the orientations generating high stress concentrations in a grain can be easily identified. Using this capacity, the neighborhood effect has been shown to be able to at least double a grain stress level without the material showing any particular texture. [ABSTRACT FROM AUTHOR]

• A new simulation framework based on the PINNs is presented for modelling crack problems. • An enriched PINNs is proposed to correctly capture the local crack-tip behavior. • The SIFs can be directly calculated with very high accuracy. • A deep-learning algorithm written in MATLAB is provided. In this paper, a method based on the physics-informed neural networks (PINNs) is presented to analyze 2D in-plane crack problems in the linear elastic fracture mechanics. Instead of using a discretizing mesh, the PINNs-based method is meshless and can be trained on batches of discretely sampled collocation points. In order to capture the asymptotic behavior of the near-tip displacement and stress fields, the standard PINNs formulation is enriched here by including the crack-tip asymptotic functions such that the local behavior in the crack-tip region can be modeled accurately without a nodal refinement. The trainable parameters of the enriched PINNs are learned to satisfy the governing partial differential equations of the cracked elastic solid and the corresponding boundary conditions. It is found that the incorporation of the crack-tip enrichment functions in the PINNs is substantially simpler and more feasible than in the conventional finite element method (FEM) or boundary element method (BEM). The present PINNs-based algorithm is tested and verified by several representative benchmark examples for different loading and crack-mode types. Numerical results show that the present PINNs-based method can provide highly accurate stress intensity factors (SIFs) with only few degrees of freedom. For interested readers, a self-contained MATLAB code and data-sets supplementing this paper are also provided in the Supplementary material. [ABSTRACT FROM AUTHOR]

This paper introduces a novel formulation, called Hybrid Discrete-Finite Element (HybriDFEM) method, for modelling one-directional continuous and discontinuous planar beam-like members, including nonlinear geometric and material effects. In this method, the structure is modelled as a series of distinct rigid blocks, connected to each other through contact pairs distributed along the interfaces. Each of those contact pairs are composed of two nonlinear multidirectional springs in series, which can represent either the deformation of the blocks themselves, or the deformation of their interface. Unlike the Applied Element Method, in which contact pairs are composed of one single spring, the current approach allows capturing phenomena such as sectional deformations or relative deformations between two blocks composed of different materials. This method shares similarities with the Discrete Element Methods in its ability to model contact interfaces between rigid or deformable units, but does not require a numerical time-domain integration scheme. More importantly, its formulation resembles that of the classical Finite Elements Method, allowing one to easily couple the latter with HybriDFEM. Following the presentation of its formulation, the method is benchmarked against analytical solutions selected from the literature, ranging from the linear-elastic response of a cantilever beam to the buckling and rocking response of continuous flexible columns, and rigid block stackings. One final example showcases the coupling of a HybriDFEM element with a linear beam finite element. • Novel hybrid discrete-finite formulation enabling coupling with classical FEM. • Structure modelled as an assembly of rigid blocks with contact faces. • Contact faces modelled with distributed pairs of nonlinear springs. • Benchmark validation of buckling behaviour of continuous and discrete systems. • Joint geometric and material nonlinearity validated with rocking of a flexible column. [ABSTRACT FROM AUTHOR]

In this paper, the Variational Iteration Method (VIM) or Extended Kantorovich Method (EKM) is formulated for the first time for flexible porous functionally graded (PFGM) plates with different boundary conditions and geometric nonlinearity according to the theory of Theodore von Karman. Its accuracy and efficiency are demonstrated. The plate is subjected to a uniform transversal load and temperature field. The displacement field of the plate is approximated based on the classical plate theory (CTP) or Kirchhoff's plate theory. The governing equations are derived using Hamilton's principle. Modified Coupled Stress Theory (MCST) is used to account for size-dependent effects. The material properties vary with thickness and are temperature dependent. Four porosity distribution patterns are considered in this study. Several examples are solved to demonstrate the proposed algorithm. The results obtained are compared with solutions obtained by the Bubnov-Galerkin Method (BGM) in higher approximations, the Finite Difference Method (FDM) of second order accuracy, as well as with results obtained by the Finite Element Method (FEM) of other authors. The results include an analysis of the effect of size dependent parameters, porosity type pattern, porosity index, functionally graded index, temperature field and different types of boundary conditions on the stress–strain state and bending deflection of plates. [ABSTRACT FROM AUTHOR]

In this paper, a homogenization method which captures intrinsic size effect associated with fiber diameter is revisited and adapted for three-dimensional laminated micro-structures. Based on a unit-cell composed of matrix and reinforcement layers, enhanced deformation gradients varying through the thickness, are introduced with the aid of an additional kinematic variable reflecting the difference between the homogenized and constituent level deformation gradients. In the current work, as opposed to the original formulation, higher order terms are preserved for both phases and therefore bending stiffness of the matrix phase can be taken into account as well. The formulation is implemented within the commercial finite element solver Abaqus through user element (UEL) subroutine considering a finite strain hyperelastic response for the reinforcement layers and a von Mises type hyper-elastoplastic one for the matrix phase. Explicitly discretized unit-cells with varying reinforcement phase fraction, layer inclination angle and layer thicknesses are used as references to assess the predictive capabilities of the homogenized model and the significance of bending stiffness of the phases. Similarly, explicitly discretized model of a beam type structure with a crossed lamellar micro-structure is used to evaluate the performance of the homogenized model under more general, non-periodic boundary conditions. The findings of both cases support the effectiveness of the homogenized model. • 3D homogenization framework for laminated micro-structures including bending effects. • Treatment of both horizontal and inclined layers. • A modular structure for the inclusion/exclusion of bending contributions. • Implementation of a two field, 3D element formulation within Abaqus through UEL subroutine. [ABSTRACT FROM AUTHOR]

In nanotechnology, flexoelectric solids exhibit notable electrical polarization induced by internal strain gradients, rendering them promising for various applications. However, inherent material imperfections are inevitable. Particularly within flexoelectric solids, substantial strain gradients exist in proximity to internal defects, resulting in localized concentration of electrical polarization and potential structural failure. Among the various defect types, circular-shaped inhomogeneity is prevalent. This paper comprehensively investigates the plane strain problem on cylindrical inhomogeneities within flexoelectric solids. The full-field analytical solution is derived for this problem for the first time. Given that flexoelectric theory encompasses pure strain gradient elasticity theory, the strain gradient elasticity solution for plane strain cylindrical inhomogeneities is also established for the first time. This study reveals that the stiffness and size of the inhomogeneity, along with the loading ratio in two directions, exert a noteworthy influence on the local electromechanical coupling behavior near the inhomogeneity. Finally, the mixed finite element method is utilized to approximate the solution numerically, and the close agreement between the finite element results and the analytical solution demonstrates this study's reliability and rigor. Therefore, this investigation imparts valuable insights into examining defects in flexoelectric solids and serves as a foundation for studying more intricate defect typologies. • The exact solution for flexoelectric cylindrical inhomogeneities is derived. • The inhomogeneity stiffness influences stress and polarization concentration. • Effects of loading conditions and inhomogeneity sizes are investigated. • A mixed finite element method is used for comparison with analytical results. [ABSTRACT FROM AUTHOR]

[Display omitted] • A contact force model is developed based on generalized Maxwell model. • Approximate treatment of contact pressure is conducted with Taylor series. • A relaxation test is carried out for determining the scale factor. • Validity of the established model is verified by finite element method. • A parametric study is presented to analyze effects of variations in parameters. This paper proposes a novel approximate model for estimating the normal contact force between a rigid sphere and a viscoelastic half-space based on the generalized Maxwell model. The relaxation function derived from the generalized Maxwell model is applied to the solution to the elastic contact problem based on the elastic–viscoelastic correspondence to obtain an integral expression of pressure for viscoelastic contact. Using the approximate method on the basis of Taylor series, the integral expression is translated into an explicit function of displacement, velocity, time and material properties. A normal contact force model is established by integrating the pressure over contact area. A relaxation test of Nafion® XL is conducted to capture the viscoelastic parameters, and these parameters are employed to simulate the contact behaviors using the finite element method (FEM) to determine the scale factor in the contact force model. In order to verify the validity of the approximate model, the outcomes obtained from the model are compared with those generated by the FEM. A parametric study is conducted to analyze the effects of variations in parameters on normal contact behaviors. The results indicate that the established model is able to predict the contact responses of the viscoelastic materials with complex mechanical characteristics. [ABSTRACT FROM AUTHOR]

Abstract Joining by plastic deformation is recognized as a promising technique to produce laminate metal composites. In this technique, metallic layers are joined together through a metallurgical bond created by severe plastic deformation. Obviously, the accurate design of these processes requires adequate numerical tools which take into account the most important factors affecting the bond formation. In this paper, first, the mechanism of joining by plastic deformation is outlined. Then, based on the microscopic description of solid-state welding, an extended version of a cohesive zone element is introduced to describe both bonding and debonding processes in finite element modeling. In this element, the bond strength between metallic layers is calculated based on the governing parameters of the bonding process such as pressure, plastic deformation and surface cleanness. Subsequently, the mathematical formulation of the introduced element and its finite element implementation are presented. Finally, a numerical example is given to demonstrate the applicability of the proposed method in cold roll bonding processes. The element formulation introduced in this paper can be adopted by other finite element subroutines to simulate the process of bonding and debonding in engineering applications. [ABSTRACT FROM AUTHOR]

Highlights • A general parameterization and a new analytic model of a honeycomb are proposed. • The radius of the inclined walls and the adhesive layer influence are considered. • Besides flexure, stretching, and shearing the mechanism of hinging is included. • In plane elastic constants are compared to those from a FEA reference solution. • The advantages and limitations of the model are presented in a case study. Abstract In the present paper a general parameterization of a periodic hexagonal honeycomb with double vertical walls (commercial honeycomb) is proposed and a new analytic model is established. More attention is paid to account for the radius of curvature of the inclined walls, the adhesive layer thickness, and adhesive fillet at nodes. Then, neglecting the skin effect, in plane elastic constants is obtained analytically using the beam theory. The deformation mechanisms of the honeycomb cells include flexure, stretching, shearing and hinging. The mechanism of hinging is included through small fictitious beams in order to balance the local effects which cannot be captured using the beam theory. Hinging can be neglected when the thickness of these beams becomes infinite or optimally chosen by a proper thickness as to minimize the cumulative errors of the analytical assumptions. The new analytic model presented in this paper can be particularized to the extended Balawi and Abot model if some parameters are adequately modified. The finite element modeling of a representative volume element is used for model calibration and validation considering different relative densities of real honeycombs. The numerical results obtained as a reference for the effective elastic constants are discussed by comparing them to the ones given by the analytic model; its advantages and pitfalls are discussed and explained through a case study and some sensitivity analyses. Numerical simulations are also done in order to establish the distribution of the stresses in cell walls and nodes to confirm the hypotheses used for determining the analytical relations and to explain some limits of the analytic model. The results provide new insights into understanding the mechanics of honeycombs and facilitate the design of new types of cellular materials, including composite hexagonal cell cores. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

This paper addresses the buckling behaviour of a long thin orthotropic plate on a tensionless rigid foundation under combined in-plane shear and bending, where the sheet can only buckle away from the foundation due to the tensionless foundation support. Two boundary conditions at the longitudinal edges ( y  = 0 and b ) are investigated, i.e. clamped and simply supported. The energy method is used to derive the explicit expression for the lateral buckling mode function. The buckling response is then obtained by solving the governing differential equation after substituting the lateral buckling mode function. Based on the analytical solutions developed in the paper, fitted formulae are given for buckling coefficients and the interaction curve. Finally, a numerical example of a corrugated sheet is given to verify the presented model through comparing the results with finite element (FE) analysis. [ABSTRACT FROM AUTHOR]

• Fretting Fatigue crack initiation behaviour in heterogenous materials. • Two-Scale Analysis approach including macroscopic and microscopic models. • Continuum Damage Mechanics approach in conjunction with Finite Element Method. • Several models to consider the effect of heterogeneity on fretting fatigue crack initiation behaviour. The phenomenon of fretting fatigue damage is related to tribological behaviour and commonly occurs at the contact interface between two bodies that sustain oscillation loads. Based on the complicated mechanical situation, several methods have been developed to predict the crack initiation location and life. The Continuum Damage Mechanics (CDM) approach in conjunction with Finite Element Method (FEM) is used in this paper. The fretting fatigue lifetime includes two parts, crack initiation lifetime and crack propagation lifetime, and this paper focuses on the crack initiation phase. Homogeneous materials are usually studied in fretting fatigue problems, and the influence of defects is necessary to be considered. In this study, the authors proposed several models to consider the effect of heterogeneity on crack initiation location and lifetime. The numerical model is a 2D one with plane strain assumption. To get more accurate numerical results with low computational cost, a Two-Scale Analysis approach is developed in this paper. Two macroscopic models and three microscopic models are proposed, including a Macroscopic homogeneous model (Macro-HOMO), a Multiscale Homogenization model with Direct Numerical Simulation (MH-DNS), a Microscopic homogeneous model (Micro-HOMO), a Microscopic Model with equivalent material properties by using Mean Field Homogenization method (Micro-MFH), and a microscopic model with Direct Numerical Simulation (Micro-DNS). The results obtained by using the CDM approach with different microscopic models are compared, and show that the prediction accuracy of the Micro-DNS is the best. In addition, in terms of computational cost, the Micro-DNS model shows great advantages as well comparing to the Macro-DNS model. [ABSTRACT FROM AUTHOR]

• A two-dimensional axial symmetric dynamic analysis model of laser shock metal disc sheet is established. • Finite difference method is used to explore the dynamic deformation behaviors of the laser shock forming. • The dynamic behaviors including displacement, velocity, and surface stress of sheet during the forming is investigated. • The effect of the applied laser shock wave pressure on sheet forming precision also is analyzed. Laser shock forming (LSF) is an advanced sheet forming technology. With the aid of forming die, it can realize sheet precise forming, and has extensive application prospects in aeronautic and electronics industries. In the paper, a two-dimensional axial symmetric numerical model of SUS304 stainless steel is established. Finite element method is utilized to explore the dynamic deformation behaviors of the laser-driving sheet impacted by the forming die. The results show that the node velocity of metal sheet increases in an oscillatory manner during initial stage and then it starts to bulge. After collision with die cavity bottom, the central region of metal sheet jumps up reversely, and experiences repeating damped vibration. The metal sheet gradually exhausts the obtained kinetic energy from the shock wave, and the flat sheet is finally shaped into the geometrical shape of die cavity. The sheet forming precision can be improved by way of increasing laser shock pressure. The corresponding experiments are also carried out to verify the predicted results. The applied method and gained results can provide a reference for theoretical research and parameters optimization in LSF. [ABSTRACT FROM AUTHOR]

In this paper, we propose a simple approach to derive a single-surface multi-failure strength domain for the in-plane behaviour of masonry. The approach, that lays the basis for homogeneous continuum model developments relies on micro-mechanical analyses employing a block-based model for masonry in which blocks, modelled as finite strength continuum bodies, interact through zero-thickness interfaces. In order to derive the strength domain, firstly three failure mechanism typologies are identified, namely crushing failure, joint failure and mixed joint-block failure. Then, the limit surface for each mechanism is obtained relying on limit equilibrium considerations, also introducing a novel rational treatment of the mixed mechanism. Accordingly, a multi-surface strength domain is built by intersecting all the limit surfaces. Finally, such multi-surface strength domain is reduced to a single-surface one exploiting the RealSoftMax function, which allows to preserve the multi-failure nature of the approach, i.e. the explicit distinction between all the failure mechanisms. Following the proposed procedure, the resulting strength domain inherits the material parameters characterizing the block-based model. A finite element block-based model and available experimental data are employed to validate the proposed strength domain. The good agreement obtained with reference results confirms the soundness of the approach. • A simple approach to obtain in-plane masonry strength domain is proposed. • The approach relies on micro-mechanical analyses. • A novel treatment of mixed joint-block failure mechanism is introduced. • The strength-domain resulting from multiple failure mechanisms is reduced to a single analytical surface. • The obtained strength domain is validated against numerical and experimental results. [ABSTRACT FROM AUTHOR]

In this paper we developed the Multicell Thin-walled Method for Solid Multimaterial Beams, which combines structural idealization used in aircraft components, thin-walled beam theory and homogenization techniques from composite materials applied to discrete models, to obtain the cross-section stress fields of solid beams made of multiple orthotropic and isotropic materials. This method idealizes a solid multimaterial cross-section as a multicell thin-walled section to accurately obtain complex stress fields while significantly reducing the solution time, as well as the computational cost, when compared to classical 3D finite element analyses. This method was implemented in a computer program and three examples were analyzed to validate results with the finite element method. Both methods show almost identical results in regions not affected by local disturbances. [Display omitted] • This method uses structural idealization, thin-walled beam theory and homogenization. • Adapted to solid beams made of multiple orthotropic and isotropic materials. • Stress fields correlate closely with FE in regions unaffected by local disturbances. • A significant reduction in solution time compared to 3D finite element method. [ABSTRACT FROM AUTHOR]

• The finite element (FE) simulation of the hemispherical punch tests was performed for AA7075-O sheets in ABAQUS/Explicit using different time dependent criteria to predict the forming limit diagram at room temperature. • In order to understand the efficiency of the FE-based time dependent criteria to predict forming limit diagrams (FLDs), an analytical-based method, namely, Marciniak-Kuczynski (M-K) was tested. • It was observed that the experimental FLD can be reproduced using various time-dependent criteria in a relatively appropriate manner but with limitations. In this study, numerical simulations and experimental validations of the simulation of hemispherical punch tests for AA7075-O aluminum sheets with various sample widths are presented. It is convincingly believed in literature that a finite element (FE) based forming limit diagram (FLD) can be predicted very well using various time-dependent criteria. This matter has been investigated and securitized deeply and the FE-based FLD was predicted using three time-dependent criteria and compared with the experimental FLD. Results show that two of the three criteria could predict the relatively appropriate shape of the FLD while one of them has failed to match. Aside from using FE simulation to predict the FLD, an analytical method, namely, Marciniak-Kuczynski (M-K) was also used to make a better evaluation about the capability of the finite element method (FEM) to predict FLD. Among the FE-based FLDs, the one predicted using the Martinez-Donaire et al., 2014 was found to be close to the one predicted using the M-K method. Although, the main objective of this paper is to investigate the capability of the FEM to predict an FLD for AA7075-O aluminum sheets, the fracture behavior for each case was predicted using a unified fracture model. Several computer runs were executed to perform the tests and reproduce the experimental results. The aim of this study was to discuss the simulation of hemispherical punch tests and analyze the numerical results and compare them with the experimental and analytical methods. It was observed that the experimental FLD can be reproduced using various time-dependent criteria in a relatively appropriate manner but with limitations especially at the equibiaxial stress state. These limitations were scrutinized and discussed in detail by comparing the results with experimental and analytical calculations. [ABSTRACT FROM AUTHOR]

This paper proposes a simple, yet effective, modified crystal plasticity framework which is capable of modelling plasticity and creep deformation. In particular, the proposed model is sufficiently versatile to capture the effects of complex load histories on polycrystals, representative of those experienced by real materials in industrial plant. Specifically, the methodology was motivated by the need in the power generation industry to determine whether cyclic pre-straining influences the subsequent creep behaviour of type 316H austenitic stainless steel as compared to non-cyclically pre-strained material. Cyclic pre-straining occurs widely in plant and it is of paramount importance to accurately account for its impact on the subsequent deformation and integrity of relevant components. The framework proposed in this paper considers the effects of dislocation glide and climb in a relatively simple manner. It is calibrated using experimental tests on 316H stainless steel subjected solely to monotonic plasticity and forward creep. Predictions are then obtained for the creep response of the same material after it had been subjected to cycles of pre-strain. The predictions are compared to experimental results and good agreement was observed. The results show slower creep strain accumulation following prior cyclic loading attributed to hardening structures developed in the material during the cyclic pre-strain. The model also highlights the importance of accounting for directionality of hardening under reverse loading. This is hypothesized to affect the development of an internal stress state at an intragranular level which is likely to affect subsequent creep accumulation. [ABSTRACT FROM AUTHOR]

This paper is dedicated to creep buckling predictions. Thin walled cylinders having an aspect ratio of one are subjected to an uniform external pressure. The material is a special type of nickel which “creeps” at ambient temperature. The material parameters for the creep law are identified from experimental results. The creep failure experiments are described and corresponding failure times are given. The paper then compares three alternatives of finite element modeling of the experiments (3D Shell with integration through the thickness with a periodic or non periodic initial imperfection are compared with COMU quasi axi-symmetric imperfect shell element). These 3 modeling show consistent predictions. The simulation time is a hundred times faster with the COMU model. It is shown that the prediction of failure time of these experiments is extremely sensitive to the initial imperfection amplitude. The effect of creep law modeling is also important. Finally a parametric analysis on different types of cylinders is given: some general trends are proposed for this type of delicate predictions. [ABSTRACT FROM AUTHOR]

This paper presents a study on the metal cutting simulation with a particular numerical technique, the Particle Finite Element Method (PFEM) with a new modified time integration algorithm and incorporating a contact algorithm capability . The goal is to reproduce the formation of continuous chip in orthogonal machining. The paper tells how metal cutting processes can be modelled with the PFEM and which new tools have been developed to provide the proper capabilities for a successful modelling. The developed method allows for the treatment of large deformations and heat conduction, workpiece-tool contact including friction effects as well as the full thermo-mechanical coupling for contact. The difficulties associated with the distortion of the mesh in areas with high deformation are solved introducing new improvements in the continuous Delaunay triangulation of the particles. The employment of adaptative insertion and removal of particles at every new updated configuration improves the mesh quality allowing for resolution of finer-scale features of the solution. The performance of the method is studied with a set of different two-dimensional tests of orthogonal machining. The examples consider, from the most simple case to the most complex case, different assumptions for the cutting conditions and different material properties. The results have been compared with experimental tests showing a good competitiveness of the PFEM in comparison with other available simulation tools. [ABSTRACT FROM AUTHOR]

Abstract: The mechanical behavior of fibrous networks is governed by complex multiple mechanisms. This study examines the effect of microstructure on the macroscopic deformation and fracture of two-dimensional random fiber networks and its practical implications for understanding the material failure in paper materials by using finite element models. Remote load is a pure mode I opening field, applied via a boundary layer. Characteristic networks, consisting of the union of solutions of several unique networks, are interpolated on a rectangular grid covering the whole problem domain. The interpolated solutions are interpreted as network-equivalent continuums representing the mechanical behavior, on average, for a specific set of structural properties. A regularization routine is included in a variational procedure in order to minimize potential energy in the body and produce continuous strains at cell borders in the grid. It is shown that using a classical continuum linear elastic fracture mechanics (LEFM) approach to describe macroscopic singular-dominated fields in fiber networks, can lead to erroneous results especially in networks having a low degree of bonds per fiber. The classical continuum description is too simple to capture the essential mechanical behavior for this class of material since a structural effect, that alters the displacement field, becomes pronounced. It is necessary to include a nonlocal theory to describe the mechanical behavior at a continuum level. By using an appropriate characteristic length in a nonlocal continuum formulation, strain energies, in the neighborhood of a dominant macroscopic singularity, are calculated that agree well with characteristic network models and hence produce fairly good agreements between the networks and the nonlocal continuum models. A key conclusion found is that, only for networks with a high degree of bonding, can the mechanical behavior around a macroscopic singularity be captured by the classical local continuum theory. In networks with a low degree of bonds per fiber, there are regions far away from the macroscopic singularity that have relatively higher magnitudes of strain energy than predicted by the classical theory. A relation between an internal length scale parameter, used in the nonlocal continuum model, and the structural properties of the network is approximated by a simple function. [Copyright &y& Elsevier]

Abstract: Finite element analysis of ink-tack delamination of paperboard were presented. The paperboard was modeled as a multilayered structure with a softening interface model connecting the paperboard plies. The paperboard plies were modeled as orthotropic linear elastic. The ink-tack loading was applied to the board in the form of a moving displacement boundary condition. The purpose of the analysis was to assess the influence from the elastic moduli of the individual layers on the ink-tack delamination event. The results indicated that in most cases of practical interest the board delaminated between the outer plies of the board, although the interface strength was lower in the middle of the board. This observation helped to explain why traditional tests for out-of-plane testing of paper by standardized methods could not uniquely predict the propensity for ink-tack delamination. [Copyright &y& Elsevier]

The present paper addresses the challenge of conducting Finite Element (FE) micromechanical simulations based on 3D X-ray data, and quantifying errors between simulations and experiments. This is of great interest, for example, in the study of ductile fracture as local comparisons and error indicators would help understanding the limitations of current plasticity and damage models. Standard methods used in the literature to conduct FE simulations at the microscale are often based on multiscale schemes. Relevant mechanical fields computed in an FE simulation at the specimen scale are used as boundary conditions for the micromechanical simulation, where the real microstructure is meshed from 3D X-ray images. These methods hence rely on an identification of material behavior at the macroscale, say, using force measurements and 2D surface images. In an earlier work by the authors, a method for conducting micromechanical simulations using measured boundary conditions thanks to Digital Volume Correlation (DVC) was proposed. The interest of this DVC-FE approach is that it uses solely 3D X-ray images acquired in-situ during the experiments. Thus, FE simulations are directly conducted at the microscale, with no dependence on specimen scale simulations or multiscale schemes. This approach also includes a methodology to perform local error measurements with respect to experimental observations. In this paper, both multiscale schemes and this DVC-FE approach are applied to new experimental results on a nodular graphite cast iron specimen with machined holes. Ductile fracture due to the nucleation, growth and coalescence of microscopic voids between the machined holes is observed in-situ thanks to synchrotron 3D imaging. The objective of this paper is to assess the accuracy of boundary conditions for each approach and conclude on the optimal choice. Based on both average and local error measurements, it is shown that void growth is underestimated with multiscale schemes, while predictions are significantly improved with the DVC-FE approach. [ABSTRACT FROM AUTHOR]

This paper presents a novel scheme to biaxially package and deploy flat membranes, in which the thickness of the membrane is accounted for through the novel concept of slipping folds. The membrane is divided into parallel strips connected by slipping folds, and specially chosen wrapping profiles that require zero slip along the edges of the membrane are identified. This packaging scheme avoids the kinematic incompatibilities that in other schemes result in local buckles and wrinkles that increase the deployment force and permanently deform the membrane. The paper also presents a scheme to apply uniform uniaxial prestress to the deployed membrane, as well as a two-stage deployment scheme. Packaging efficiencies of up to 83% have been demonstrated for meter-scale models, although for large membranes the packaging efficiency approaches 100%. [ABSTRACT FROM AUTHOR]

In this paper a complete pathway to construct a constitutive model well suited for finite element analysis of viscoelastic media undergoing large deformation and damage is described. In particular, a systematic calibration, verification and validation procedure of the implementation of a solid propellant constitutive model was developed. As a first step a three dimensional model valid for all deformation ranges was selected and implemented as a user material into commercial finite element software. The second step consisted of calibrating the model without damage and verifying the algorithm against the built-in material model available in the software. In the third step the damage parameters were determined using a set of solid propellant test data. Finally, the full constitutive model was validated by comparing the results with the test data not used in the calibration. For both verification and validation, homogeneous and inhomogeneous deformation states were considered, and various element types were investigated. The comprehensive approach outlined in the paper aims to emphasize the need of a methodology to be followed for a successful use of a constitutive model in a computational stress analysis. [ABSTRACT FROM AUTHOR]

This paper provides finite elements predictions for the effective tangent properties of microcracked viscoelastic masonry. This model relies on two steps. The first one is based on the identification at the short and long terms of an approximate analytical creep function for the mortar. Following (Nguyen et al., 2011) for a microcracked homogeneous material, this step rests on the coupling between the Griffith’s brittle fracture theory and stress-based dilute homogenization scheme. It allows to avoid recourse to ‘heavy’ numerical inversion of the Laplace–Carson transform. The second step provides orthotropic overall properties of masonry by means of finite elements method used to carry out periodic homogenization on masonry. This step relies on the calculation of the localization strain tensors in each phase (brick and mortar). This paper proposes an alternative model to an incremental homogenization of masonry which is heavier to carry out since it depends on additional parameters such as time increment and prestresses in viscoelastic phases added to the crucial computation step of strain localization tensors in each phase. In this work, for the sake of simplicity and as a first approach, only time-dependent crack densities (Shrive et al., 1997; Reda Taha and Shrive, 2006) are considered at short and long-terms. Results provided by the proposed finite elements model can be considered as reference solution enabling a rigorous assessment of recently analytical model proposed by Nguyen et al. (2014) and Rekik et al. (2016) as a generalization of the Cecchi & Taliercio model (Cecchi and Taliercio, 2013) initially available for uncracked masonries. This comparison is carried out for different mortar thicknesses and brick’s dimensions. The case of a compressed wall is also considered at the long term. [ABSTRACT FROM AUTHOR]

Of interest in this work is the multi-physics modeling of electrically sensitive materials known to have viscoelastic properties. We show how the current state of the art in the modeling of electro-mechanics in deformable media can easily be integrated within the unified framework of continuum thermodynamics, this latter being crucial in setting the convenient forms for the constitutive laws and evolution equations. The formulation is developed within the finite strain range and we adopt the nowadays well-accepted multiplicative decomposition of the deformation gradient into elastically relaxing and viscous parts giving rise to an intermediate configuration on which the electric field vectors can eventually be transported. The paper discusses in depth such a formulation. Among others, it is implicitly found that the electric displacement and polarization vectors can be split into equilibrium and non-equilibrium parts. A model example is proposed for the purpose of demonstration to study some phenomena qualitatively. The paper presents also the numerical design of a simplified version within the context of the finite element method to illustrate the effectiveness of the proposed framework for structural simulations. [ABSTRACT FROM AUTHOR]

Numerical and analytical modelling approaches are often competing to describe a desired phenomenon. However, there is no reason to look for a single method and complementarities between distinct modelling ways are always profitable. This paper, the first of a set of two consecutive papers published in this volume, provides such a modelling methods reconciliation in the case of transport phenomena acting in transversely isotropic multi-phased materials. Microstructural Finite Element Modelling (FEM) helps supplying the analytical implementation for a better description of interactions between the constituents. As an application example, the case of molecular diffusion within a unidirectional composite medium is investigated without any restriction for considering any other transport mechanism. Based on a rational microstructure description, this study proposes a model able to predict the overall diffusion tensor of the composite and investigates more particularly diffusivity effects of interphase areas and fibre packings. For this purpose, a “ n -phase” Generalized Self-Consistent Scheme (GSCS) coupled with a Morphologically Representative Pattern (MRP) approach has been developed. This first part is focused on the modelling strategy and the concept of “transfer matrices” has been used. This approach is applied in Part II (Joannès and Hervé-Luanco, 2016) to study the influence of fibre packings on the effective behaviour of composite materials made of insulated fibres embedded in a diffusive matrix. [ABSTRACT FROM AUTHOR]

The Strong Discontinuity Approach (SDA) is a popular method to incorporate cracks as displacement discontinuities into finite elements. In the first part of the paper, different SDA formulations (denoted as SOS, KOS and SKON) are assessed numerically based upon different error norms including a norm to evaluate the variational consistency of SDA elements. Results are compared with analytical solutions as well as with results from interface elements and the element erosion technique for cohesionless cracks. In the second part of the paper, a new method to improve the computational robustness of SDA analyses is proposed. In addition to using arc-length control to solve the nonlinear equation system, a sequential un- and reloading scheme is proposed with the crack state frozen during unloading to avoid, that more than one new crack segment is activated within an increment. The performance of the algorithm is demonstrated by numerical analyses of a tension test on a dog-bone shaped specimen by means of different variants of the SDA and, for comparison, also using interface elements. [ABSTRACT FROM AUTHOR]

Alkali-Silica Reaction (ASR) is a particular type of chemical reaction in concrete, which produces cracking and overall expansion of the affected structural element due to the formation of expansive reaction products within the cracks. This paper develops the formulation of a coupled Chemo-Mechanical (C-M) Finite Element (FE) model for simulating ASR expansions in soda-lime glass concrete at the meso-scale. The model considers several C-M coupling mechanisms, including a reaction-expansion mechanism qualitatively proposed by the authors elsewhere on the basis of experimental results, which is introduced in order to reproduce the effect of compressive stresses on the development of ASR expansions. The model has the characteristic ingredient of using zero-thickness interface elements for modelling the C-M mechanisms leading to the propagation of cracks due to the formation of ASR products within them. This fact has required the development of: (i) a new FE formulation for diffusion-reaction processes occurring within discontinuities represented by interface elements, and (ii) a new mechanical constitutive law for interface elements, which is able to reproduce the propagation of a crack induced by the development of an internal pressure exerted by solid reaction products formed within it. In addition, the numerical implementation of the diffusion-reaction formulation has been advantageously performed with clear separation between the boundary-value or 'structural' governing equations (i.e. continuity and concentration gradient relations), and the 'constitutive' (i.e. chemical) equations. The model is illustrated with some application examples. [ABSTRACT FROM AUTHOR]

Size effects are important in nano-energy applications. In this paper, a novel gradient theory is introduced to describe nonlocal heat transport in nano-scale structures. This is achieved by considering the second derivatives of temperature in the constitutive equation for the high-order heat flux in an advanced continuum model. The variational principle is then applied to derive the governing equations for the coupled phonons and electrons in thermoelectric materials. The general two-dimensional boundary-value problem in the thermoelectric solid is then analyzed by the finite element method (FEM). The mixed FEM with the C0 continuous interpolation for temperature and temperature gradients is developed. A collocation approach for constraints between temperature and its gradients is applied. Numerical examples are presented to study the influence of the internal size on the temperature and electric potential, demonstrating clearly significant enhancement of thermoelectric properties via the internal material size. [ABSTRACT FROM AUTHOR]

• Error using only force in the constitutive characterization of heterogeneous strain. • Use of heterogeneous deformation field for accurate constitutive characterization. • Use of the non-conflicting concept to assess the performance of constitutive models. The mechanical characterization of thermoplastics submitted to finite strain is a non-trivial procedure since they may present necking and cold-drawing. These phenomena are associated with heterogeneous strain fields that may mask the real stress–strain curve and lead to mistaken conclusions about the capability of constitutive models to represent the material mechanical response. Aiming to shed light on this issue, this paper presents a numerical study based on a Finite Element Method Updating (FEMU) technique to obtain the true stress–strain curve of a thermoplastic specimen. FEMU technique is employed to characterize three elastoplastic models with different mathematical frameworks. Inverse problems are constructed considering force response and displacement data of a heterogeneous strain field on the specimen due to the necking and neck propagation kinematics. Results shown that even a very simple multilinear elastoplastic model, available in commercial software, is capable of representing force response of a tensile test when only experimental force data is considered. However, when the necking kinematics is taken into account, the studied models present different results and poor mechanical behavior representation, indicating that only the force data obtained from a tensile test is not enough to establish conclusions about the performance of a constitutive model when heterogeneous strain field occurs. Since none of the models was capable of accurately reproduce the experimental force and kinematics data, to evaluate which model performs better, it is proposed a multi-objective analysis of Pareto front results. [ABSTRACT FROM AUTHOR]

• The homogenized elastic response of seven cubic hollow truss lattices are computed. • Differentiable elastic response models are used in multiscale topology optimization. • Hollow bend-dominated lattices increase their stiffness at constant relative density. • Many hollow trusses can obtain perfect isotropy over large ranges of relative density. Elastic meta-materials, which we will treat herein as synonymous with elastic micro-architected materials, derive their unique combination of properties from the fine scale geometry of their solid and void regions. Recent advances in additive manufacturing have made the fabrication of such micro-architected materials feasible, and have driven interest in their properties. We consider the class of elastic meta-materials whose micro-architectures are composed of a network of straight struts connected at nodes arranged within a repeating unit cell; the octet truss is one well-known example of such truss lattices. Heretofore, the majority of work characterizing such truss lattices has considered solid struts and has been based on rod theory, a simplification of continuum elasticity which is accurate in the limit of low relative densities. In this paper, we use full continuum theory, solved with finite element analysis on adaptively refined meshes, to characterize the elastic performance of seven truss lattices with cubic geometric symmetry, and whose struts and nodes are hollow; we consider a wide range of strut wall thicknesses and truss relative densities. Varying the wall thickness provides an additional dimension of control, so that stiffness and anisotropy can, to an extent, be decoupled from the relative density of a given truss lattice. We show that a truss' stiffness can be increased at fixed relative density, with bend-dominated truss lattices showing significantly greater improvement than stretch-dominated designs. Increases in stiffness by a factor of greater than five are observed, and increases by a factor of 100 or more are obtainable. Bend-dominated structures with hollow struts can be found that are stiffer than stretch-dominated ones at nearly all relative densities, contradicting a common rule of thumb. For some trusses, including the octet truss, choosing the wall thickness appropriately allows one to obtain isotropic response over a large range of volume fractions. We use topology optimization to find maximally stiff multiscale structures comprised of micro-architected materials and find that all the trusses we consider perform similarly, with anisotropic trusses resulting in slightly stiffer structures for a given load. [ABSTRACT FROM AUTHOR]

In the present paper, we develope a 3-D M srf -integral to evaluate the surface energy that is corresponding to formation of multiple surface cracks. The M srf -integral is formulated by modifying the conventional 3-D M-integral with deliberate origination of the coordinate system and proper delimitation of the integral surface. The integral is demonstrated to be surface-independent in a modified manner and so can be accurately evaluated provided an integration surface remote from the crack fronts is selected. With this feature, the theory of integration can be straightforwardly incorporated into the finite element method. In fact, it is not necessary to simulate the near-front regions with very fine FE simulations to obtain accurate solutions of M srf. [ABSTRACT FROM AUTHOR]