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The morphology of the active layer significantly influences the performance of organic photovoltaics (OPVs). Recent advances in experimental techniques have facilitated the visualization and digitization of complex microstructures within the OPV active layer, paving the way to construct quantitative structure–property relationships. Given a digitized morphology, detailed physics-based simulations can provide accurate characterization; however, performing these simulations on the full digitized morphology is computationally prohibitive, thus impeding high-throughput characterization and exploration. To address this issue, we propose a fast mathematical approach to select small sub-volumes of the full digitized morphology, which exhibit similar performance characteristics as the full morphology. The selection of such 'representative volume elements (RVE)' consists of two main steps: (a) Identification of a small set of morphology features (or 'descriptors') that are computationally light to calculate and that are correlated with the property of interest. These descriptors serve as a surrogate for the true property of interest. (b) Integrating this surrogate model with an adaptive Bayesian-based approach to efficiently identify sub-volumes of the morphology exhibiting nearly identical features to the full morphology. We illustrate the utility of this approach using large discretized morphologies containing greater than 64 million voxels, reconstructed using electron tomography. This approach produces a ∼ 400 fold reduction in computational effort with less than 1% reduction in accuracy. While our application focus is on OPVs, the methodology presented is generally applicable to problems where detailed physics simulations bottleneck quantitative structure–property relationships, including in fields like catalysis, membranes, and bioelectronics. [Display omitted] [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • Microscopic plastic behavior of DP steels is studied using artificial RVEs. • Shear band accommodations are investigated for the RVEs under different loadings. • Deformation induced twisting of martensite grains are found during shear loading. • Strain localization rises by longer martensite-ferrite interface due to clustering. Abstract In this paper, a topology optimization based numerical method is proposed to investigate the micromechanical plastic behavior of dual-phase (DP) steels. Representative volume elements (RVEs) are constructed using the topology optimization based artificial microstructures. Micromechanical behavior under various loading conditions are predicted for the RVEs to investigate the plasticity, strain localization and strengthening mechanism affected by the microstructural characteristics of DP steels. Plastic strain patterns including shear band are found during the deformation. Due to the twisting movement of martensite grains, the direction of the strain localization bands in the shear loading case is 0 ° or 90 ° to the loading direction, while it is 45 ° in the tensile and compressive cases. Moreover, the effective flow behavior of the material under shear loading is lower than those found in tensile and compressive cases. The influence of various microstructural features, such as, martensite fraction, distribution of each phase, on the effective flow properties and the local strain partitioning has also been identified. Both of the effective flow properties and strain localization exhibit the tendency to be strengthened with the increase of martensite phase fraction. Furthermore, the RVE with more uniform martensite distribution leads to the decrease of effective flow properties and strain localization. Longer martensite-ferrite interface results from the clustering of martensite, which increases the strain localization effect during the plastic deformation. [ABSTRACT FROM AUTHOR]

At the microscale, various materials from biological tissues to nanoporous metals are formed by networks of ligaments. Here we propose a highly efficient simulated annealing (SA) framework for generating synthetic representative volume elements (RVE) of such materials. It can produce RVE where the microstructural characteristics both on the network level (e.g., node valency and ligament length) and on the level of individual ligaments (e.g., curvature) can be predefined by the user via probability distributions. As an application example of our framework, we generate a large variety of RVEs, analyze their mechanical properties by the finite element method, and establish through this approach links between microstructural descriptors and macromechanical properties of materials with ligamentous microstructures. [Display omitted] • Two-stage algorithm to generate ligamentous microstructure. • Networks with tailor-made descriptors of the network level and the ligament level. • Application in study of nanoporous materials to discover generalized scaling law. [ABSTRACT FROM AUTHOR]

A significant question in the study of microstructurally small cracks (MSCs) is: What is the minimum microstructural volume that should be included in studies involving MSCs? To answer this, representative volume elements for microstructurally small cracks (RVE MSC), or the minimum volume of microstructure required around an MSC to achieve convergence of crack-front parameters with respect to volume size, were previously determined using finite element (FE) simulations. The large computational expense of determining RVE MSC via FE simulations motivated the implementation of convolutional neural networks (CNNs) to expedite the determination of RVE MSC (Part I). In addition to expediting the determination of RVE MSC , trained CNNs provide the opportunity to gain insights about RVE MSC predictions through various interpretation methods, which we investigate in the current work. First, an inspection of CNN predictions reveals trends learned by the CNN. Second, an input sampling grid study offers insights into the volume of microstructure around an MSC that most influences predictions of RVE MSC. Third, an input feature sensitivity analysis compares the influence of microstructural and geometrical features on RVE MSC predictions. Fourth, visual inspections of saliency maps reveal the local microstructure that is most important to the CNN when predicting RVE MSC. The CNN interpretation results show that microstructural features are more critical than geometrical features to the CNN predictions. Despite inherent limitations in interpreting saliency maps, the results demonstrate that the CNN can learn to identify various microstructural arrangements at individual crack-front points. Overall, this study highlights the importance of considering a variety of microstructural instantiations when determining RVE MSC , as RVE MSC should be a conservative minimum volume requirement that applies across a wide range of microstructural instantiations. [Display omitted] • We use various interpretation methods to study black-box CNN predictions of RVE MSC. • Some, but not all, physics-based trends are captured in CNN predictions of RVE MSC, i. • Microstructure within 2 to 3 grains of a crack is most important to CNN predictions. • Microstructural inputs are found to be more important than geometrical inputs. • Conservative RVE MSC estimates must consider various microstructural instantiations. [ABSTRACT FROM AUTHOR]

The mechanical properties of dual-phase (DP) steel are mostly derived from its microstructure, e.g., volume fraction, size, distribution and morphology of each constituent phase. An artificial microstructure generator with an enhanced novel phase assignment algorithm based on material topology optimization is proposed to investigate the mechanical properties of DP steel. With this algorithm, phase assignment process is performed on a modified Vorono ï tessellation to achieve the targeted representative volume element (RVE) with a good convergence. This method also includes a proper orthogonal decomposition (POD) reduction of flow curves (snapshots) to identify the optimal controlling parameters for DP steel. This numerical method significantly improves the representation of the generated RVE with low computational cost. The proposed method is verified using a DP590 steel which indicates a good agreement with experimental material behavior and RVE predictions based on real microstructures. Predictions of plastic strain patterns including shear bands using the artificial microstructure closely resemble the actual material behavior under similar loading conditions. Robustness of this approach provides a new dimension for RVE development based on artificial microstructure which can effectively be implemented in material characterization. [ABSTRACT FROM AUTHOR]

In the present study, the plasticity and creep behaviors of heterogeneous composites containing randomly distributed particles were considered to predict the effect of boundary conditions (BCs) numerically derived solutions. Modeling was performed using two dimensional representative volume elements (RVEs) with different sizes and particle volume fraction. Structural heterogeneity along the model boundaries considerably influenced the overall numerical solutions that developed stress/strain fluctuations, while inner part of the model showed almost the same strain fields. In both plasticity and creep models, the thickness of BC-affected region was larger in plastic or creep strain fields than in elastic strain fields when dividing the total strain of volume elements into elastic, and plastic or creep strain. When the particle volume fraction increased, the thickness of the BC-affected region reached a critical size with the exception of the plasticity model. Comparing the results of the linear and nonlinear problems, the thickness was larger in the nonlinear problem than the linear one. The results suggested that the mechanism proposed for the elasticity model could be applied to nonlinear models to determine the size of the RVE for the specific research purposes or predicting potential errors to estimate the effective properties. [ABSTRACT FROM AUTHOR]

In this paper, the numerical homogenization technique and morphological analysis are used in order to compute the thermal conductivity in microscale of porous materials. The computational thermal homogenization is based on a 3D random material with spherical and ellipsoidal pores. Two types of microstructures are considered: microstructure 1 with random distribution of identical non overlapping pores and microstructure 2 with overlapping pores, based on the boolean model. The objective is to quantify the difference between these morphologies, in order to find some relationships between their morphological parameters and their macroscopic effective thermal conductivities. Periodic boundary conditions are applied on the representative volume element, RVE , of microstructures, for thermal modeling by finite element method. The covariance notion and integral range are introduced for morphological characterization. The deterministic RVE size is related with all microstructure parameters. The equivalent morphology concept for thermal conductivity is introduced after development of some relationships between morphological parameters. [ABSTRACT FROM AUTHOR]

The aim of the work is to predict the onset and the progression of damage in the continuous fiber reinforced composite laminates taking into consideration the different mechanical behavior of the constituents in the composite under different loading conditions. The stresses in the constituents are obtained using a representative volume element (RVE) approach. Finite element analysis is carried out to extract the stresses in the constituents and the overall effective properties of the composite material. To consider the realistic behavior of the matrix of the composite material, a modified Drucker–Prager failure criterion is used. Direct test data on the individual constituents are used in this approach to model the failure of each of the constituents separately using the extracted stresses in the individual constituents. Failure envelope plotted for a unidirectional fiber reinforced composite material using the proposed model clearly shows that the initiation of damage is different in different constituents of the composite material. This is more realistic compared to the popularly used macroscopic criteria such as Tsai–Wu criterion. Propagation of failure in fiber reinforced composite is captured using a simple progressive damage model. It is also found that the hexagonal RVE has more predictive capabilities than the square RVE since the average distance between the fiber may play a major role in the strength prediction of composites. [ABSTRACT FROM AUTHOR]

This paper introduces a multiscale modeling approach to simulate the macromechanical properties of cementitious composites with polyurethane reinforcement. The polyurethane inclusions to hydrated cement paste matrix are represented by continuum 3D elements. Simulations of the real phenomenon that occur at the micro level of the composite have been done by mean-field homogenization technique and finite element analysis. The multiscale model presented in this work enables us to evaluate the stress–strain behavior and other engineering properties. Different configurations of polyurethane cement composite have been studied including variation of loading conditions, weight fraction of polyurethane and the aspect ratios of the polyurethane inclusion. The effect of shape and alignment of polyurethane on the stiffness of the composite has also been evaluated. Strength and stiffness values obtained from the proposed approach are in good agreement with that obtained from open literature. [ABSTRACT FROM AUTHOR]

Highlights: [•] Fiber waviness significantly affects E 11; other properties are moderately affected. [•] E 22 initially decreases and then increases as a function of fiber waviness. [•] Material property mismatch has a strong influence on the effective properties. [•] Fiber spatial distribution has a weak influence on the effective properties. [•] Fiber/matrix interphase has a strong influence on the effective properties. [Copyright &y& Elsevier]

Highlights: [•] Effect of the interphase on the quasi-solid state forming is modelled. [•] Effects of the interphase on morphology evolution are considered. [•] The interphase has a significant effect on the forming stresses. [•] Strain-stiffening at large strains is affected by the interphase. [•] Interphase must be considered in the prediction of nanocomposite forming. [ABSTRACT FROM AUTHOR]

Highlights: [•] Predicting effective properties using different representative volume elements. [•] Comparing different multi-scale models to predict effective properties. [•] Comprehensive methodology for micro-structures characterization. [•] Potential applications to study and predict effective properties in alloys. [ABSTRACT FROM AUTHOR]

Highlights: [•] Stochastic perturbation method and RVE strain energy homogenization approach. [•] 3D model of the composite: stronger matrix and rubber spherical particles. [•] First four probabilistic moments of effective elasticity tensor obtained via FEA. [ABSTRACT FROM AUTHOR]

Highlights: [•] CNT/epoxy composites are modelled via 2D and 3D RVE approaches. [•] The accuracy of the approaches in capturing the finite strain response is studied. [•] Effects of CNT morphology and high strain rates are considered. [•] The response cannot be accurately captured by 2D RVEs. [•] Using CNTs raises the yield peak and changes post-yield softening into hardening. [ABSTRACT FROM AUTHOR]

Highlights: [•] Combined EBSD and EPMA were applied to quantify bainite in commercial DP steel. [•] 2D RVEs were created based on KAM and EPMA carbon distribution map. [•] Flow curve of bainite was modelled using dislocation density based approach. [•] Influence of small bainite fraction on macroscopic behaviour was quantified. [•] Taking into account bainite in RVE approach yields improved flow curve prediction. [Copyright &y& Elsevier]

Convolutional neural networks (CNNs) are implemented to expedite the determination of representative volume elements for microstructurally small cracks (RVE MSC). By definition, RVE MSC is the minimum volume of microstructure required around a microstructurally small crack (MSC) to achieve convergence of crack-front parameters with respect to volume size. In a previous study, RVE MSC was determined using a computationally expensive finite-element (FE) framework involving the simulation of many microstructural instantiations. With the aim of increasing the computational efficiency of determining RVE MSC , CNNs are leveraged herein to reduce the number of FE simulations required to determine RVE MSC. Using data from the previous FE-based RVE MSC study, CNNs are trained to predict RVE MSC, ip values, which quantify crack-front parameter convergence with respect to volume size for microstructural instantiation i evaluated at individual crack-front points p , given local microstructural and geometrical information. Predicted RVE MSC, ip values are subsequently used to estimate RVE MSC values. Studies are carried out to determine the optimal amount of training data, assess CNN-based RVE MSC estimation performance, and demonstrate the use of CNNs as microstructural-instantiation screening tools by enabling downselection of microstructures that are considered critical in terms of volume requirements. Individual and ensemble CNN predictions are compared. While CNNs are not found to be accurate enough to replace all FE simulations, CNNs are found to be effective as a rapid screening tool for improving the efficiency of the FE-based RVE MSC determination framework and for expediting future RVE MSC studies. [Display omitted] • CNNs are trained to support predictions of RVE MSC given microstructure as input. • CNNs are inadequate for completely replacing FE simulations in determining RVE MSC. • However, CNNs can serve as screening tools to expedite the determination of RVE MSC. • Averaging multiple CNN predictions in an ensemble approach improves predictions. • Performance of CNN varies depending on RVE MSC parameter being predicted. [ABSTRACT FROM AUTHOR]

Highlights: [•] The proof of the Hill–Mandel-condition is given more detailed in the Appendix. [•] Cubical RVE are considered also. [•] Many minor changes have been incorporated. [ABSTRACT FROM AUTHOR]

Highlights: [•] Study of thermal conductivity in two-phase, 2D checkerboards at 50% volume fraction. [•] Determine a scaling function that very closely fits many material combinations. [•] A Material scaling diagram is constructed to estimate the RVE for a given contrast. [ABSTRACT FROM AUTHOR]

Highlights: [•] Study of the pseudo elastic response of SMA foams as a function of the porosity. [•] Determination of a three dimensional Representative Volume Element. [•] Determination of scaling relations as a function of porosity. [•] Comparison with experimental results from literature. [ABSTRACT FROM AUTHOR]

Abstract: The Young’s moduli of Al356/SiC (particle) Metal Matrix Composite (MMC) with different particle aspect ratios were estimated by Finite Elements Analysis (FEA), using a simple 3-D model. The results were compared to a 2-D axisymmetric FEA model, to the experimental results, and the predicted values obtained from the Rule of Mixtures and the Halpin–Tsai (HT) model. FEA software ANSYS 11.0 was used. The 3-D model consisted on taking the one-eight part of a unit cell, with particles having cylindrical shape, a volume fraction of 0.12 and aspect ratio from 0.2 to 1.8. The estimated Young’s moduli presented significant differences, mainly at aspect ratios higher than 1.0, resulting the 3-D model estimations closer to the experimental values. The results from the selected 3-D model were found to have higher accuracy when compared to traditional axisymmetric 2-D model. Besides, the efficiency of this high symmetry 3-D model showed that a more complex 3-D model is not necessary. [Copyright &y& Elsevier]

Abstract: The statistical volume element (SVE) technique is commonly used for the estimation of the effective properties of a micro-structured material. Mostly, cubical SVEs with periodic boundary conditions are employed, which result in a better convergence, compared to the uniform boundary conditions. In this work, the possibility of using spherical SVEs is discussed, since their use promises a reduction of the influence of the boundary, and thus a more efficient estimation of the effective material properties. We discuss the applicability of boundary conditions which are similar to the periodic boundary conditions to spherical SVEs. Then we assess the convergence (subject 1) of spherical and cubical SVEs to the effective material behavior for the uniform and periodic boundary conditions, focusing on the elastic and plastic properties of a macroscopically isotropic matrix-inclusion material. It is shown that the spherical SVEs perform indeed better than the cubical SVEs. Also, unlike the spherical SVEs, the cubical SVEs with periodic boundary conditions induce a spurious anisotropy (subject 2), which is quantified for the effective elastic properties. Finally, we examine the effect of the periodicity frame on the localization behavior (subject 3) of cubical SVE, since cubical SVE with periodic boundary conditions are commonly used to estimate macroscale material failure. It is demonstrated that the orientation of the periodicity frame affects the overall SVE response significantly. The latter is not observed for spherical SVE. [Copyright &y& Elsevier]

Abstract: Prediction of strength reduction for intercalated epoxy–clay nanocomposites is addressed in this work. For this purpose a 2D multiscale finite element (FE) methodology is developed, which accounts for the hierarchical morphology of the nanocomposite and possible failure mechanisms detected experimentally such as gallery failure and interfacial debonding. At first the intercalated morphology is reconstructed using a random dispersion of clay tactoids within the epoxy matrix, where the gallery is modelled using the cohesive zone concept. Effects of different clay volume fractions, gallery fracture energies, tactoid aspect ratios and tactoid orientations on gallery failure and macroscopic nanocomposite behaviour are investigated systematically. Then, the mutual effect of gallery failure and external interfacial debonding is considered using the cohesive zone concept for galleries and matrix–tactoid interfaces. Effects of different combinations of gallery and interfacial fracture energies on the failure and macroscopic behaviour are investigated. Results indicate that gallery failure is a cause of nanocomposite strength reduction and, depending on the morphology, interfacial debonding is as important as gallery failure in affecting the nanocomposite strength. [Copyright &y& Elsevier]

Abstract: As a result of their microstructures being made up by constituents with strong distinctions in mechanical properties, multiphase steels exhibit high energy absorption as well as an excellent combination of strength and ductility. Furthermore, the microstructural composition influences the failure behaviour of such kind of steels because of the occurrence of different fracture mechanisms in parallel. When the failure behaviour of dual phase (DP) steels is investigated, several types of failures are typically observed, such as the ductile failure of ferrite, the brittle failure of martensite and the interface debonding between phases. Hence, a reliable microstructure-based simulation approach must be developed that describes material deformation and failure under any given loading condition. In this work, two different damage mechanics methods were employed to study the interaction between failure modes in DP steels by means of a representative volume element (RVE). In order to consider the characteristics of a real microstructure, all involved phases were modelled with a precise volume fraction. Firstly, the extended finite element method (XFEM) was used to study the damage onset and progression in martensitic regions without prescribing the crack path. Secondly, a damage curve was derived and employed for the ductile ferritic phase. By combining these two damage models in the RVE model on microscopic scale, development of different failures modes in DP steels could be investigated. [Copyright &y& Elsevier]

Abstract: Dual-phase steels (DP) are well suited for automotive application due to their attractive mechanical properties, such as high strength and good formability. These properties are achieved by the dispersion of hard martensite particles in the soft and ductile ferrite matrix. The current work aims to predict the mechanical properties of dual-phase steels. A microstructure based approach by means of representative volume element (RVE) was employed for this purpose. Available and novel routines were used to create the 2D RVEs from the real microstructures. Periodic and homogeneous boundary conditions were imposed. Dislocation based model was implemented to predict the flow behaviour of the single phases. Computational first order homogenization strategy was employed to obtain the true stress–true strain curves from the RVE calculations. The implementation of the periodic boundary condition results in a better agreement with the converged effective value compared to the displacement boundary condition. Equiaxed microstructures show higher strength and work hardening compared to that of the banded microstructures. In the same fraction of martensite, the yield stress of DP steels decreases by increasing the aspect ratio of martensite bands. [Copyright &y& Elsevier]

Abstract: Multiphase steels have become a favoured material for car bodies due to their high strength and good formability. Concerning the modelling of mechanical properties and failure behaviour of multiphase steels, representative volume elements (RVE) have been proved to be an applicable approach for describing heterogeneous microstructures. However, many multiphase steels exhibit inhomogeneous microstructures which result from segregation processes during continuous casting. These segregations lead to a formation of martensite bands in the microstructure causing undesirable inhomogeneities of material properties. The aim of this work is to develop an FE evaluation procedure for predicting a microcrack formation provoked by banded martensitic structures. A micromechanism based damage curve was applied as a failure criterion for the softer ferritic matrix in the microstructure in order to simulate the propagation of cracks resulting from the failure of martensitic bands. The parameters of the damage curve were determined by in situ miniature bending tests and tensile tests with notched samples. The presented approach provides the basis for an assessment criterion of the component safety risk of multiphase steels with inhomogeneous microstructures. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a new straightforward methodology for stress analysis and prediction of the steady-state creep deformation of discontinuously reinforced metal matrix composites was proposed using finite element analysis. A three dimensional representative volume element of a SiC whisker reinforced Al6061 composite was modeled and analyzed to study its creep behaviors. In the model, periodic 30 unidirectional whiskers were generated using a modified random sequential algorithm to produce a random morphology. The numerical predictions were compared and contrasted with those from commonly used 2D and 3D unit cell models. Through the numerical analyses, it was found that the presence of localized stress concentrations seemed to be one of the main factors affecting the creep performance of composites. The steady-state creep rate predicted by present model showed satisfactory agreement with the results of experimental literatures. [Copyright &y& Elsevier]

Abstract: For car body design, a reliable prediction of material formability is required. Stretch-flangeability has become an especially important formability parameter in addition to tensile properties, particularly for complicated auto body parts or parts under heavy deformation conditions. The hole expansion ratio of multiphase steel is strongly influenced by microstructures and their distribution. Therefore, failure behaviour by the stretch-flangeability analysis of this steel has to be described as a function of microstructure. In this work, hole expansion tests were carried out for steel sheets with different microstructures and their local fracture surfaces were afterwards investigated. In the failure modelling, an FE approach is presented by means of Representative Volume Elements (RVE) in combination with continuum damage mechanics in order to consider the influence of multiphase microstructure on mechanical properties and complex fracture mechanisms. At the failure moment, the local strain distributions between different phases were studied, and correlated with macroscopic deformability results. The influence of material properties of individual phases and the local states of stress on formability as well as failure behaviour could be examined. In conclusion, a microstructure based stretch-formability analysis for the characterisation of multiphase sheet steels is aimed. [Copyright &y& Elsevier]

Smart composite materials have been an active field of research in the last few decades. Magnetorheological elastomers (MREs) are examples of such smart composites and they show a coupling between magnetism and elasticity. MREs are heterogeneous materials and they consist of magnetic particles and a silicone-based elastomer. To describe and predict the behaviour of the macroscopic continuum accurately, microstructural information needs to be taken into account in the analysis of heterogeneous materials. Therefore, a combined approach called multi-scale analysis is used to consider various scales of observation simultaneously. The concept of Representative Volume Element (RVE) is typically employed by multi-scale approaches to describe the micro scale, and thus the size of RVE becomes a model parameter in such techniques. This has motivated the determination of the RVE size and the derivation of magnetoelastic constitutive relations in terms of the RVE sizes in our paper. The finite element method and a statistical analysis based on the coefficient of variation have been used to determine the RVE size of MREs. The results show that it is possible to determine a lower bound of the RVE size for an MRE. Furthermore, a parametric study has been conducted to examine the sensitivity of the RVE size on the different material properties of the constituents. It was found that the RVE size is primarily set by the contrast of the different material properties, i.e. the stiffness, permeability and magnetoelastic coupling coefficients. • A statistical analysis followed to determine lower bound of the RVE sizes for an MRE. • Contrast in material properties of the constituents can affect the minimum RVE sizes. • For practical purposes one may assume same RVE size for all RVEs. • A piezomagnetic continuum model developed with gradients in terms of RVE sizes. [ABSTRACT FROM AUTHOR]

Abstract: Computational modeling of glass (silica) fibers having micro-scale outer dimensions and nano-scale internal structures was performed to assess its mechanical behavior. Self-assembly technique was used to synthesize the individual fibers of approximately 5μm in length with a hexagonal cross-section (2μm between two opposite sides) and honeycomb-like internal nano-structures. These fibers have several potential applications including synthesis of multifunctional composite materials. Numerical modeling of the individual fibers was performed using continuum mechanics based approach wherein linear elastic elements were utilized within a commercial finite element (FE) analysis package. A representative volume element approach was adopted for computational efficiency. Appropriate loads and boundary conditions were used to derive stress–strain relationship (stiffness matrix) which has six independent constants for the individual fiber. Force–displacement relationships under simulated nanoindentation were obtained for the actual fiber (with six independent constants) and under transversely isotropic approximation. The contact problem was solved for the transversely isotropic case, which indicates a much stiffer fiber compared to the FE predictions. This difference is likely due to the geometric nonlinearity considered in FE analysis yielding accurate results for large displacements. [Copyright &y& Elsevier]

Abstract: In this paper, the effective stress–strain behaviours of four typical low-density 2D structures are comparatively studied by means of finite element analysis using the representative volume element approach. The relation between the relative density and cell wall thickness-to-length ratio for the structures are determined based on geometry analysis and periodic boundary conditions are employed in models of comparable densities. The dependence of the Young’s moduli and the collapse strength on cell parameters have been established and compared with analytical solutions. The effect of defects in the form of broken cell walls on deformational behaviour is studied systematically and correlated to the connectivity of the foam based on percolation analysis. [Copyright &y& Elsevier]

Abstract: A micromechanics-based model is developed to predict the effective thermo-mechanical properties of energetic materials, which are composite materials made from agglomeration of particles of a range of sizes. A random packing algorithm is implemented to construct a representative volume element for the heterogeneous material based on the experimentally determined particle diameter distribution. The effective mechanical properties of the material are then evaluated through finite element modeling, while its thermal properties are determined through a finite volume approach. The model is first carefully validated against results from the literature and is then used to estimate the thermo-mechanical properties of particular energetic materials. Good agreement is found between experimental results and predictions. The stress-bridging phenomenon in the particulate materials is captured by the model. Thermodynamic averaging is shown to be a poor representation for the estimation of thermo-mechanical properties of these heterogeneous materials. [Copyright &y& Elsevier]

Abstract: The aim of presenting this paper is to evaluate the effective material properties of randomly distributed short fibre (RDSF) and transversely randomly distributed short fibre (TRDSF) composites with change in volume fraction, and aspect ratio of fibres. A numerical homogenization technique based on the finite element method (FEM) is used to evaluate the effective material properties with periodic boundary conditions. A modified random sequential adsorption algorithm (RSA) is applied to generate the three-dimensional unite cell models of randomly distributed short cylindrical fibre composites. The developed numerical homogenization technique is used to calculate effective material properties in order to systematically evaluate different material systems. The numerical results are also compared and verified with different analytical methods. [Copyright &y& Elsevier]

Abstract: A 3D model for elastic aggregate composites such as bituminous materials is presented. In this model, rigid angular particles are embedded into an elastic matrix; inter-particle contacts are modeled by a linear interface constitutive equation; Dirichlet tessellation and its dual Delaunay network are used to generate the particles and to connect them. The predictions of the model are compared with finite element estimates on periodic unit cells consisting of polyhedral particles. Simulations on several realizations of random materials are used for the determination of the minimum representative volume element (RVE) size. [Copyright &y& Elsevier]

The microstructure of low alloyed ferritic–martensitic dual-phase steels as used for deep drawn parts in automotive applications consists of coarse grained hard martensitic inclusions embedded in a soft ferritic matrix. In tensile tests commercially produced dual-phase steels show an unexpected dependence of their initial yield behaviour on the content of martensite. The impact of the thermomechanical history on the mechanical properties of the material is demonstrated by means of a fully three-dimensional finite element analysis. A work-hardened ferritic skeleton formed during rapid cooling connects the martensitic inclusions and governs the initial stages of plastic deformation. The model correctly predicts both the experimentally observed dependence of the proof stress on the amount of martensite and a lower initial slope of the stress–strain diagram. [Copyright &y& Elsevier]

[Display omitted] • Generation of random fiber networks with tailor-made morphological descriptors. • Relating the microstructure of fibrous materials to macroscopic mechanical properties. • Four properties govern the (linear elastic) mechanical properties of fiber networks. Materials whose microstructure is formed by random fiber networks play an important role both in biology and engineering. So far, it still remains unclear which geometric properties of the fiber network determine the macroscopic mechanical properties of such materials. This paper presents a computational study based on a large number of representative volume elements of random fiber networks. Our study reveals that the linear mechanical properties of fiber networks (i.e., Young's modulus and Poisson's ratio) are largely determined by only four scalar key descriptors. These are the number of fibers per volume, the mean node valency, the mean fiber length, and the mean direction cosine between fibers adjacent to the same node. Number of fibers per volume and node valency were found to be responsible for around 80% of the variance of the mechanical properties, making them the two by far dominant microstructural descriptors. In the part of the configuration space covered by our study, we observed a linear or quadratic relationship between the above four scalar microstructural descriptors and the Young's modulus. For the number of fibers per unit volume we propose a theoretical explanation for this simple relation. [ABSTRACT FROM AUTHOR]

[Display omitted] We have investigated the reinforcement mechanics of capsule-based self-healing composites (CSC) comprising poly(urea–formaldehyde) (PUF) capsules embedded in epoxy matrix using a micro-scale representative volume element (RVE) model. Finite element analysis was used to model four stages of loading, corresponding to elastic loading and fracture of pristine CSC (containing epoxy-filled capsules) and, following healing, of repaired CSCs (containing capsules depleted of healants), respectively. Predictions of the elastic modulus (E) during elastic loading and the local damage pattern within the CSC during fracture were obtained. The E was most sensitive to capsule volume fraction (V p) but least sensitive to capsule distribution pattern. The E also depended on the state of the capsule. The E increased with increasing V p in epoxy-filled capsule composite, suggesting that epoxy-filled capsules could provide reinforcement to the epoxy-based composite. However, E decreased with increasing V p in empty capsule composites, indicating that empty capsules could not be depended upon for reinforcing the composite. When fracture began, capsules at close proximity, especially in agglomerates, could interact to promote further damage regardless of whether they were filled or empty; the damage pattern observed could be a prelude to mode 1 type fracture. These predictions led to wider implications concerning how agglomerates in the CSC could influence the mechanics of elastic loading and fracture of the composite. [ABSTRACT FROM AUTHOR]

• Implementation and exploitation of a novel anisotropic Voronoi algorithm. • Generation of microstructures with spatially varying grain growth directions. • An ellipsoidal growth field closely mimics underlying solidification proces. • Extraction of grains in a grain-conforming and non-grain-conforming manner. • Two demonstration cases show a pronounced correspondence to input data. In this paper, a novel anisotropic Voronoi algorithm is presented, along with its implementation and two application cases. In contrast to standard Voronoi tessellations, the proposed algorithm takes into account preferred growth directions, aspect ratios and areas of individual grains. Therefore, an elliptical growth field, which is defined on a per grain basis, is adopted which specifies the time a single grain seed point needs to grow to a specific point in the domain of interest. Grains can be extracted in a grain-conforming or non-grain-conforming manner. The latter case is applicable to simulations in which a predetermined mesh is used, e.g. voxel-mesh based simulations. The extraction can then be done in a straightforward manner. For the former case, a more elaborate extraction algorithm is presented. Finally, the characteristics of the resulting microstructural geometries of two application cases (wire + arc additively manufactured and cast metal microstructure) are studied. A pronounced correspondence with the experimental grain morphology is obtained. This algorithm is highly versatile for generating polycrystalline (metal) microstructures, especially since it closely mimics the underlying solidification process. However, it is more generally applicable to generate an anisotropic tessellation with spatially varying preferential growth directions. [ABSTRACT FROM AUTHOR]

• Sheet molding compound composites exhibit an inherent three-scale structure. • Exact closure approximation allows for accurate microstructure reconstruction. • Quasi-random orientation sampling improves accuracy of generated microstructures. • Fast and robust generation of unit cells based on random sequential addition. • Sensitivity analyses of effective composite stiffness w.r.t. material parameters. Sheet molding compound (SMC) composites combine high lightweight potential with excellent formability and are frequently used in industrial applications. To reduce safety factors in dimensioning SMC parts, the influence of processing parameters and stochastic variation of microstructural and physical properties needs to be quantified accurately. Taking into account the inherent three-scale structure of SMC, we improve the microstructure generator of Chen et al. [Compos. Struct. 188, pp. 25–38, 2018] in various respects. Firstly, we consistently rely upon state-of-the-art closure approximations for the fourth order fiber orientation tensor. More precisely, we show that for a planar fiber orientation state, there is an explicit formula for the fast exact closure approximation of Montgomery-Smith et al. [J. Fluid Mech. 680, pp. 321–335, 2011]. Secondly, we exploit the use of quasi-random numbers in sampling the fiber orientation distribution, leading to dramatic improvements in accuracy compared to pseudo-random Monte Carlo sampling. Last but not least, we rely upon fast Fourier transform based methods for rapid computational homogenization. With these methodological improvements at hand, we thoroughly investigate the influence of the mechanical and microstructural parameters on the effective elastic properties of SMC composites, and compare the results to direct numerical simulations on large scale digital volume images and mean-field estimates. [ABSTRACT FROM AUTHOR]