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This work is concerned with synthetic microstructure models of polycrystalline materials. Once a representation of the microstructure is generated, the individual grains need to be furnished with suitable crystal orientations, matching a specific crystal orientation distribution. We introduce a novel method for this task, which permits to prescribe the orientations based on tensorial Fourier coefficients. This compact representation gives rise to the texture coefficient optimization for prescribing orientations method, enabling the determination of representative orientations for digital polycrystalline microstructures. We compare the proposed method to established and dedicated algorithms in terms of the linear elastic as well as the non-linear plastic behavior of a polycrystalline material. [ABSTRACT FROM AUTHOR]

As an anode material for lithium-ion batteries, amorphous silicon offers a significantly higher energy density than the graphite anodes currently used. Alloying reactions of lithium and silicon, however, induce large deformation and lead to volume changes up to 300%. We formulate a thermodynamically consistent continuum model for the chemo-elasto-plastic diffusion-deformation behavior of amorphous silicon and it’s alloy with lithium based on finite deformations. In this paper, two plasticity theories, i.e. a rate-independent theory with linear isotropic hardening and a rate-dependent one, are formulated to allow the evolution of plastic deformations and reduce occurring stresses. Using modern numerical techniques, such as higher order finite element methods as well as efficient space and time adaptive solution algorithms, the diffusion-deformation behavior resulting from both theories is compared. In order to further increase the computational efficiency, an automatic differentiation scheme is used, allowing for a significant speed up in assembling time as compared to an algorithmic linearization for the global finite element Newton scheme. Both plastic approaches lead to a more heterogeneous concentration distribution and to a change to tensile tangential Cauchy stresses at the particle surface at the end of one charging cycle. Different parameter studies show how an amplification of the plastic deformation is affected. Interestingly, an elliptical particle shows only plastic deformation at the smaller half axis. With the demonstrated efficiency of the applied methods, results after five charging cycles are also discussed and can provide indications for the performance of lithium-ion batteries in long term use. [ABSTRACT FROM AUTHOR]

In this article, we combine a Fast Fourier Transform based computational approach and a supervised machine learning strategy to discover models for the anisotropic effective viscosity of shear-thinning fiber suspensions. Using the Fast Fourier Transform based computational approach, we study the effects of the fiber orientation state and the imposed macroscopic shear rate tensor on the effective viscosity for a broad range of shear rates of engineering process interest. We visualize the effective viscosity in three dimensions and find that the anisotropy of the effective viscosity and its shear rate dependence vary strongly with the fiber orientation state. Combining the results of this work with insights from literature, we formulate four requirements a model of the effective viscosity should satisfy for shear-thinning fiber suspensions with a Cross-type matrix fluid. Furthermore, we introduce four model candidates with differing numbers of parameters and different theoretical motivations, and use supervised machine learning techniques for non-convex optimization to identify parameter sets for the model candidates. By doing so, we leverage the flexibility of automatic differentiation and the robustness of gradient based, supervised machine learning. Finally, we identify the most suitable model by comparing the prediction accuracy of the model candidates on the fiber orientation triangle, and find that multiple models predict the anisotropic shear-thinning behavior to engineering accuracy over a broad range of shear rates. [ABSTRACT FROM AUTHOR]

The purpose of the current work is the experimental investigation and modeling of Portevin–Le Châtelier (PLC) band development in AlMg3 aluminum alloys, in particular in AA5754. The experimental investigation employs both mechanical and thermal (infrared) radiation measurement methods. The former involve force, displacement, and strain measurements using strain gauges. The latter employ a high-speed infrared camera to capture PLC band trajectories and evolution. In addition, the critical strain for band nucleation, as well as band characteristics such as velocity, type, and strain state, have been determined. To model the experimental results, a modification of the Estrin–McCormick model (e.g., Estrin and McCormick, 1991) due to Böhlke et al. (2009) is employed. In this modification, the saturation value of the Cottrell–Bilby–Louat (CBL) contribution to the effective flow stress due to dynamic strain aging is not constant, but rather is assumed to be linearly dependent on the accumulated effective inelastic strain. This model is incorporated into a finite-element model for the experimental specimens constructed with the help of convergence and mesh-sensitivity studies. Using selected mechanical test data, model parameters for AA5754 are then identified. With the identified model, a number of comparisons between experimental results and model predictions are carried out for validation purposes. Attention is focused here in particular on aspects of PLC band nucleation and propagation. Nucleation behavior is studied in particular with respect to stress gradients. It was found that the stress gradient is not the main trigger for PLC band nucleation, and is less relevant with increasing strain. The comparison of experimental and simulation results for spatio-temporal strain patterns and stress distribution shows that strong stress drops are correlated with the start of longitudinal propagation of a fully evolved PLC band. Small oscillations between large stress drops during propagation of type B bands indicate the consecutive nucleation, propagation and disappearing of these bands. The transition region from normal to inverse behavior (decreasing strain rate) denotes the transition from type A to type B. A transition with increasing strain is observed both experimentally and in the simulation. For lower strain rates and higher strains, type C bands are observed as well. Generally speaking, the band velocity decreases with decreasing strain rate and increasing strain. On the other hand, the band strain is found to increase with increasing strain, and only slightly with increasing strain rate. Simulation and experimental results, generally, show very good agreement. [ABSTRACT FROM AUTHOR]

Understanding the effective viscosity of fiber-filled polymer melts is essential for predicting the local fiber orientation of injection molded short-fiber reinforced components. To circumvent the intrinsic difficulties of experimentally determining the strongly anisotropic viscosity of such particle-reinforced melts, an FFT-based computational homogenization method for computing the effective quasi-static viscosity of a particle-suspended Newton fluid is introduced, based on a dual formulation. The dependence of the effective viscosity on microstructural parameters, like fiber volume fraction, fiber aspect ratio and fiber orientation are investigated by computational experiments on representative volume elements, and the results are compared to an analytical model for the effective viscosity. Based on the computational findings, a closed-form approximation for the effective viscosity is provided. [ABSTRACT FROM AUTHOR]

The failure of engineering slopes may cause great property loss and casualties, against which the slope deformation monitoring and instrumentation are needed. To investigate the relationship between safety factors and the displacements/strains of slopes, ten synthetic numerical models with different slope heights, slope angles, ranges of loading and soil parameters were designed and tested via finite difference code FLAC. By applying incremental load on the top of slope, the distribution of strain field and safety factor of slope were analyzed. The results indicated that there are three different modes of strain development inside the slope under uniform strip loading. During failure progress, the factors of safety and the corresponding total strain amounts at different loading stages have been analyzed. Based on the results, a modified empirical formula relating safety factor to the average maximum horizontal strain was proposed, which can be used as a theoretical guidance for preliminary slope stability check based on the instrumented strains. [ABSTRACT FROM AUTHOR]

We study fast and memory-efficient FFT-based implicit solution methods for small-strain phase-field crack problems for microstructured brittle materials. A fully implicit first order formulation of the problem coupling elasticity and damage permits using comparatively few, but large, time steps compared to semi-explicit schemes. We investigate memory-efficient FFT-based solution techniques, and identify the heavy ball scheme as particularly powerful. We discuss the memory-efficient implementation and present demonstrative numerical examples. • Memory-efficient FFT-based solution methods for implicit phase field damage. • A novel fast gradient method, staggered and memory-efficient solver. • Demonstration of advantages compared to semi-explicit approaches. • Application to fiber reinforced composite microstructures of large scale. [ABSTRACT FROM AUTHOR]

Computational homogenization schemes based on the fast Fourier transform (FFT) enable studying the effective micromechanical behavior of polycrystalline microstructures with complex morphology. In the conventional strain-based setting, evaluating the single crystal elasto-viscoplastic constitutive law involves solving a non-linear system of equations which dominates overall runtime. Evaluating the inverse material law is much less costly in the small-strain context, because the flow rule is an explicit function of the stress. We revisit the primal and dual formulation of the unit cell problem of computational homogenization and use state of the art FFT-based algorithms for its solution. Performance and convergence behavior of the different solvers are investigated for a polycrystal and a fibrous microstructure of a directionally solidified eutectic. • We exploit the cheap evaluation of the inverse material law for crystal plasticity. • The implementation of modern FFT-based solvers in the dual setting is discussed. • The computation time is reduced up to a factor of 20 in the dual setting. • The dual Barzilai–Borwein scheme is identified as fast and memory efficient. • We investigate a polycrystal and a directionally-solidified fibrous microstructure. [ABSTRACT FROM AUTHOR]

In this work, we investigate the fiber orientation dependent viscosity of fiber suspensions using a computational homogenization method. To improve computational prediction capabilities for the viscosity of fiber suspensions, we extend an existing, Fast Fourier Transform based computational approach for fiber suspensions with linear viscous, i.e., Newtonian, matrix behavior to nonlinear viscous matrix behavior. Specifically, a Cross-type shear-thinning rheology is assumed for the matrix fluid. We employ composite voxels to lower resolution requirements and find through resolution studies that the resolution error decreases for certain shear rates. Furthermore, we conduct a volume element study and find that the representative volume element sizes for engineering considerations in a specific Newtonian case and the investigated Cross-type case are highly similar. For shear rates of engineering process interest we visualize the effective suspension viscosity in three dimensions and study the effects of the fiber volume fraction and the imposed macroscopic shear rate tensor on the suspension viscosity. We find that the elongational viscosity and the degree of anisotropy of the suspension viscosity vary stronger with the shear rate for higher fiber volume fractions. In a comparison with an analytical mean-field model for the suspension viscosity, the deviations between the computational and analytical results turn out to be substantial. • Complete 3D visualization of the shear rate dependent suspension viscosity • Degree of anisotropy of the suspension viscosity varies with the shear rate • Shear rate influence on the suspension viscosity grows with the fiber volume fraction [ABSTRACT FROM AUTHOR]

We present an algorithm for generating short fiber-reinforced microstructures with almost planar fiber orientation. The orientation corrected shaking (OCS) method achieves a high accuracy regarding the volume fraction, fiber length distribution and fiber orientation state. Additionally, the algorithm is capable of generating microstructures for industrial materials, e.g., for a PA66GF35 material with a volume fraction of 19.3% and an aspect ratio of 33. For typical manufacturing processes, short fiber-reinforced composites show a mainly planar fiber arrangement. Therefore, we extend the two-step shaking algorithm of Li et al. [J. Ind. Text. 51(1), pp. 506–530, 2022] for a user-selected rectangular size of the unit cell and periodic boundary conditions. Additionally, the hidden closure structure of the algorithm is uncovered and a precise realization of the fiber orientation state achieved. We examine the representative volume element size for the OCS method, observing representative errors below 2% even for unit cells with edge lengths smaller than the mean fiber length. Additionally, the influence of different closure approximations on the stiffness is investigated. When applied to an industrial PA66GF35 material with sandwich structure, the OCS method demonstrates differences below 2% and 9% for the computed directional Young's moduli E 1 and E 2 compared to experimental data. [ABSTRACT FROM AUTHOR]

This paper presents a micromechanical high cycle fatigue damage model for short fiber reinforced composite materials. Because the damage processes within such materials are influenced strongly by their microstructure, we use a mean field homogenization framework to compute the macroscopic behavior of the composite as well as the microscopic stresses and strains in the constituent phases. This allows us to account for damage phenomena related to both the fiber phase as well as in the matrix material. Fiber and fiber-interface damage is modeled using a Tsai–Wu and Weibull-based approach and the progressive damage due to cyclic loading is described by a progressive matrix damage model. The latter includes a novel coupling term in which the matrix damage progression is linked to the damage state of the reinforcing fibers. A cycle-based numerical formulation is used to overcome the computational limits of such load cases in the time domain. While the approaches are in principle applicable to different types of fiber–matrix composite, a short glass fiber reinforced polyamide 6.6 is used as an example material, for which microstructural analyses as well as tensile and fatigue tests are reported. The model's capabilities with regard to complex fiber orientations and different fiber fractions are studied using different grades of this material class. Furthermore, the model is analyzed via benchmarks of the numerical schemes and by parameter sensitivity studies. The results show that the approach is capable of modeling the complex and microstructure-dependent fatigue damage and fatigue limits for the different material grades with limitations only becoming visible at very high fiber fractions. [ABSTRACT FROM AUTHOR]

Abstract The hot stamping process of sheet metals into a w-shape profile is considered in experiments and numerical simulation using the FEM tool ABAQUS. The influence of the processing parameters of the hot stamping process on the final shape and the residual stress state are investigated. Tensile tests of thermomechanically treated specimens serve as a starting point for the modeling of the thermomechanical behavior of the steel grade 22MnB5. Based on the thermo-micromechanical (TMM) model for small deformations suggested by Neumann and Böhlke (2016) , the updated Lagrangian formulation is used to render the finite deformation process. The model captures in a two-scale framework the temperature dependent elasto-plastic effect of the different phases, the phase transformation effect, and the phase transformation accompanying transformation strain occurring during the quenching of the austenitized sheet metal. Additionally, a model for the transformation induced plasticity (TRIP) effect in the context of the two-scale approach is suggested. The homogenization and localization of the thermomechanical properties is performed with a HashinöShtrikman (HS) type homogenization scheme. In this work, a reduced formulation for isotropic elastic behavior of the different phases is found reducing the amount of numerical costs. Furthermore, a self-consistent scheme based on the HS type method is introduced. Finally, the suggested TMM model is validated by considering the time-temperature-transformation- (TTT) and continuous-cooling-time-curves (CCT), dilatation tests under external load, and the hot stamping of w-shape profiles. The TMM model is compared to both experimental results and a phenomenological reference model usually used for the simulation of hot stamping processes. It is found that the suggested TMM model fits the final shape and the residual stress state of hot stamped parts better than the phenomenological reference model. [ABSTRACT FROM AUTHOR]

This paper presents an anisotropic, micromechanical damage model for sheet molding compound (SMC) composites, that is a thermoset matrix reinforced with long ( ≈ 25 mm ) glass fibers. The model captures the dominant damage mechanisms – matrix damage and fiber-matrix interface debonding – in a Mori-Tanaka homogenization framework. Matrix damage is modeled as a phase-averaged isotropic stiffness degradation. The interface damage is governed by an equivalent interface stress on the lateral fiber surface. Hereby, the inhomogeneous stress distribution in the fiber-matrix interface is taken into account in the definition of the equivalent stress. A Weibull distribution for the interface strength is assumed. The model can account for an anisotropic distribution and evolution of load-carrying fibers with intact interfaces. The model is validated by means of tensile tests on unsaturated polyester polyurethane hybrid and epoxy resin systems with different glass fiber contents (23-50vol.%). The model yields satisfyingly accurate predictions under uniaxial and biaxial stress states. [ABSTRACT FROM AUTHOR]

Analytic shear-lag models enjoy great popularity for assessing and interpreting microstructure dependent stationary creep in fibrous metal composites, especially the formulation of Kelly-Street (Kelly and Street, 1972 [2]). Beyond the original model's scope, i.e. large aspect ratios of inclusions, predictions are highly inaccurate, which was recently pointed out by Wicht et al. (Wicht et al., 2022 [10]), by comparing model predictions to micromechanical Fast-Fourier-Transform-based simulations. In this study we therefore modify basic Kelly-Street model assumptions, concerning effective creep rate, stress transfer and inclusion spacing to arrive at a modified model with an extended scope. To validate the modified model, we benchmark the model against Fast-Fourier-Transform-based micromechanical simulations. We show, that the proposed modifications are successful in extending the model's scope to inclusions with small aspect ratios ≤20. Thus, the reformulated model is a powerful tool to describe and interpret microstructure dependent creep. [ABSTRACT FROM AUTHOR]

The manufacturing process of Sheet Molding Compound (SMC) influences the properties of a component in a non-deterministic fashion. To predict this influence on the mechanical performance, we develop a virtual process chain acting as a digital twin for SMC specimens from compounding to failure. More specifically, we inform a structural simulation with individual fields for orientation and volume fraction computed from a direct bundle simulation of the manufacturing process. The structural simulation employs an interpolated direct deep material network to upscale a tailored SMC damage model. We evaluate hundreds of virtual specimens and conduct a probabilistic analysis of the mechanical performance. We estimate the contribution to uncertainty originating from the process-induced inherent random microstructure and from varying initial SMC stack configurations. Our predicted results are in good agreement with experimental tensile tests and thermogravimetric analysis. [Display omitted] [ABSTRACT FROM AUTHOR]

In this work, we propose to use deep material networks (DMNs) as a surrogate model for full-field computational homogenization to inversely identify material parameters of constitutive inelastic models for short fiber-reinforced thermoplastics (SFRTs). Micromechanics offers an elegant way to obtain constitutive models of materials with complex microstructure, as these emerge naturally once an accurate geometrical representation of the microstructure and expressive material models of the constituents forming the material are known. Unfortunately, obtaining the latter is non-trivial, essentially for two reasons. For a start, experiments on pure samples may not accurately represent the conditions present in the composite. Moreover, the manufacturing process may alter the material behavior, and a subsequent modification is necessary. To avoid modeling the physics of the manufacturing process, one may identify the material models of the individual phases of the composite based on experiments on the composite. Unfortunately, this procedure requires conducting time-consuming simulations. In the work at hand, we use Deep Material Networks to replace full-field simulations, and to carry out an inverse parameter optimization of the matrix model in a SFRT. We are specifically concerned with the long-term creep response of SFRTs, which is particularly challenging to both experimental and simulation-based approaches due to the strong anisotropy and the long time scales involved. We propose a dedicated fully coupled plasticity and creep model for the polymer matrix and provide details on the experimental procedures. • We propose an inverse calibration method for the matrix model in a fiber reinforced thermoplastic. • A novel creep plasticity model is introduced. • Deep Material Networks are used to replace full-field micromechanical simulations. • Potential error sourced in the microstructure characteristics are investigated. • The approach is validated with creep tests in complimentary directions. [ABSTRACT FROM AUTHOR]

The onset of nonlinear effects in metals, such as plasticity and damage, is strongly influenced by the heterogeneous stress distribution at the grain level. This work is devoted to studying the local stress distribution in fcc polycrystals using FFT-based solvers. In particular, we focus on the distribution of shear stresses resolved in the slip systems as the critical driving force for plastic deformations. Specific grain orientations with respect to load direction are investigated in the linear elastic regime and at incipient plastic deformations based on a large ensemble of microstructures. The elastic anisotropy of the single crystal is found to have a crucial influence on the scatter of the stress distribution, whereas the Young's modulus in the respective crystal direction governs the mean stress in the grain. It is further demonstrated that, for higher anisotropy, the shear stresses deviate from the normal distribution and are better approximated by a log-normal fit. Comparing the full-field simulations to the Maximum Entropy Method (MEM), reveals that the MEM provides an excellent prediction up to the second statistical moment in the linear elastic range. In a study on the spatial distribution of shear stresses, the grain boundary is identified as a region of pronounced stress fluctuations and as the starting point of yielding during the elastic–plastic transition. • Large-scale (200 realizations) FFT-based investigation of local stress distribution. • Statistical variance of stresses in a grain increases for higher anisotropy. • Local shear stress distributions are not exact Gaussian normal distributions. • Elastic MEM predicts grain stress means and covariances close to full-field results. • Plastification starts close to the grain boundary, expanding inwards from there. [ABSTRACT FROM AUTHOR]

The mechanical properties of long fiber reinforced thermoplastics (LFT), which highly depend on the fiber orientation induced through manufacturing on a direct LFT line, are predicted for compression molded rectangular plates. Therefore, three two-scale structural mechanical simulation schemes are applied and discussed: a two-step approach, the Mori-Tanaka scheme and the self-consistent method. Fiber orientation tensors based on measured micro computed tomography data of selected samples as well as on filling simulations are used for the determination of mechanical properties, as e.g. the storage modulus. The results have been compared with dynamic mechanical analysis measurements of tensile specimens. The influence of the initial strand position on the effective mechanical properties of the plate and the variation of those are examined. [ABSTRACT FROM AUTHOR]

The main contribution of this work lies in the detailed comparison of the predictions of linear elastic properties of mean field homogenization approaches and full field, voxel-based homogenization methods for short-fiber reinforced materials. In the former case, the self-consistent, the interaction direct derivative and a two-step-bounding approach, applying the Hashin–Shtrikman bounds, are used. In the latter case, the boundary value problem for representative volume elements is solved using fast Fourier transformation. Model microstructures with unidirectional aligned and two misaligned fiber configurations are considered exemplarily. Fiber volume fractions of 13%, 17% and 21% and phase contrasts of 44, 100 and 1000 in the elastic moduli have been taken into account. The different homogenization schemes are compared by means of effective directional dependent Young’s modulus. This detailed comparison shows that mean field and full field solutions deliver similar results for moderate phase contrasts and volume fractions. Especially in the range of realistic phase contrasts like 44 for a composite of polypropylene and glass, the mean field approaches pose reliable alternatives for full field solution. Large phase contrasts result in relative deviations of up to 68%. [ABSTRACT FROM AUTHOR]

We present a holistic multiscale approach for constructing anisotropic criteria describing the macroscopic failure of sheet molding compound composites based on full-field simulations of microscale damage evolution. We use an anisotropic damage model on the microscale that directly operates on the compliance tensor, captures matrix and bundle damage via dedicated stress-based damage criteria and allows for a comparison of simulation and experimental results. To identify the damage material-parameters used in the non-linear and time-consuming full-field simulations, we utilize Bayesian optimization with Gaussian processes. We validate the full-field predictions on the microscale and subsequently identify macroscopic failure criteria based on distributions taken from experimental findings. We propose failure surfaces in stress space and stiffness-reduction triggered failure surfaces to cover both a structural analysis and a design process perspective. • SMC composites show a macroscopic strain hardening behavior due to accumulation of damage on the microscale that eventually leads to abrupt failure. • We utilize a modular and convex damage model in the framework of generalized standard materials that fulfills Wulfinghoff's damage growth criterion. • We define specific extraction tensors motivated by Puck's laminate theory in combination with a pencil glide approach to account for maximum stress states, describing damage evolution in fiber bundles and matrix. • We present a holistic multiscale approach for constructing anisotropic criteria describing the macroscopic failure based on microscale full-field damage evolution. • Failure surfaces in stress space and stiffness-reduction triggered failure cover both a structural analysis and a design process perspective. [ABSTRACT FROM AUTHOR]

[Display omitted] Directionally solidified eutectics of NiAl matrix and fibrous refractory metals, like Mo, can form cellular mesostructures with significant fiber misalignment and changing fiber volume fraction, for example, when being solidified at high growth rates or when increased solidification intervals are present in the alloys. In order to reveal the deteriorating impact of the mesostructure, i.e., the volume fraction and aspect ratio of the well-aligned cells, on the creep response of such cellular eutectics, we rely on scale-bridging numerical simulations, using the level-set framework by Sonon et al. [1] for microstructure generation and FFT-based solvers for computing the creep response. Our results indicate, firstly, that the fraction of properly aligned regions in cellular NiAl composites is lower than estimated in earlier experimental studies, due to the existence of degenerated regions surrounding the well-aligned cell interiors. Secondly, studying the influence of the cell aspect ratio shows that the apparent stress exponent of the composite is very sensitive with respect to this parameter, providing a possible explanation for the large scatter of experimentally determined stress exponents in previous studies. A comparison of the numerical simulations to a linear rule of mixtures and the frequently applied analytical Kelly-Street model illustrates that both fail to accurately describe the magnitude of minimum creep rates in the investigated ranges of volume fractions and aspect ratios. The heterogeneity of the strain-rate field on the mesoscale is identified as the primary error source, demonstrating that either numerical simulations or more sophisticated analytical models are required for reliably predicting for the creep response of cellular materials. [ABSTRACT FROM AUTHOR]

Ideas from the mathematical theory of optimal transport have recently been transferred to the micromechanics of polycrystalline materials, leading to fast methods for generating polycrystalline microstructures with grains of prescribed volume fraction in terms of centroidal Laguerre tessellations. In this work, we improve the state of the art solvers. For a given set of seeds and corresponding volume fractions summing to unity, there is a set of Laguerre weights such that the corresponding Laguerre tessellation realizes the prescribed volume fractions exactly. Furthermore, the Laguerre weights are unique up to a constant and can be determined by solving a convex optimization problem. However, whenever the optimization algorithm encounters a weight vector leading to an empty cell, the optimization problem is no longer locally strictly convex. To account for the latter, backtracking strategies are typically employed. We show that modern gradient-based optimization algorithms devoid of backtracking, like the Malitsky–Mishchenko method and the Barzilai–Borwein scheme easily overcome the described difficulty, leading to a significant speed-up compared to more traditional solvers. Furthermore, for computing centroidal Laguerre tessellations of prescribed volume fraction, we propose an Anderson-accelerated version of Lloyd's algorithm, and show, by numerical experiments, that it consistently reduces the run-time. We demonstrate the capabilities of our proposed methods for generating microstructures of polycrystalline materials with prescribed grain size distribution. • Fast method for computing polycrystalline microstructures for given grain-size distribution. • Laguerre-based convex optimization solver based on the Barzilai–Borwein method. • Anderson-accelerated Lloyd algorithm for centering. • Application to polycrystalline materials with prescribed grain size distribution. [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]

As a result of the injection molding process, short glass fiber reinforced thermoplastics (SFRT) exhibit complex microstructures with fibers of different length and orientation as well as spatially varying fiber volume fractions. Their mechanical and functional performance can therefore only be predicted and ensured based on precise knowledge of said microstructure. To that end, x-ray micro-computed tomography (μCT) is commonly employed, with analysis software most-often yielding the fiber orientation tensors but lacking more detailed results. In order to increase the quality of the microstructural data, more accurate analysis techniques are necessary that include single fiber information for detailed correlations of microstructural parameters. In this work, a novel algorithm is suggested that relies on an iterative single fiber segmentation and merging procedure to obtain the fiber characteristics: orientation, location, radius and length. The algorithm is implemented in an efficient manner in Python, making heavy use of parallelization techniques. It is then applied to μCT scans and artificially generated 3D data of short glass fiber reinforced polyamide 6.6 with fiber mass fractions of 35 %. The algorithm has been validated using reference data, commercial software and experimental fiber length data from an incinerated specimen and was shown to be both robust and accurate. [ABSTRACT FROM AUTHOR]