This study employs a multiscale computational homogenization framework to investigate the microstructure-driven evolution of yield surface and texture during the cup-drawing stage of a multi-step battery-can forming process. At the macroscale, the 3D Vegter yield criterion combined with isotropic hardening was employed to simulate the forming process, while the microscale response was modelled using the Crystal Plasticity Finite Element Method (CPFEM). The resulting deformation histories from selected material points were extracted and imposed on Representative Volume Elements (RVEs) within CPFEM framework to resolve the underlying microstructural response.Full ODF analysis reveals a loss of orthorhombic symmetry and a tendency towards alignment of texture components along the local loading (drawing) direction, leading to increased circumferential similarity with increasing deformation. Electron Backscatter Diffraction (EBSD) measurements at the cup rim confirm the predicted texture trends. The evolving texture is accompanied by the development of grain-scale (type-II) residual stresses, here modelled as the microscale stress fluctuations within the RVE and together with the evolution of the macroscopic yield locus. In lightly deformed regions, the yield response remains close to the Vegter prediction with predominantly isotropic expansion. In contrast, strongly deformed zones exhibit both a rigid translation of the yield locus, indicative of kinematic hardening, along with some change in shape. These findings demonstrate that non-evolving phenomenological yield models based solely on isotropic hardening are inadequate to describe the evolving anisotropy observed during forming, and therefore require constitutive formulations that incorporate kinematic and distortional hardening to capture the progressive material evolution in multi-step sheet forming.

Limpet teeth contain a desirable combination of material properties: they are auxetic (i.e., they have a negative Poisson’s ratio) and have high stiffness and strength. In contrast, synthetic auxetic structures presented in the literature to date are typically accompanied by low stiffness. Hence, limpet teeth microstructures are an attractive candidate for bio-inspired synthetic structures that have both auxeticity and high stiffness. The microstructure consists of iron oxide hydroxide crystal nanorods embedded in an amorphous hydrated silica matrix. Moreover, a portion of the nanorods are arranged into oriented bundles which are surrounded by a chiral arrangement of the remaining nanorods. Many synthetic structures achieve auxeticity by means of a similar chiral arrangement of rods. However, such structures are typically continuous, whereas the limpet teeth structures are not. In this work, a mechanistic description of such microstructural arrangements is provided by means of a computational parametric study of idealized microstructures comprising bimodal particle reinforcements with chiral confinement. The influence of microstructural geometry on the effective mechanical properties is investigated by varying parameters such as particle shape, bundle design, rod orientation, and others. It is shown that chiral rods that impinge on the central bundle are crucial for auxeticity and high material stiffness.

In this work, we introduce Enyxe, the Enschede Numerical Yield Function eXploration Environment. It is a mod ular, open-source simulation toolkit for investigating the elastoplastic response of polycrystalline aggregates, utilizing the D & uuml;sseldorf Advanced Material Simulation Kit (Damask) as a solver backend. Implemented workflows automate the generation, execution, and interpretation of simulation jobs required for characterizing the effective plastic behavior of microstructures to investigate yield locus evolution. The onset of macroscopic yielding can be identified through various criteria including offset yield stress and plastic work density. The framework enables live monitoring of jobs through stress-strain curves, automated termination of jobs upon detection of yielding, fitting of yield function parameters, and extensive logging of job information and results, as well as re-use of existing result files when applicable. The modular architecture permits the implementation of any yield criterion, extending the choice of readily available Hill48 and Cazacu-Plunkett-Barlat (CPB06) formulations. Additional workflows facilitate the imposition of arbitrary deformation paths and homogenization of the elastic response of the investigated material microstructure.

We present a methodology for the generative reconstruction of 3D microstructures from 2D cross-sectional electron backscatter diffraction micrographs. The method is applied to Ti-6Al-4V processed by laser powder bed fusion, where a high amount of basketweave morphology is observed, which arises from the solid-state beta -> alpha-transition upon cooling. Prior-beta-grain reconstruction is performed and the out-of-plane orientation of the observed grains is obtained leveraging Burgers orientation relationship. Microstructural descriptors related to convolutional neural networks are extracted from the 2D micrographs, and used for cross-section-based optimization of pixel values in a 3D volume. In order to reconstruct crystallographic orientations, the orientation distribution of the basketweave microstructure is reduced to a discrete set of characteristic orientations, which are sequentially reconstructed as separate components. Our reconstructions capture the characteristic lath morphology that is typically observed in powder bed fusion-processed Ti-6Al-4V and perform well in comparisons of chord length, as well as grain size, aspect ratio, and axis orientation distributions.

In the Drawing and Wall Ironing (DWI) process used in battery can-making, thin sheets experience high contact pressures and out-of-plane shear, necessitating advanced yield criteria in finite element simulations. Vegter and van den Boogaard, in [1], introduced a 2D (plane stress) yield criterion based on second-order Bezier curves designed to fit the experimental yield points exactly. This criterion was later extended to 3D by van Riel and van den Boogaard [2]. The accuracy of such advanced yield criteria in predicting earing patterns during typical cup drawing simulations is well established. However, their validity in simulating DWI processes remains poorly understood, particularly under low clearance between the die and punch. This study investigates the limitations and applicability of the isotropic hardening Vegter 3D model in the DWI simulations of battery can-making. The yield point evolution was analyzed using Crystal Plasticity Finite Element Method (CPFEM) simulations under DWI strain conditions. By comparing these simulation results with the predictions of the isotropic hardening Vegter 3D model, the aim is to determine its validity boundaries and explore its effectiveness for accurately modeling the DWI process.

Rolling is a metal forming process where slabs are passed through rollers to produce strips with specific dimensions and mechanical properties. This process is performed in hot or cold formats. In hot rolling, the workpiece is initially heated above its recrystallization temperature. During the hot rolling process, plastic deformation occurs as the material’s thickness decreases and elongation takes place along the longitudinal axis of the workpiece. Due to the incompressibility of plastic deformation, the material also expands in the transverse direction, a phenomenon known as spread or lateral flow. Modeling spread is crucial for sustainability considerations and meeting customer expectations regarding the quality of the final product. Current prediction methodologies, such as the accurate but slow Finite Element (FE) method or the fast but inaccurate analytical metal forming analysis, are impractical for optimal control. To tackle these challenges, hybrid frameworks have emerged as a promising alternative. The present work aims to develop a fast and accurate model for predicting spread in hot rolling. Specifically, machine learning improves analytical models by leveraging data from a high-fidelity FE model. Initially, we review analytical models for spread, which address key aspects of the problem’s physics. To generate the ground truth (GT) space, an automated FE model for hot strip rolling is created. Moreover, the model’s sensitivity to both process and material parameters is investigated. In the Analytical Predictor Machine Learning Corrector scheme, the analytical models generate initial predictions of GT. In the correction step, a data-driven machine learning model is used to refine these predictions by compensating for deviations from high-fidelity FE simulations. The proposed hybrid framework improves the accuracy of the existing analytical models while preserving their computational efficiency.

The prediction of failure behavior in metal matrix composites remains a significant challenge in both composition design and process optimization. An accurate prediction of metal matrix composites damage evolution is a crucial for enhancing the quality of metal matrix composites forming. As the material undergoes plastic deformation, it experiences void initiation and growth, resulting in consequential microstructural transformations, stiffness degradation, and mechanical property shifts. In this work, we employed a model to predict damage progression and stiffness decay in metal matrix composites. Leveraging the Gurson-Tvergaard-Needleman framework, this homogenization model accounts for the impact of the evolution of voids and reinforcing phases, on the composite's mechanical properties. The influences of reinforcing phases on voids nucleation and growth were particularly considered, and also the interaction of voids, matrix, reinforcing phases, and stiffness were integrated to discuss their impacts on damage evolution and mechanical performances of the metal matrix composites. The model was implemented as an Abaqus VUMAT subroutine, with its validity gauged by analyzing the influence of model parameters on failure mechanisms and inherent elastoplastic traits. Utilizing the flanging process of carbon nanotube-reinforced aluminum matrix composites as a case study, a significant agreement was observed between experimental and simulated force-displacement profiles, as well as crack evolution routes.

We apply physics -informed neural networks (PINNs) to first -order, two -scale, periodic asymptotic homogenization of the property tensor in a generic elliptic equation. The problem of lack of differentiability of property tensors at the sharp phase interfaces is circumvented by making use of a diffuse interface approach. Periodic boundary conditions are incorporated strictly through the introduction of an input -transfer layer (Fourier feature mapping), which takes the sine and cosine of the inner product of position and reciprocal lattice vectors. This, together with the absence of Dirichlet boundary conditions, results in a lossless boundary condition application. Consequently, the sole contributors to the loss are the locally -scaled differential equation residuals. We use crystalline arrangements that are defined via Bravais lattices to demonstrate the formulation's versatility based on the reciprocal lattice vectors. We also show that considering integer multiples of the reciprocal basis in the Fourier mapping leads to improved convergence of high -frequency functions. We consider applications in one, two, and three dimensions, including periodic composites, composed of embeddings of monodisperse inclusions in the form of disks/spheres, and stochastic monodisperse disk arrangements.

We present a methodology for the generative reconstruction of 3D Volume Elements (VE) for numerical multiscale analysis of Ti-6Al-4V processed by Additive Manufacturing (AM). The basketweave morphology, which is typically dominant in AM-processed Ti-6Al-4V, is analyzed in conventional Electron Backscatter Diffusion (EBSD) micrographs. Prior \b{eta}-grain reconstruction is performed to obtain the out-of-plane orientation of the observed grains leveraging Burgers orientation relationship. Convolutional Neural Network (CNN) - based microstructure descriptors are extracted from the 2D data, and used for cross-section-based optimization of pixel values on orthogonal planes in 3D, using the Microstructure Characterization and Reconstruction (MCR) implementation MCRpy [16]. In order to utilize MCRpy, which performs best for binary systems, the basketweave microstructure, which consists of up to twelve distinct grain orientations, is decomposed into several separate two-phase systems. Our reconstructions capture key characteristics of the titanium basketweave morphology and show qualitative resemblance to experimentally obtained 3D data. The preservation of volume fraction during assembly of the reconstruction remains an unadressed challenge at this stage.

Computational material modeling using advanced numerical techniques speeds up the design process and reduces the costs of developing new engineering products. In the field of multiscale modeling, huge com-putation efforts are expected for modeling heterogeneous materials while trying to reach high accuracy levels. In this work, a machine learning approach, namely the convolutional neural network (CNN), is developed as a solution providing a high level of accuracy while being computationally efficient. The input for the CNN model consists of two/three-dimensional images of artificial periodic and biphasic microstructures in the form of nonoverlapping and overlapping, mono-and polydisperse circular/spherical inclusion systems, which are generated by a random sequential inhibition process. These correspond to Statistical Volume Elements (SVE). Considering linear magnetostatics at the microscale, the output is the apparent permeability of the SVE. Training and testing data for the apparent properties is produced with finite element method-based two-scale asymptotic homogenization. The model efficiency is revealed by employing some representative examples in two and three-dimensional settings. In this regard, the performance of the CNN model is assessed with the applied computational homogenization method relating to the accuracy and computational efficiency. The results with the CNN model show high accuracy in predicting the homogenized permeability and a significant decrease in computation time.

Abstract. We determine the effective (macroscopic) thermoelastic properties of two-phase composites computationally. To this end, we use a physics-informed neural network (PINN)-mediated first-order two-scale periodic asymptotic homogenization framework. A diffuse interface formulation is used to remedy the lack of differentiability of property tensors at phase interfaces. Considering the reliance on the standard integral solution for the property tensors on only the gradient of the corresponding solutions, the emerging unit cell problems are solved up to a constant. In view of this and the exact imposition of the periodic boundary conditions, it is merely the corresponding differential equation that contributes to minimizing the loss. This way, the requirement of scaling individual loss contributions of different kinds is abolished. The developed framework is applied to a planar thermoelastic composite with a hexagonal unit cell with a circular inclusion by which we show that PINNs work successfully in the solution of the corresponding thermomechanical cell problems and, hence, the determination of corresponding effective properties.

A panoptic view of architectured planar lattices based on star-polygon tilings was developed. Four star-polygon-based lattice sub-families, formed of systematically arranged triangles, squares, or hexagons, were investigated numerically and experimentally. Finite-element-based homogenization allowed computation of Poisson’s ratio, elastic modulus, shear modulus, and planar bulk modulus. A comprehensive understanding of the range of properties and micromechanical deformation mechanisms was developed. Adjusting the star-polygon angle achieved an over 250-fold range in elastic modulus, over a 10-fold range in density, and a range of -0.919 to +0.988 for Poisson’s ratio. Additively manufactured lattices, achieved by novel printing strategies, showed good agreement in properties. Parametric additive manufacturing procedures for all lattices are available on www.fullcontrol.xyz/#/models/1d3528. Three of the four sub-families exhibited in-plane elastic isotropy. One showed high stiffness with auxeticity at low density and a primarily axial deformation mode as opposed to bending deformation for the other three lattices. The range of achievable properties, demonstrated with property maps, proves the extension of the conventional material-property space. Lattice metamaterials with Triangle-Triangle, Kagome, Hexagonal, Square, Truncated Archimedean, Triangular, and Truncated Hexagonal topologies have been studied in the literature individually. Here, it is shown that these structures belong to the presented overarching lattice family.

We present a computational framework for two-scale asymptotic homogenization to determine the intrinsic magnetic permeability of composites. To this end, considering linear magnetostatics, both vector and scalar potential formulations are used. Our homogenization algorithm for solving the cell problem is based on the displacement method presented in Lukkassen et al. 1995, Composites Engineering, 5(5), 519-531. We propose the use of the meridional eccentricity of the permeability tensor ellipsoid as an anisotropy index quantifying the degree of directionality in the linear magnetic response. As application problems, 2D regular and random microstructures with overlapping and nonoverlapping monodisperse disks, all of which are periodic, are considered. We show that, for the vanishing corrector function, the derived effective magnetic permeability tensor gives the (lower) Reuss and (upper) Voigt bounds with the vector and scalar potential formulations, respectively. Our results with periodic boundary conditions show an excellent agreement with analytical solutions for regular composites, whereas, for random heterogeneous materials, their convergence with volume element size is fast. Predictions for material systems with monodisperse overlapping disks for a given inclusion volume fraction provide the highest magnetic permeability with the most increased inclusion interaction. In contrast, the disk arrangements in regular square lattices result in the lowest magnetic permeability and inadequate inclusion interaction. Such differences are beyond the reach of the isotropic effective medium theories, which use only the phase volume fraction and shape as mere statistical microstructural descriptors.

In this paper, macroscopic behavior obtained from crystal plasticity finite element simulations of irregularly shaped 3D and 2D volume elements (VEs) are compared. These morphologically periodic VEs are generated using the open-source software library Voro++. Periodic boundaryconditions are utilized to homogenize the material response employing a prescribed macroscopic deformation gradient tensor. To accelerate the assignment of periodic boundary conditions, a conformalmesh is employed by which periodic couples of faces on the hull of the volume element have identicalmesh patterns. In the simulations, plane strain conditions are assumed, which means that the averagethickness strain in 3D VEs is set to zero. However, grains are allowed to strain in the thickness direction. In the case of 2D VEs, plane strain elements are used. The principal goal of this comparison isto evaluate the accuracy of 2D VEs simulations. In the current study, two kinds of 2D VEs are generated: 1) Slicing 3D VEs normal to the thickness direction, 2) Separately generating 2D VEs. The firstmethod corresponds to sectioning 3D microstructures using EBSD. This approach is generally usedas an assumed more accurate alternative to 2D VEs. Based on the results, there is a large gap betweenthe flow curves of 2D and 3D VEs. Additionally, 2D sectioning of 3D VEs does not necessarily endup in higher precision in material behavior predictions.

We investigate the predictive performance of specific analytical and numerical methods to determine the effective magnetic properties of two-phase steels at the macroscale. We utilize various mixture rules reported in the literature for the former, some of which correspond to rigorous bounds, e.g., Voigt (arithmetic) and Reuss (harmonic) averages. For the latter, we employ asymptotic homogenization together with the finite element method (FEM) and periodic boundary conditions (PBC). The voxel-based discretization of the representative volume element is conducted with digital image processing on the existing micrographs of DP600-grade steel. We show that unlike the considered isotropic mixture rules, which use only the phase volume fraction as the statistical microstructural descriptor, finite element method-based first-order asymptotic homogenization allows prediction of both phase content and directional dependence in the magnetic permeability by permitting an accurate consideration of the underlying phase geometry.

Materials displaying negative Poisson’s ratio, referred to as auxeticity, have been found in nature and created in engineering through various structural mechanisms. However, uniting auxeticity with high strength and high stiffness has been challenging. Here, combining in situ nanomechanical testing with microstructure-based modeling, we show that the leading part of limpet teeth successfully achieves this combination of properties through a unique microstructure consisting of an amorphous hydrated silica matrix embedded with bundles of single-crystal iron oxide hydroxide nanorods arranged in a pseudo-cholesteric pattern. During deformation, this microstructure allows local coordinated displacement and rotation of the nanorods, enabling auxetic behavior while maintaining one of the highest strengths among natural materials. These findings lay a foundation for designing biomimetic auxetic materials with extreme strength and high stiffness.

Gradient structured materials have been proven to have excellent mechanical properties, such as strength–ductility synergy and excellent strain hardening. In this study, the deformation mechanism of heterostructured bulk aluminum with submicron deformation mechanisms was investigated using a mechanism-based strain-gradient plasticity model, whose gradient information was obtained using a discrete gradient computation method. The model was then used to simulate bending of the material and investigate extra strain hardening. The microstructure of the material was characterized using electron backscattered diffraction analysis. The complicated dislocation reactions occurring during the deformation of multilayer deposition material were determined from the simulation results. The distribution and evolution of geometrically necessary dislocations (GNDs) were numerically determined. The simulation results demonstrate that the GNDs and the number of material gradient cycles have a direct influence on plastic hardening. Inclusion of more layer periods in the material resulted in additional large-scale strain gradient across its thickness. The results of this study advances the understanding of the underlying deformation mechanisms that control ductility and strengthening over periods and gradients and provides the possibility of obtaining multilayer materials with exceptional mechanical properties.

Correct prediction of the fracture time and location and their evolution in metallic materials has always been a research hotspot in the field of metal forming. To this end, and in the context of metal forming process simulation, an advanced mathematical material model is crucial. In this paper, we investigate the accuracy of two fully-coupled damage models, one of which is phenomenologically-based and the other one micromechanically-based, in predicting the failure in DP900 steel plates subject to various loading paths. These are applied throughout tests, including tensile tests on unnotched and notched specimens with different notch radii as well as butterfly wing shear tests. Through the comparisons of the numerical and experimental results, in terms of force-displacement curves and fracture strains (or ductility) under wide range of strain paths, the accuracy of the proposed two coupled damage models are discussed.

Nanoporous metals have favourable characteristics for many applications. These materials have, however, failed to show suitable attributes in tension: showing an extremely weak and brittle response. This issue has been addressed through the impregnation of a polymer constituent into the nanoporous ligament network, creating a strong and malleable material in both tension and compression. In this work, this improvement is investigated by comparing nanoporous gold and its polymer filled nanocomposite counterpart using computational microspecimen compact-tensile tests. We examine crack initiation and propagation within these materials. The micromechanical response is also explored to reveal the influence of the polymer impregnation on fracture mechanisms. It is shown that, in agreement with the findings in the literature, the failure of a few gold ligaments in nanoporous gold leads to the complete failure of the material with a relatively small resistance to failure and a characteristically brittle fracture. Polymer impregnation, on the other hand, effectively delays the complete material failure as the polymer stabilizes the individual ligaments. This results in a significantly increased ductility under tension which is vital for it to be considered for use in structural applications.

Metamaterials are man-made, usually periodically microstructured materials with at least one uncommon property, e.g., auxeticity. Often, their properties are due to their specific microstructural layouts in addition to their constituent materials. In this work, we explore the influence of constituent materials on the effective elasticity of a two-phase composite consisting of a infilled re-entrant honeycomb microstructure. We show that the composite with non-auxetic constituent materials becomes auxetic if the Young’s modulus contrast between the two phases exceeds a certain critical value. We reveal the existence of a phase contrast mediated switch of auxetic mechanism — a finding reported for the first time in this paper. If the re-entrant honeycomb phase is stiffer than the filling phase, the auxeticity stems from the conventional re-entrant mechanism, similar to re-entrant honeycomb structures. However, if the re-entrant honeycomb phase is softer than the filling phase, the auxeticity originates from the relative microscopic sliding between adjacent fillings under macroscopic axial loading. Our results provide guidelines on tuning the effective elasticity and the auxeticity of such composites by educated choices of the constituent materials and the underlying microstructural geometry.