Generation Of Representative Volume Elements Research Articles

DRAGen in Application-An Approach for Microstructural Fatigue Predictions of Non-Oriented Electrical Steel Sheets.

This study investigates multiple cyclic loading scenarios of non-oriented electrical steel sheets through both experimental and numerical approaches. The numerical simulations were conducted using Representative Volume Elements generated with DRAGen. DRAGen allowed for the generation of Representative Volume Elements with a non-cubic shape to cover the complete sheet thickness and enough grains to represent the material's texture. The experimental results, on the other hand, are utilized to calibrate and validate a prediction model, highlighting the significance of accumulated plastic slip as a suitable parameter correlated with fatigue life. Using the accumulated plastic slip from the simulations, a fatigue fracture locus is introduced, which describes a 3D surface dependent on the maximum stress, fatigue life, and the fatigue stress ratio. The study shows reliable results for the fatigue life prediction using the calibrated fatigue fracture locus. While substantial progress has been made in predicting the fatigue life at multiple fatigue stress ratios, notable disparities between experimental and simulation results suggest the need for further investigations regarding the influence of the surface quality. This observation motivates ongoing research efforts aimed at refining simulation methodologies to better incorporate surface roughness effects. In summary, this study presents a validated model for predicting fatigue life in non-oriented electrical steel sheets, offering valuable insights into material behavior at different loading scenarios and informing future research directions for enhanced structural performance and durability.

Incorporation of compaction effects in the automated generation of 3D woven composites representative volume elements by geometrical modelling

Advanced 3D woven composites have become an enabling technology in many industrial applications due to their proven benefits, particularly the improvement of the out-of-plane mechanical behavior with respect to other reinforcement schemes. The latter property has been shown to be strongly affected by the effects of compaction during manufacturing. The present study proposes an automated framework, based on heuristic procedures, for the generation of representative volume elements (RVEs) of 3D woven composites, allowing to include global and local geometrical features induced by transverse compaction, such as overall thickness reduction, changes in yarn cross-sections and consistent global/local fiber fractions. The methodology is illustrated for three types of reinforcement, namely a plain weave, an angular through-thickness interlock and a 3D orthogonal RVE. The resulting geometries generated by the proposed method compare favourably with typical observations from the literature in a quantitative manner. Finally, the proposed framework is integrated with a previously developed meshing strategy to allow damage studies for a selected architecture (plain weave) under torsional loading, presenting a complete computational chain by building cohesive zone finite element models from compacted RVEs. The torque-angle response curves obtained after the damage simulations show a decrease in stiffness and an increase of damage levels with compaction, which is in line with the expectations.

Geometric void-multiscale model for evaluating the effect of bead width and layer height on voids in FDM parts

PurposeThis paper aims to present a geometrical void model in conjunction with a multiscale method to evaluate the effect of interraster distance, bead (raster) width and layer height, on the voids concentration (volume) and subsequently calculate the final mechanical properties of the fused deposition modeling parts at constant infill.Design/methodology/approachA geometric model of the voids inside the representative volume element (RVE) is combined with a two-scale asymptotic homogenization method. The RVEs are subjected to periodic boundary conditions solved by finite element (FE) to calculate the effective mechanical properties of the corresponding RVEs. The results are validated with literature and experiments.FindingsBead width from 0.2 to 0.3 mm, reported a decrease of 25% and 24% void volume for a constant layer height (0.1 and 0.2 mm – 75% infill). It is reported that the void’s volume increased up to 14%, 32% and 36% for 75%, 50% and 25% infill by varying layer height (0.1–0.2 and 0.3 mm), respectively. For elastic modulus, 14%, 9% and 10% increase is reported when the void’s volume is decreased from 0.3 to 0.1 mm at a constant 75% infill density. The bead width and layer height have an inverse effect on voids volume.Originality/valueThis work brings values: a multiscale-geometric model capable of predicting the voids controllability by varying interraster distance, layer height and bead width. The idealized RVE generation slicer software and Solidworks save time and cost (<10 min, $0). The proposed model can effectively compute the mechanical properties together with the voids analysis.

Identification of Martensite Bands in Dual‐Phase Steels: A Deep Learning Object Detection Approach Using Faster Region‐Based‐Convolutional Neural Network

Martensite banding in dual‐phase steels is an important research topic in the field of materials design, since it affects the local damage properties of the material largely. Therefore, it is necessary to quantify the amount and the geometrical details of the bands in a specific microstructure, for example, for simulative approaches. A convolutional neural network is trained on manually labeled scanning electron microscopy images of DP800 steel and a subsequent effort is made to transfer these results to statistical quantities for the generation of representative volume elements (RVE). As exact geometric definitions of martensite bands in 2D are difficult, the influence of different band definitions is investigated. The result of the training shows good prediction accuracy but is strongly dependent on the chosen band definition and the underlying human bias from the labeling process. A statistical analysis using cross‐validation shows that reliable results can already be achieved with only small datasets of around 50–100 training images due to the transfer learning approach. This is an important outcome as it eliminates the need to generate a large dataset which can only be obtained from time‐consuming microscopy work and manual labeling of the images.

A computationally efficient approach for generating RVEs of various inclusion/fibre shapes

A computationally efficient method for generating virtual periodic representative volume element (RVE), capable of handling arbitrary inclusion shapes, is developed. A universal collision/overlap detection and repair method is proposed, where each inclusion shape is represented as a union of n-Spheres (UnS). A constrained optimization problem is formulated and solved to remove inclusion overlaps; a closed-form solution is derived for calculating the degree of inclusions overlap and its gradient vector with respect to inclusion position. RVE generation is illustrated with circular, spherical, four non-circular and four non-spherical inclusion shapes. Computational efficiency is demonstrated using an elaborate RVE generation time study. The generated RVEs are evaluated using various statistical metrics; results confirm the random distribution of inclusions. Effective properties of RVEs, representing unidirectional composites, are determined using homogenization with various fibre cross-section shapes; obtained mechanical properties have shown transverse isotropy.

Homogenisation of micromechanical modelling results for the evaluation of macroscopic material properties of brittle ceramics

This paper presents an approach to evaluate the macroscopic properties of ceramic materials based on the homogenisation of the results of micromechanical simulations performed on Representative Volume Elements (RVEs) of polycrystalline microstructures. The RVEs are defined using a bespoke algorithm to generate numerical model geometries statistically representative of the microstructure of polycrystalline ceramics. The material properties of single crystals and grain boundaries, obtained from direct experimental measurements at the relevant scales, are used for the generation of RVEs, which are then subjected to unit load cases. The results of the numerical simulations, performed using the explicit Finite Element Method (FEM), are used to calculate the macroscopic material parameters governing elastic deformation, and brittle failure due to initiation and propagation of cracks at the grain scale. The automated approach adopted to generate and analyse the response of RVEs under a specified set of loading conditions permits a statistically relevant number of simulations to be performed on different combinations of microstructural morphologies, distributions of crystallographic orientations, and defects, thus demonstrating a homogenisation and upscaling methodology that captures several important aspects of the stochastic variability typically exhibited by ceramic materials. The numerical simulations of elastic deformation and brittle failure of polycrystalline alumina (Al2O3) are compared against both experimental measurements and analytical calculations, showing good agreement for both elastic deformation - expressed in terms of homogenised elastic moduli - and failure strength - observed both as changes in the crack pattern at the microscale and when measured as the value of the stress at the onset of failure.

Reduced-order models for microstructure-sensitive effective thermal conductivity of woven ceramic matrix composites with residual porosity

This paper presents a data-driven framework for the development of reduced-order models to predict microstructure-sensitive effective thermal conductivity of woven ceramic matrix composites (CMCs) with residual porosity. The main components of the proposed framework include (i) digital generation of representative volume elements (RVEs), (ii) estimation of the effective thermal conductivities of the RVEs using finite element (FE) models, (iii) low dimensional representation of the microstructure in the RVEs using 2-point spatial correlations and principal component analysis (PCA), and (iv) an active learning strategy based on Gaussian process regression (GPR) that minimizes the size of the training dataset through the selection of microstructures with the highest potential for information gain. The reduced-order models are demonstrated to provide high fidelity predictions on new RVEs.

An algorithm for generation of RVEs of composites with high particle volume fractions

This work proposes a new algorithm entitled “sequential absorption algorithm” to generate Representative Volume Elements (RVEs) of randomly distributed spherical particles reinforced composites by combining the Random Sequential Absorption (RSA) algorithm and the molecular dynamics based method. The proposed algorithm overcomes limitations of the RSA algorithm and is capable of efficiently generating the RVEs with the high Particle Volume Fractions (PVFs) (≥50.0%). The proposed algorithm comprises of the modified RSA algorithm, the detection algorithms of the collisions between particles and between a particle and matrix surface(s), the post-collision particle velocity update algorithm, the particle periodic image generation algorithm and the acceleration algorithm. Particle distribution in the generated RVEs is analyzed through several statistical functions and consistent with the completely spatial random pattern. Regarding the elastic properties of composites, the critical sizes of RVEs and meshed elements are determined. The agreement of the elastic properties of composites with the different PVFs acquired using the finite element homogenization method, the experimental tests and the analytical models exhibits the validation of the proposed algorithm to generate RVEs of composites.

A multivariate grain size and orientation distribution function: derivation from electron backscatter diffraction data and applications.

Two of the microstructural parameters most influential in the properties of polycrystalline materials are grain size and crystallographic texture. Although both properties have been extensively studied and there are a wide range of analysis tools available, they are generally considered independently, without taking into account the possible correlations between them. However, there are reasons to assume that grain size and orientation are correlated microstructural state variables, as they are the result of single microstructural formation mechanisms occurring during material processing. In this work, the grain size distribution and orientation distribution functions are combined in a single multivariate grain size orientation distribution function (GSODF). In addition to the derivation of the function, several examples of practical applications to low carbon steels are presented, in which it is shown how the GSODF can be used in the analysis of 2D and 3D electron backscatter diffraction data, as well as in the generation of representative volume elements for full-field models and as input in simulations using mean-field methods.

Generating Input Data for Microstructure Modelling: A Deep Learning Approach Using Generative Adversarial Networks.

For the generation of representative volume elements a statistical description of the relevant parameters is necessary. These parameters usually describe the geometric structure of a single grain. Commonly, parameters like area, aspect ratio, and slope of the grain axis relative to the rolling direction are applied. However, usually simple distribution functions like log normal or gamma distribution are used. Yet, these do not take the interdependencies between the microstructural parameters into account. To fully describe any metallic microstructure though, these interdependencies between the singular parameters need to be accounted for. To accomplish this representation, a machine learning approach was applied in this study. By implementing a Wasserstein generative adversarial network, the distribution, as well as the interdependencies could accurately be described. A validation scheme was applied to verify the excellent match between microstructure input data and synthetically generated output data.

Three-scale asymptotic homogenization of short fiber reinforced additively manufactured polymer composites

In this research, prediction of mechanical properties of short fiber-reinforced composites manufactured with the help of fused filament fabrication (FFF) process is investigated. Three-scale formulation of asymptotic homogenization is employed to upscale the properties from microscale to mesoscale and from mesoscale to macroscale. Since generating microscale representative volume element (RVE) infused with short fibers requires sophisticated modeling tools, the algorithm for the microscale RVE generation is presented and discussed. Homogenization was performed for microscale RVEs with random and aligned (fibers aligned with the beads on mesoscale) fiber orientations, and for mesoscale RVEs with unidirectional and 0/90 layup formation. Tensile tests were performed for different short carbon fiber concentrations 5, 7.5 and 10% (by volume) to validate predicted homogenized properties. Moreover, to analyze the morphology of 3D printed specimens, microstructural analysis using SEM was performed on all the printed specimens. Surface morphology helped to gain more insight into the bead structure and fiber distribution. It was concluded that Young's modulus prediction using random fiber orientation has low relative errors tested in bead direction. Overall, this study has unique contribution to mechanical property prediction for FFF-made short fiber-reinforced composite parts.

Representative volume element generation and its size determination for discontinuous composites made from chopped prepregs

In the present study, the composites made from chopping prepregs in rectangular chips, called discontinuous composites derived from chopped prepreg (DCCP) were modeled for stiffness prediction. Standard mechanics approach with displacement boundary conditions is used for stiffness prediction. The minimum size of the representative volume element (RVE) for this material is determined. An algorithm based on the random sequential adsorption technique (RSA) has been exploited to generate the 3D RVEs. RVEs of five different aspect ratios of the cuboid-shaped inclusions are developed using this technique. The chips are completely randomly oriented with a constant volume fraction. A detailed study was carried out in each case by further generating the RVEs with different increasing sizes, and the smallest size of RVE with geometric periodicity was identified. Further, the characteristics of these RVEs have been investigated for different aspect ratios, varying the chip volume fraction for the influence of volume fraction on RVE size and the material properties. The efficacy of the developed approach is demonstrated through repetitiveness of the effective properties prediction for various scenarios studied. The resulting material showed isotropy in the plane where chips are distributed randomly while overall isotropy about 80% is seen in most of the RVEs studied.

Weave geometry generation avoiding interferences for mesoscale RVEs

An algorithm which allows the generation of representative volume elements (RVEs) for complex woven and warp-interlaced fiber-reinforced composite topologies while avoiding unphysical tow intersections is presented. This is achieved by extending an existing RVE generation strategy in two significant ways: (1) the local cross section shape of the tow is adjusted depending on the local tow curvature in a way that preserves the cross sectional area of the tow, and (2) the elementary crimp interval is separated into a planar and a transition region. The modifications facilitate the generation of a wide range of elaborate textile topologies without tow intersections, which are present without the proposed modifications unless complex tow to tow contact models are introduced. The mechanical properties of plain weaves were predicted based on the topology generated with the proposed algorithm as well as based on RVEs which were constructed based on actual micrographs, i.e. a “digital twin” of the actual microstructure. A comparison of the predicted mechanical properties based on finite element and Multiscale Generalized Method of Cells techniques shows close agreement. However, some differences exist with respect to experimentally determined material parameters due to the finite dimensions of the specimens. Lastly, mechanical properties of multilayered weaves are predicted with the finite element method. The considered material systems are carbon fiber in epoxy matrix as well as C/C-SiC. However, the procedure is applicable to a wide range of material systems.

An Abaqus™ plug-in for the geometry generation of Representative Volume Elements with randomly distributed fibers and interphases

This paper proposes a plug-in called RVE for composites for the commercial software Abaqus™. This tool generates 2D as well as 3D multi-fiber microstructure geometries for unidirectional composites with random distributions. Its originality resides on the fact of taking into account the interphase region between each fiber and the matrix. Instructions for users on how to install and execute the plug-in are presented. Several images of the graphical user’s interface are showed in order to introduce the features of the tool. Finally, an example using a geometry generated by the plug-in with an experimentally based finite dimension for the interphase, is provided and includes a numerical/experimental macroscale comparison for validation. This plug-in represents an aid to the conception by helping Abaqus™ users to save time in an early stage of the analysis which is the geometry generation. Further improvements are suggested to extend the capabilities of the tool.

Skeletonization-based beam finite element models for stochastic bicontinuous materials: Application to simulations of nanoporous gold

An efficient representative volume element generation strategy is developed in modeling nanoporous materials. It uses periodic 3D beam finite element (FE) models derived from skeletonization of spinodal-like stochastic microstructures produced by a leveled random field. To mimic stiffening with agglomeration of the mass at junctions, an increased Young’s modulus is assigned to the elements within the junction zone. The effective Young’s modulus, Poisson’s ratio, and universal anisotropy index are computed. A good agreement of the Young’s modulus predictions with those obtained from experimental results for phase volume fractions 0.20<{phi _{cal B}}<0.50 is observed. Moreover, the elastic anisotropy index of the generated beam networks shows sufficient proximity to isotropy. Finally, it is demonstrated that, as compared to the simulation statistics of voxel-FE models, for the beam-FE models over 500-fold computational acceleration with 250-fold less memory requirement is provided.

Level set-based generation of representative volume elements for the damage analysis of irregular masonry

Computational homogenization has been used extensively over the past two decades for the analysis of masonry structures based on various averaging schemes (periodic homogenization, transformation field analysis,...), focusing on regular periodic masonry. Irregular masonry has subsequently also been scrutinized using multiscale approaches. In such efforts, an efficient strategy is required for the generation and meshing of realistic representative volume elements (RVEs) geometries. In complement to existing generation approaches, the present contribution deals with a level set-based methodology to generate irregular masonry RVE geometries. Starting from inclusion-based RVEs, combinations of distance fields are used to produce typical geometries of irregular masonry RVEs. The resulting geometries are described by implicit functions. Such implicit geometry descriptions are next exploited in an automated procedure for producing high quality conformal 2D finite element meshes on implicit geometries. This automated RVE generation and discretization procedure is then illustrated by producing failure envelopes for irregular masonry, using an implicit gradient damage formulation. The interest of recently developed gradient models with decreasing interaction length parameters is also illustrated on a specific example.

An advanced approach for the generation of complex cellular material representative volume elements using distance fields and level sets

A general and widely tunable method for the generation of representative volume elements for cellular materials based on distance and level set functions is presented. The approach is based on random tessellations constructed from random inclusion packings. A general methodology to obtain arbitrary-shaped tessellations to produce disordered foams is presented and illustrated. These tessellations can degenerate either in classical Voronoï tessellations potentially additively weighted depending on properties of the initial inclusion packing used, or in Laguerre tessellations through a simple modification of the formulation. A versatile approach to control the particular morphology of the obtained foam is introduced. Specific local features such as concave triangular Plateau borders and non-constant thickness heterogeneous coatings can be built from the tessellation in a straightforward way and are tuned by a small set of parameters with a clear morphological interpretation.

Measure of combined effects of morphological parameters of inclusions within composite materials via stochastic homogenization to determine effective mechanical properties

In our previous papers we have described efficient and reliable methods of generation of representative volume elements (RVE) perfectly suitable for analysis of composite materials via stochastic homogenization.In this paper we profit from these methods to analyze the influence of the morphology on the effective mechanical properties of the samples. More precisely, we study the dependence of main mechanical characteristics of a composite medium on various parameters of the mixture of inclusions composed of spheres and cylinders. On top of that we introduce various imperfections to inclusions and observe the evolution of effective properties related to that.The main computational approach used throughout the work is the FFT-based homogenization technique, validated however by comparison with the direct finite elements method. We give details on the features of the method and the validation campaign as well.

An efficient and automated 3D FE approach to evaluate effective elastic properties of overlapping random fibre composites

The paper deals with an automated and double-scale finite element (FE) model to evaluate the effective elastic properties of 3D overlapping random fibre composites. An efficient and perfectly reliable approach to generate meshes in the context of random heterogeneous media for which some difficulties are encountered, is proposed. The basic idea is to attain an approximation of the geometry relative to a grid of regular hexahedral elements. The concept called voxelisation is tremendously sped up using an adaptive mesh refinement (AMR) which enables one to locally and efficiently smooth each heterogeneity. Thus, a fast, reliable and fully automated generation of representative volume elements (RVE) is possible whatever the complexity of the geometry is. In the present work, algorithms to generate RVE according to the concept of voxelisation are provided. In addition, numerical tests are performed to evaluate both the efficiency of the model and the reliability of the results in the framework of linear elasticity and random fibre composites.

On efficient and reliable stochastic generation of RVEs for analysis of composites within the framework of homogenization

In this paper we describe efficient methods of generation of representative volume elements (RVEs) suitable for producing the samples for analysis of effective properties of composite materials via and for stochastic homogenization. We are interested in composites reinforced by a mixture of spherical and cylindrical inclusions. For these geometries we give explicit conditions of intersection in a convenient form for verification. Based on those conditions we present two methods to generate RVEs: one is based on the random sequential adsorption scheme, the other one on the time driven molecular dynamics. We test the efficiency of these methods and show that the first one is extremely powerful for low volume fraction of inclusions, while the second one allows us to construct denser configurations. All the algorithms are given explicitly so they can be implemented directly.