Multiscale Modelling Strategies for Heterogeneous Materials

A computational homogenization technique for modeling diffusion in concrete is introduced with emphasis on the influence of the aggregate content and variability. The highly heterogeneous material is investigated on different scales by combining Variationally Consistent Homogenization on numerical microstructures with analytical techniques accounting for lower, unresolved, length scales. The concrete structure consists of the cement paste, the embedded aggregates, and the Interfacial Transition Zone (ITZ) in between the two. Diffusion takes place in the cement phase, as well as in the ITZ. Since the thickness of the ITZ is, typically, much smaller than the diameter of the aggregates, the effect of the ITZ can be modelled as a surface transport around the aggregates. The occurrence of different aggregate sizes is described via the Particle Size Distribution for given sieve curves, as described in design codes. The Particle Size Distribution curve is split into two parts. The effect of smaller aggregates is homogenized analytically using a mixture rule. This results in an effective matrix material consisting of cement paste and the smaller aggregates. Synthetic structures are then generated numerically to account for the larger aggregates. At first, a dense sphere packing is created based on the Particle Size Distribution. This information is used to generate a weighted Voronoi diagram, which is modified by a shrinking process. This procedure allows us to create periodic Representative Volume Elements for numerical investigations.The overall diffusivity of the concrete mixture is evaluated upon using Variationally Consistent Homogenization, in the context of Finite Element analysis, for the generated RVEs and compared with analytical homogenization results and experimental data. It is found that, depending on the Particle Size Distribution, the ITZ has a large effect on the effective properties.

This paper addresses a first-order and a second-order framework for the multiscale modelling of heterogeneous and multiphase materials. The macroscopically required (first-order or second-order) constitutive behavior is retrieved directly from the numerical solution of a boundary value problem at the level of the underlying microstructure. The most important features of computational homogenization schemes are: no constitutive assumptions on the macro level; large deformations and rotations on the micro and macro level; arbitrary physically nonlinear and time-dependent material behavior on the micro level; independent of the solution technique used on the micro level; applicable to evolving and transforming microstructures. In particular, a second-order computational homogenization scheme deals with localization and size effects in heterogeneous or multiphase materials. Higher-order continua are naturally retrieved in the presented computational multiscale model, through which the analysis of size and localization effects can be incorporated. The paper sketches a brief introductory overview of the various classes of multiscale models. Higher-order multiscale methods, as typically required in the presence of localization, constitute the main topic. Details on the second-order approach are given, whereas several higher-order issues are addressed at both scales, with a particular emphasis on localization phenomena. Finally, the applicability and limitations of the considered first-order and second-order computational multiscale schemes for heterogeneous materials are high-lighted.

Multiscale modeling and characterization of coupled damage-healing-plasticity for granular materials in concurrent computational homogenization approach

Computational homogenization of effective permeability in three-phase mesoscale concrete

Computational second-order homogenization of materials with effective anisotropic strain-gradient behavior

Representative volume element (RVE) is a technique to determine and predict the mechanical and physical effective properties of any random homogeneous or heterogeneous composite material models. An optimal size of RVE model became a major objective in order to be statistically equivalent to the real composite material. In this paper, possible approaches to solving the RVE size problem is by developing a particles dispersion model in implementing microstructure of silver (Ag) micro-particle composite for electrical purpose. In this technique, a micro scale of scanning electronic microscope condition was observed for verification on Ag morphology in an epoxy matrix. The morphological analysis is used to guide the particles dispersion model that can be considered to repeat the whole macro-scale of the composite. In the RVE size study, the various composite model sizes were analyzed on the electrical conductivity for convergence study. The model size was determined by a ratio between width of RVE model and the particle size which given in ? = W/D. The numbers of RVE size (?) were set in a size of 3, 4, 5, 6, 7, 8 and 9. The efficiency of size that represents the precision of the estimation of the electrical purpose has been successfully determined by a particle dispersion model developed at model size of ? = 7. The predicted conductivity at model size of ? = 7 shows a good agreement with experimental data with the results presented at 5.06 × 10?1 and 2.69 × 10?1 S/cm for modeling and experiments, respectively.

Periodic mesh generation and homogenization of inclusion-reinforced composites using an element-carving technique with local mesh refinement

Determination of effective elastic properties of ferritic ductile cast iron by computational homogenization, micrographs and microindentation tests

A coupled hygro-thermo-mechanical computational model is proposed for fibre reinforced polymers, formulated within the framework of Computational Homogenisation (CH). At each macrostructure Gauss point, constitutive matrices for thermal, moisture transport and mechanical responses are calculated from CH of the underlying representative volume element (RVE). A degradation model, developed from experimental data relating evolution of mechanical properties over time for a given exposure temperature and moisture concentration is also developed and incorporated in the proposed computational model. A unified approach is used to impose the RVE boundary conditions, which allows convenient switching between linear Dirichlet, uniform Neumann and periodic boundary conditions. A plain weave textile composite RVE consisting of yarns embedded in a matrix is considered in this case. Matrix and yarns are considered as isotropic and transversely isotropic materials respectively. Furthermore, the computational framework utilises hierarchic basis functions and designed to take advantage of distributed memory high performance computing.

The modeling of the mechanical behavior of quasi-brittle materials is still a challenge task, mainly in failure processes when fracture and plasticity phenomena become important actors in dissipative processes which occur in materials like concrete, as instance. Many homogenization-based approaches have been proposed to deal with heterogeneous materials in the last years. In this context, a computational homogenization modeling for concrete is presented in this work using the concept of Representative Volume Element (RVE). The material is considered as a three-phase material consisting of interface zone (ITZ), matrix and inclusions-each constituent modeled by an independent constitutive model. The Representative Volume Element (RVE) consists of inclusions idealized as circular shapes symmetrically and non-symmetrically placed into the specimen. The interface zone is modeled by means of cohesive contact finite elements. The inclusion is modeled as linear elastic and matrix region is considered as elastoplastic material. A set of examples is presented in order to show the potentialities and limitations of the proposed modeling. The consideration of the fracture processes in the ITZ is fundamental to capture complex macroscopic characteristics of the material using simple constitutive models at mesoscopic level.

Identification of RVE length scale in fiber composites via combined optical and SEM digital image correlation

Computational generation of open-foam representative volume elements with morphological control using distance fields

The FE computational homogenization method is a predictive multi‐scale method without the need for constitutive assumptions and/or potential function postulates at the macro engineering scale. Instead, the effective micro‐structural responses are extracted directly from a representative volume element (RVE) underlying each macro point. However, the FE method is still computationally too expensive for most practical uses, since the micro‐macro FE coupling is done at each loading step/iteration for the entire domain. To this end, the machine learning method has been utilized in the literature for the offline training of a surrogate model to predict the RVE homogenized response for general loading conditions. In this contribution, the neural network (NN) is incorporated into the macro finite element framework in a non‐intrusive manner. This is termed as the FE‐NN framework, in analogy to the FE method. In general, online simulations in the FE‐NN method is very efficient, with predictions matching closely to those obtained from reference direct numerical simulations (DNS). A bottleneck with the FE‐NN framework, however, is the high computational cost associated with the data generation for offline NN model setup. In this paper, focusing on the FE‐NN multi‐scale framework for non‐linear elastic deformation of heterogeneous materials, a sequential training strategy with knowledge transfer is proposed, to enable an efficient offline microscopic NN model setup. For a given target RVE, we first consider a simplified source RVE, where data can be generated rapidly, for the NN pre‐training of surrogate model. The pre‐trained network parameters are next downloaded to initialize the target NN surrogate model, followed by a fine‐tuning training process, using only a small dataset generated by the computationally expensive high‐fidelity RVE. The efficiency of the proposed sequential learning method over the conventional NN training, as well as, its excellent predictive capability for multi‐scale analyses, are demonstrated for a multi‐phase composite material. The proposed FE‐NN‐KT approach can be implemented easily without complicated pre‐processing procedures, since the data generation only involves the standard extraction of effective responses from RVEs, together with a standard NN architecture.

A multiscale experimental approach to characterize micro-to-macro transition length scale in polymer foams

This study provides a methodology for exploring the microstructural and mechanical properties of the Haynes®282® alloy produced via the Powder Bed Fusion-Electron Beam (PBF-EB) process. Employing 2D Electron Backscatter Diffraction (EBSD) data, we have successfully generated 3D representations of columnar microstructures using the Representative Volume Element (RVE) method. This methodology allowed for the validation of elastic properties through Crystal Elasticity Finite Element (CEFE) computational homogenization, revealing critical insights into the material behavior. This study highlights the importance of accurately representing the grain morphology and crystallographic texture of the material. Our findings demonstrate that created virtual models can predict directional elastic properties with a high level of accuracy, showing a maximum error of only ~5% compared to the experimental results. This precision underscores the potential of our approach for predictive modeling in Additive Manufacturing (AM), specifically for materials with complex, non-homogeneous microstructures. It can be concluded that the results uncover the intricate link between microstructural features and mechanical properties, underscoring both the challenges encountered and the critical need for the accurate representation of grain data, as well as the significance of achieving a balance in EBSD area selection, including the presence of anomalies in strongly textured microstructures.