An artificial Neural Network (NNW) is designed to serve as a surrogate model of micro-scale simulations in the context of multi-scale analyzes in solid mechanics. The design and training methodologies of the NNW are developed in order to allow accounting for history-dependent material behaviors. On the one hand, a Recurrent Neural Network (RNN) using a Gated Recurrent Unit (GRU) is constructed, which allows mimicking the internal variables required to account for history-dependent behaviors since the RNN is self-equipped with hidden variables that have the ability of tracking loading history. On the other hand, in order to achieve accuracy under multi-dimensional non-proportional loading conditions, training of the RNN is achieved using sequential data. In particular the sequential training data are collected from finite element simulations on an elasto-plastic composite RVE subjected to random loading paths. The random loading paths are generated in a way similar to a random walking in stochastic process and allows generating data for a wide range of strain-stress states and state evolution. The accuracy and efficiency of the RNN-based surrogate model is tested on the structural analysis of an open-hole sample subjected to several loading/unloading cycles. It is shown that a similar accuracy as with a FE 2 multiscale simulation can be reached with the RNN-based surrogate model as long as the local strain state remains in the training range, while the computational time is reduced by four orders of magnitude.

This paper presents an automated approach to build computationally Representative Volume Elements (RVE) of open-foam cellular materials, enabling the study of the effects of the microstructural features on their macroscopic behavior. The approach strongly relies on the use of distance and level set functions. The methodology is based on the extraction of random tessellations from inclusion packings following predetermined statistical packing distribution criteria. With the help of simple recombination operations on the distance fields, the tessellations are made to degenerate in Laguerre tessellations. Predetermined morphological characteristics like strut cross-section variation based on commercially available materials are applied on the RVE to ensure the extraction of closely matching models using simple surface extraction tools, and a detailed morphology quantification of the resulting RVEs is provided by comparing them with experimental observations. The extracted RVE surface is then treated with smoothening criteria before obtaining a 3D tetrahedralized model. This model can then be exported for multi-scale simulations to assess the effects of microstructural features by an upscaling methodology. The approach is illustrated by the simulation of a compression test on an RVE incorporating plasticity with geometrically non-linear behavior.

The present article introduces an automated procedure to construct geometrical representative volume elements (RVE) of open‐foam cellular materials from computerized tomography (CT) images, with the final aim of generating meshable geometries usable in the finite element method (FEM) used in order to analyse their mechanical behavior. The methodology consists in growing and fitting a set of ellipsoids to each of the foam cells. These ellipsoids are seeded by local maxima of the distance to the struts obtained from computer tomography images. This methodology is thus fully voxel‐based and does not depend on any assumption about statistical distributions of the foam cells. Therefore, it is able to reproduce an accurate geometrical model of the foam's microstructure and its possible irregularities. Moreover, this procedure allows the processing of large 3D data sets that do not fit the random access memory (RAM) by slicing it into smaller independent chunks. The effectiveness of the proposed approach is illustrated by comparing it to FEM simulations for which meshes are obtained from a feature reconstruction approach. Both FEM simulations are then compared with experimental results of uniaxial compressions of an open foam.