Convolutional neural network-based mapping of material micro-structures to deep material networks for non-linear mechanical response prediction

Abstract

peer reviewedData-driven approaches make the development of surrogates of complex heterogeneous material responses possible. After being trained using a previously generated data-set during an offline stage, the surrogates can be used as a material law to conduct structural simulations during the online stage. Nevertheless, in view of accounting for the uncertainty and variability of the heterogeneous materials, the surrogates should be able to account for the micro-structure variability, which remains a challenge. Among the possible surrogate candidates, (Interaction-Based-)Deep-Material Networks ((IB-)DMN) offer the advantage that they can extrapolate the response for new material model parameters of the heterogeneous material phases and for arbitrary loading histories outside of their training range. This advantage results from their thermodynamics consistency and from the fact that the IB-DMN learnable parameters represent solely the micro-structure organization and not the phases material response. However, a trained IB-DMN remains an image of a given micro-structure spatial organization realization in terms of clustering etc. A new microstructure realization thus requires a new training process, limiting the interest of the IB-DMN for stochastic multi-scale analyses. In order to address this limitation, we define the learnable or topological arameters of the IB-DMN from a combination of convolution encoder and neural network, with the micro-structure image serving as input data. After training a CNN encoder-decoder, the encoder part allows extracting the feature vectors of the heterogeneous material directly from micro-structure images. These feature vectors then serve as input of a trained feedforward neural network (FNN) that predicts the topological parameters of the IB-DMN, yielding a “Image to IB-DMN” framework. The methodology is first illustrated in the context of Unidirectional (UD) composites, for which Stochastic Volumes Elements (SVEs) serve as images of the micro-structure realizations. In a second step we show that the machine learning tools can be trained by considering simultaneously composite families of different inclusion shapes such as circular, elliptical and squared. Despite training considering only elastic data, the predictions for a complex pressure-sensitive elasto-plastic model remain accurate. These results demonstrate the complementary roles of the two networks: the CNN encoder–decoder efficiently extracts reduced feature vectors from micro-structure images with diverse inclusion geometries, and the FNN accurately maps these features to the topological parameters of the IB-DMN, establishing a robust, end-to-end image-to-model framework capable of generalizing across different micro-structural configurations.This research has been funded by the Walloon Region under the agreement no. 2010092-CARBOBRAKE in the context of the M-ERA.Net Join Call 2020 funded by the European Union under the Grant Agreement no. 958174.9. Industry, innovation and infrastructur