Artificial Intelligence accelerated multi-scale simulations of Composite Materials

Multi-scale simulations of composite materials, although attractive from the scientific point of view, are often unpractical for complex non-linear material responses because of their inherent computational cost.
Data-driven methods allow to train surrogate models from a synthetic dataset built using offline simulations. Once trained, the surrogate can substitute the micro-scale BVP resolution of a multi-scale simulation while reducing the computation time by several orders of magnitude. In this work we compare two surrogate models in the case of complex non-linear material responses of composite materials, such as stochastic responses, or damage.
A neural-networks (NNWs) offer a potential of reducing the computation time by more than 5 orders of magnitude. In order to introduce the history dependency, recurrent neural networks (RNNs) were shown to be efficient and accurate in approximating the history-dependent homogenized stress-strain relationships [1]. However, they have no possibility of extrapolating responses and thus require a large dataset for their training.
A physics informed alternative is the deep material network (DMN) approach [2] which consists in a network of mechanistic building blocks. During the training process, the DMN “learns” the weight ratio and interactions of the building blocks. Once trained, the DMN is able to predict nonlinear responses, including for unseen material responses and loading conditions, in a thermodynamically consistent way. Although they are less computationally efficient than the NNWs in their online stage, their extrapolation capabilities in terms of constitutive behaviors, loading paths [3], or even composite volume fraction [4] make them good candidates for virtual testing, or to construct an extensive dataset as required by NNWs.
[1] L. Wu and L. Noels. "Self-consistency Reinforced minimal Gated Recurrent Unit for surrogate modeling of history-dependent non-linear problems: Application to history-dependent homogenized response of heterogeneous materials." Comput. Meth. in Appl. Mech. and Engng., Vol. 424 116881 (2024)
[2] Z. Liu, C. Wu, M. Koishi, “A deep material network for multiscale topology learning and accelerated nonlinear modelling of heterogeneous materials”, Comput. Meth. in Appl. Mech. and Engng. Vol. 345, pp. 1138–1168, (2019)
[3] V. D. Nguyen, L. Noels, “Interaction-based material network: A general framework for (porous) microstructured materials”, Comput. Meth. in Appl. Mech. and Engng. Vol. 389, pp. 114300, (2022)
[4] L. Wu and L. Noels. "Stochastic deep material networks as efficient surrogates for stochastic homogenisation of non-linear heterogeneous materials." Comput. Meth. in Appl. Mech. and Engng. Vol. 441 pp. 117994 (2025)