AI and data-driven methods for composite multi-scale analyses

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 investigate two surrogate models in the case of complex non-linear material responses of composite materials, such as stochastic responses and failure. Neural networks (NNWs) offer the potential of reducing the computational 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. More specifically, a RNN cell independent to the increment step (called self-consistent) was developed for elasto-plastic RVEs. In this work, we extend the approach to composite failure. The simulations with damage are challenging because after an initial phase in which the damage is diffuse, there is a localization of the damage in a thin band which is dependent on the macro-scale mesh size. To circumvent this problem, a non-local formulation that embeds the machine learning based surrogate predictions is developed in order to recover the solution uniqueness at the macro-scale. However, NNWs have no possibility of extrapolating responses and thus require a large dataset for their training. As a data-driven surrogate of heterogenous material responses, a Deep Material Network (DMN) is built by combining analytical homogenisation solutions and material constitutive relations into a neural network architecture. DMN was reformulated from the interaction view-point as the Interaction-Based DMN (IB-DMN), in order to improve its training performance. In this ...