Data-driven homogenisation of the response of heterogeneous ductile solids with isotropic damage

Abstract

We propose a computational procedure to derive a data-driven surrogate constitutive model capturing the elastic–plastic response and progressive damage of a heterogeneous solid. This is demonstrated by analysing the response to deformation of a volume element of a non-linear, n-phase random composite, used in this study as a model material. Finite Element simulations are conducted, imposing pseudo-random, multiaxial, non-proportional histories of macroscopic strain to such volume element. The corresponding predicted histories of macroscopic stresses and other variables are recorded, to form part of a training dataset for the surrogate model. Essential additional training data is obtained by recording the changes in the homogenised stiffness matrix of the volume element during the deformation, by performing a series of linear perturbation analyses. Supervised machine learning is applied to the data, proposing suitable sets of inputs and outputs and implementing a phenomenological constitutive model based on simple neural networks. This results in a data-driven model of high accuracy.