Data-driven constitutive models for brittle solids displaying progressive anisotropic damage

Abstract

We propose and demonstrate a computational framework to obtain data-driven surrogate constitutive models capturing the mechanical response of anisotropic brittle solids displaying progressive anisotropic damage. We train the constitutive models on data obtained from the analysis of a volume element of a material of interest; the data is generated by a constitutive model for braided composites, displaying a complex anisotropic damage evolution progressively transitioning from transversely isotropic to orthotropic. Training involves imposing six-dimensional random strain histories on the physical model and recording the histories of stress, strain and homogenised stiffness matrix of the material, obtained by a set of linear perturbation analyses. Supervised machine learning and dimensionality reduction are applied to the data and a structure for a surrogate model is proposed. The surrogate predicts the evolution of the stiffness of the solid consequent to an arbitrary imposed six-dimensional strain increment, thereby calculating the corresponding increment in stress. The model displays high accuracy and is able to reproduce the homogenised material's response via simple neural networks.