A simple machine learning-based framework for faster multi-scale simulations of path-independent materials at large strains

Abstract

Coupled multi-scale finite element analyses have gained traction over the last years due to the increasing available computational resources. Nevertheless, in the pursuit of accurate results within a reasonable time frame, replacing these high-fidelity micromechanical simulations with reduced-order data-driven models has been explored recently by the modelling community. In this work, two classes of machine learning models are trained for a porous hyperelastic microstructure to predict (i) whether the microscopic equilibrium problem is likely to fail and (ii) the stress–strain response. The former may be used to identify critical macroscopic points where one may fall back to the high-fidelity analysis and possibly apply convergence bowl-widening techniques. For the latter, both a linear regression with polynomial features and artificial Neural Networks have been used, and the required stress–strain derivatives for solving the equilibrium problem have been derived analytically. A weight regularisation is introduced to stabilise the tangent operator and several strategies are discussed for imposing null stresses in undeformed configurations for both regression models. The regression techniques, here analysed exclusively in the context of porous hyperelastic materials, evidence very promising prospects to accelerate multi-scale analyses of solids under large deformation.