A multiscale, data-driven approach to identifying thermo-mechanically coupled laws-bottom-up with artificial neural networks

摘要

In this paper a multiscale data-driven approach is developed to model the effective macro-scale thermo-mechanical properties for isotropic, hyperelastic materials, subjected to finite deformation. Two independent artificial neural networks (ANNs) are designed to describe a stress-strain law with temperature dependence, and a heat-conduction law with gradients informed by updated nodal positions. A dimensionless representative volume element (RVE) is designed to generate training data. The ANNs are thus trained offline with this RVE data, to serve as a reliable replacement of classical constitutive equations and macro-scale homogenization, which systematically bypasses the need for their often daunting mathematical formalisms. Our trained ANNs are thus used to drive the online solution of boundary value problems (BVPs) within a commercial finite element (FEM) package. Illustrative examples for homogeneous and heterogeneous microstructures are herein presented, which demonstrate that our approach yields reliable thermo-mechanical predictions, and obtains accurate results when compared against direct numerical simulation (DNS).