Model-data-driven constitutive responses: Application to a multiscale computational framework

Computational multiscale methods for analyzing and deriving constitutive responses have been used as a tool in engineering problems because of their ability to combine informa-tion at different length scales. However, their application in a nonlinear framework can be limited by high computational costs, numerical difficulties, and/or inaccuracies. In this pa-per, a hybrid methodology is presented which combines classical constitutive laws (model -based), a data-driven correction component, and computational multiscale approaches. A model-based material representation is locally improved with data from lower scales ob-tained by means of a nonlinear numerical homogenization procedure, leading to a model -data-driven approach. Therefore, macroscale simulations explicitly incorporate the true mi-croscale response, maintaining the same level of accuracy that would be obtained with online micro-macro simulations but with a computational cost comparable to classical model-driven approaches. In the proposed approach, both model and data play a funda-mental role allowing for the synergistic integration between a physics-based response and a machine learning black-box. Numerical applications are implemented in two dimensions for different tests investigating both material and structural responses in large deforma-tions. Overall, the presented model-data-driven methodology proves to be more versatile and accurate than methods based on classical model-driven, as well as pure data-driven techniques. In particular, a lower number of training samples is required and robustness is higher than for simulations which solely rely on data. (c) 2021 Elsevier Ltd. All rights reserved.