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

TL;DR

This paper introduces a hybrid multiscale computational framework that combines classical constitutive laws with data-driven corrections, enabling accurate nonlinear material simulations at reduced computational costs.

Contribution

It presents a novel model-data-driven approach that integrates microscale data into macroscale simulations, improving accuracy without high computational costs.

Findings

Achieves macroscale simulations with microscale accuracy

Maintains computational efficiency comparable to classical models

Successfully applied to large deformation problems in 2D

Abstract

Computational multiscale methods for analyzing and deriving constitutive responses have been used as a tool in engineering problems because of their ability to combine information 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 paper, 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 obtained by means of a nonlinear numerical homogenization procedure leading to a model-data-driven approach. Therefore, macroscale simulations explicitly incorporate the true microscale 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 fundamental 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 deformation.