Model-data-driven constitutive responses

Application to a multiscale computational framework

authored by

Jan Niklas Fuhg, Christoph Böhm, Nikolaos Bouklas, Amelie Fau, Peter Wriggers, Michele Marino

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 deformations. 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.

Organisation(s)

Institute of Continuum Mechanics
PhoenixD: Photonics, Optics, and Engineering - Innovation Across Disciplines

External Organisation(s)

Université Paris-Saclay
Tor Vergata University of Rome
Cornell University

Type

Article

Journal

International Journal of Engineering Science

Volume

167

ISSN

0020-7225

Publication date

01.10.2021

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Materials Science(all), Engineering(all), Mechanics of Materials, Mechanical Engineering

Electronic version(s)

https://arxiv.org/abs/2104.02650 (Access: Open)
https://doi.org/10.1016/j.ijengsci.2021.103522 (Access: Closed)