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
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)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{52d8dbdaaae547788cbb13e175d754e6,
title = "Model-data-driven constitutive responses: Application to a multiscale computational framework",
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.",
keywords = "Computational homogenization, Machine-learning, Model-data-driven, Multiscale simulations, Ordinary kriging",
author = "Fuhg, {Jan Niklas} and Christoph B{\"o}hm and Nikolaos Bouklas and Amelie Fau and Peter Wriggers and Michele Marino",
note = "Funding Information: JF acknowledges the support from the Deutsche Forschungsgemeinschaft under Germanys Excellence Strategy within the Cluster of Excellence PhoenixD (EXC 2122, Project ID 390833453). CB and PW acknowledge the financial support to this work by the German Research Foundation (DFG, Deutsche Forschungsgemeinschaft) in the framework of the collaborative research center 1153 Tailored Forming (SFB 1153) with the sub-project C04 modelling and simulation of the joining zone, project number 252662854. MM acknowledges the funding by the Italian Ministry of Education, University and Research (MIUR) within the 2017 Rita Levi Montalcini Program for Young Researchers (Programma per Giovani Ricercatori - anno 2017 “Rita Levi Montalcini”). Finally, the financial support of the French-German University through the French-German doctoral college “Sophisticated Numerical and Testing Approaches” (SNTA), grant CDFA/DFDK 04-19 is acknowledged. ",
year = "2021",
month = oct,
day = "1",
doi = "10.1016/j.ijengsci.2021.103522",
language = "English",
volume = "167",
journal = "International Journal of Engineering Science",
issn = "0020-7225",
publisher = "Elsevier Ltd.",
}