Model-data-driven constitutive responses

Application to a multiscale computational framework

verfasst von: 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.
Organisationseinheit(en): Institut für Kontinuumsmechanik
PhoenixD: Simulation, Fabrikation und Anwendung optischer Systeme
Externe Organisation(en): Universität Paris-Saclay
Università degli studi di Roma Tor Vergata
Cornell University
Typ: Artikel
Journal: International Journal of Engineering Science
Band: 167
ISSN: 0020-7225
Publikationsdatum: 01.10.2021
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Allgemeine Materialwissenschaften, Allgemeiner Maschinenbau, Werkstoffmechanik, Maschinenbau
Elektronische Version(en): https://arxiv.org/abs/2104.02650 (Zugang: Offen)
https://doi.org/10.1016/j.ijengsci.2021.103522 (Zugang: Geschlossen)
: Details im Forschungsportal „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.",
}