TY - JOUR

T1 - Model-data-driven constitutive responses

T2 - Application to a multiscale computational framework

AU - Fuhg, Jan Niklas

AU - Böhm, Christoph

AU - Bouklas, Nikolaos

AU - Fau, Amelie

AU - Wriggers, Peter

AU - Marino, Michele

N1 - 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.

PY - 2021/10/1

Y1 - 2021/10/1

N2 - 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.

AB - 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.

KW - Computational homogenization

KW - Machine-learning

KW - Model-data-driven

KW - Multiscale simulations

KW - Ordinary kriging

UR - http://www.scopus.com/inward/record.url?scp=85109450773&partnerID=8YFLogxK

U2 - 10.1016/j.ijengsci.2021.103522

DO - 10.1016/j.ijengsci.2021.103522

M3 - Article

AN - SCOPUS:85109450773

VL - 167

JO - International Journal of Engineering Science

JF - International Journal of Engineering Science

SN - 0020-7225

M1 - 103522

ER -