Model-data-driven constitutive responses: Application to a multiscale computational framework. (1st October 2021)

• Record Type: Journal Article
• Authors: Fuhg, Jan Niklas; Böhm, Christoph; Bouklas, Nikolaos; Fau, Amelie; Wriggers, Peter; Marino, Michele
• Is Part Of: International journal of engineering science. Volume 167(2021)
• Publication Date: 2021-10-01
• Subjects: Model-data-driven -- Multiscale simulations -- Machine-learning -- Computational homogenization -- Ordinary kriging; Engineering -- Periodicals; Ingénierie -- Périodiques; Engineering; Periodicals; 620
• DOI: 10.1016/j.ijengsci.2021.103522
• Languages: English
• ISSNs: 0020-7225

Abstract

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.