Non-parametric data-driven constitutive modelling using artificial neural networks

Video recording:

Speaker: Vu M. Chau (Department of Engineering; Faculty of Science Technology and Medicine; University of Luxembourg)
Title: Non-parametric data-driven constitutive modelling using artificial neural networks
Time: Wednesday, 2022.04.13, 10:00 a.m. (CET)
Place: fully virtual (contact Dr. Jakub Lengiewicz to register)
Format: 30 min. presentation + 30 min. discussion

Abstract: This seminar talk addresses certain challenges associated with data-driven modelling of advanced materials — with special interest in the non-linear deformation response of rubber-like materials, soft polymers or biological tissue. The underlying (isotropic) hyperelastic deformation problem is formulated in the principal space, using principal stretches and principal stresses. The sought data-driven constitutive relation is expressed in terms of these principal quantities and to be captured by a non-parametric representation using a trained artificial neural network (ANN).

The presentation investigates certain physics-motivated consistency requirements (e.g. limit behaviour, monotonicity) for the ANN-based prediction of principal stresses for given principal stretches, and discusses the implications on the architecture of such constitutive ANNs. The neural network is exemplarily constructed, trained and tested using PyTorch.

The computational embedding of the data-driven material descriptor is demonstrated for the open-source finite element framework FEniCS which builds on the symbolic representation of the constitutive ANN operator in the Unified Form Language (UFL). We discuss the performance of the overall formulation within the non-linear solution process and will explain some future directions of research.