MS04 - Data-driven methods for constitutive modeling

Keywords: constitutive modeling; physics-augmented machine learning; multiphysics; inelasticity; parameter identification; multiscale simulation

Organizers:
Dominik K. Klein (1) – klein@cps.tu-darmstadt.de
Max Rosenkranz (2) – max.rosenkranz@tu-dresden.de
Karl A. Kalina (3) – karl.kalina@tu-dresden.de
Miguel A. Moreno-Mateos (4) – miguel.moreno@fau.de
Moritz Flaschel (4) – moritz.flaschel@fau.de

Affiliations:
(1) Cyber-Physical Simulation Group, TU Darmstadt, Germany
(2) Institute of Artificial Intelligence, TU Dresden, 01062 Dresden, Germany
(3) Institute of Solid Mechanics, TU Dresden, 01062 Dresden, Germany
(4) Lehrstuhl für Technische Mechanik, FAU Erlangen-Nürnberg, 91058 Erlangen, Germany

Abstract:

Constitutive modeling is one of the pillars of continuum solid mechanics, which enables the mathematical description of different materials such as polymers, soft biological tissue, or active materials. In the past, a variety of constitutive models, often denoted as classical constitutive models, were proposed. However, based on a human choice of model equations, classical models are mostly limited to simple, only moderately flexible functional relationships. This often limits their applicability when considering highly nonlinear, inelastic, or multiphysical materials. In recent years, machine learning (ML)-based or data-driven methods have emerged as a new class of models. These approaches have been developed to circumvent the limitations of classical models, e.g., by using expressive neural networks to overcome their lack of flexibility. Approaches of this class offer unprecedented flexibility for the constitutive model equations, making them a promising alternative to models formulated in the classical way. It is widely agreed that ML-based constitutive models should be designed to fulfill physical conditions such as thermodynamic consistency and objectivity, which can be coined as physics-augmented or physics-constrained ML modeling. By that, the extraordinary flexibility of ML-methods is combined with a sound mechanical basis.

While ML-based constitutive modeling approaches have become well-established for simple material classes such as isotropic hyperelasticity, there is still much ground to cover. Challenges remain in the representation of complex phenomena such as anisotropy, inelasticity and multiphysics, modeling aspects such as interpretability and sparsity, and the calibration of ML constitutive models with experimental data. This minisymposium aims to bring together experts in ML-based constitutive modeling, and to discuss some of these current challenges and trends. Topics of interest include but are not limited to:

  • Constitutive modeling based on ML-methods such as neural networks and Gaussian processes

  • Modeling of complex material behavior including: (i) energy-conserving and dissipative effects; (ii) multiphysics such as thermo-, magneto-, or electro-mechanics; (iii) damage and fracture mechanics; and (iv) parametric dependencies

  • Fulfillment of physical constraints, interpretability, sparsity, and uncertainty for ML-based constitutive models

  • Constitutive model parameter calibration and material model discovery, e.g., using full-field data

  • Efficient implementation in numerical schemes such as multiscale simulation and topology optimization