A thermodynamically consistent, inelastic constitutive modeling framework based on artificial neural networks

• Applicant: Professor Dr. Oliver Weeger
• Subject Area: Mechanics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 492770117

Constitutive models describe the mechanical behavior of materials and indicate the relationship between strains and stresses, internal energy, and dissipation. To be physically meaningful and mathematically well defined, these models have to meet numerous requirements, such as thermodynamic consistency, material frame indifference and symmetry, as well as ellipticity. Although such material models have been developed for decades, there are no universal approaches that can be applied equally effective to a wide variety of material classes and thereby meet the required properties. In particular, novel metamaterials and composites made of polymers and biomaterials show highly nonlinear, anisotropic, and inelastic effective material behavior that cannot be represented with the current analytically formulated models.Within the scope of this project, a constitutive modeling approach will be developed that can be flexibly applied to strongly nonlinear and inelastic, dissipative material behavior at large deformations and thereby fulfills all essential physical and mathematical requirements. This is to be realized on the basis of the "Generalized Standard Materials" concept, which ensures thermodynamic consistency, as well as through the representation of the energy and dissipation potentials with the aid of artificial neural networks (ANN). ANNs are characterized by their universal approximation property, so they can approximate any nonlinear functions. In contrast to other common data-driven approaches, however, they can be formulated and structured in such a way that essential mathematical requirements such as convexity and symmetries are ensured.Starting from analytically formulated material models and their structure, we will gradually develop constitutive models for visco-hyperelasticity and damage due to the Mullins effect, which will be based on physics-informed ANNs. The physical interpretability of these models is preserved through the choice of the internal state variables and the model structure with regard to the representation of the potentials and evolution equations. To demonstrate the flexibility of this novel approach, we will apply it to the effective material modeling and multiscale simulation of cubic 3D beam lattice structures, which are characterized by large deformations, instabilities, viscous behavior, and the Mullins effects. For this purpose, we will also develop an efficient open-source finite implementation of these ANN models, which uses parallelization and GPU evaluation. Future applications and extensions of such ANN-based constitutive models could then include plasticity, phase transformations, thermo-mechanical or multi-physical behavior and thus show the universal applicability to any material classes and metamaterials.

• DFG Programme: Research Grants