Analysis for thermo-mechanical models with internal variables

• Applicant: Dr. Matthias Liero, since 10/2023
• Subject Area: Mathematics
• Term: from 2020 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 441470105

We consider nonlinear, coupled material models with internal variables. Based on thermodynamical principles we derive gradient structures that are used to solve the partial differential equations analytically. We will derive existence results for thermo-elasto-plastic models with finite-strain deformations. The concept of Balanced-Viscosity solutions will be generalized to be applicable for models in continuum mechanics, in particular the concept of multirate systems, where the different viscous effects have relaxation times of different order. The theory of evolutionary Gamma convergence will be exploited to derive new model hierarchies for thermo-elasto-plastic plate theories. On the basis of energetic solutions for rate-independent systems we describe the evolution of microstructures in simplified plasticity models.

• DFG Programme: Priority Programmes
• Subproject of: SPP 2256: Variational Methods for Predicting Complex Phenomena in Engineering Structures and Materials
• Ehemaliger Antragsteller: Professor Dr. Alexander Mielke, until 9/2023