Variational modeling of parameter-dependent plasticity - relaxation approaches and numerical concepts

• Applicants: Professor Dr. Georg Dolzmann; Professor Dr. Klaus Hackl
• Subject Area: Mathematics ; Mechanics
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 441468770

Parameter dependent models of plasticity are present in many applications in solid mechanics, for example in granular media, ductile damage of metals, or glassy phases of metals and elastomers. Both the modeling and the mathematical analysis of these problems is an active field of research at the interface between mathematics and mechanics that offers a wealth of deep open problems. Current models are often wanting and require critical rethinking of the constitutive assumptions. This revisiting is in particular mandatory in order to develop well-adjusted models capable of both capturing the microstructures in the material and allowing for the application of non-monotone loading paths, which are of particular importance in applications. The mathematical analysis of these models requires the development of new approaches in the theory of relaxation in order to derive effective models, which can be solved with novel numerical schemes. In this project, this line of research will be carried out for the aforementioned material systems and experimentally validated in the case of granular media.

• DFG Programme: Priority Programmes
• Subproject of: SPP 2256: Variational Methods for Predicting Complex Phenomena in Engineering Structures and Materials