FOR 797: DFG Research Unit "Analysis and computation of microstructure in finite plasticity"
Subproject P5: Regularizations and relaxations of time-continuous problems in plasticity


Researchers:

Project Head: Prof. Dr. Alexander Mielke
Investigators: Dr. Dorothee Knees,  Dr. Sebastian Heinz

Description:

The theory of finite-strain elastoplasticity has been developed quite rapidly during the last decade. The major impulses for this were twofold: on the one hand, the discovery that time-incremental problems can be formulated as minimization problems and, on the other hand, the recent developments in the field of microstructures generated by infimizing sequences of functionals. In mathematical theory, the formation of microstructure is mostly treated via global minimization for static problems. In contrast to that, our aim is to derive models for the evolution of microstructure under slowly varying loads.
This project is devoted to the study of temporal evolution models for plasticity and for systems with microstructure in general. Using spatial regularization via higher gradients and temporal regularization via viscosity, we first want to derive mathematical models that allow for an existence theory of solutions without microstructure. The temporal regularization will lead to time-continuous solutions and thus avoid the problems occuring through global minimization. Starting from these solutions, we then generalize the recently developed energetic formulation for rate-independend processes.
As a prelimenary step, this program will be studied via simplified model problems, for which existence, uniqueness and convergence of numerical schemes can be proven and tested. Finally, the more difficult case of geometrically exact finite-strain elastoplasticity will be attacked. Funding began in 2007.

Collaborations:

Activities:

Publications: