DFG FG 797/2: "Analysis and computation of microstructure in finite plasticity" - Participating project P1-1: "Numerical algorithms for the simulation of finite plasticity with microstructures"

The occurrence of microstructures in solid mechanics and, in particular, in finite plasticity can be attributed to a loss of the convexity of the underlying energy potentials. While the material deforms macroscopically, structures in the form of shear bands, cracks or laminates arise on microscopic scales. Common to these examples is that their macroscopic simulation have to be based on the quasiconvexification of the energy functional. The projects within the research group either concern the modelling or the simulation. In contrast, the object of this project is the justification of computer simulations with an analysis of discretisation and design of converging adaptive mesh-refining algorithms. The mathematical justification concerns numerical simulations on the microscopic scale (a), on the macroscopic scale (b), for time-evolving microstructure (c).

The occurrence of microstructures in solid mechanics and, in particular, in finite plasticity can be attributed to a loss of the convexity of the underlying energy potentials. While the material deforms macroscopically, structures in the form of shear bands, cracks or laminates arise on microscopic scales. Common to these examples is that their macroscopic simulation have to be based on the quasiconvexification of the energy functional. The projects within the research group either concern the modelling or the simulation. In contrast, the object of this project is the justification of computer simulations with an analysis of discretisation and design of converging adaptive mesh-refining algorithms. The mathematical justification concerns numerical simulations on the microscopic scale (a), on the macroscopic scale (b), for time-evolving microstructure (c).

Duration of project

Start date: 10/2010

End date: 06/2016

Research Areas