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

Participating project in "Analysis and computation of microstructure in finite plasticity". The occurrence of microstructures in solid mechanics can be attributed to a loss of the convexity characteristics of the underlying energy potentials. Specific model problems include, for instance, phase transitions in crystalline solids, material instabilities in finite strain plasticity, and material deterioration due to damage processes. While the material deforms macroscopically, structures in the form of shear bands, cracks or laminates can be formed on microscopic scales. Common to these examples is the lack of (quasi-)convexity of energy functionals of the corresponding boundary value problem. As a result, the numerical simulation of those problems through energy minimisation poses a very challenging task because of the enforced high oscillatory character of the developed microstructure. Within the research group the projects either concern the modelling or the simulation. In contrast, the object of this project is the justification of simulations with an analysis of the discretization and the construction of powerful efficient algorithms.

Participating project in "Analysis and computation of microstructure in finite plasticity". The occurrence of microstructures in solid mechanics can be attributed to a loss of the convexity characteristics of the underlying energy potentials. Specific model problems include, for instance, phase transitions in crystalline solids, material instabilities in finite strain plasticity, and material deterioration due to damage processes. While the material deforms macroscopically, structures in the form of shear bands, cracks or laminates can be formed on microscopic scales. Common to these examples is the lack of (quasi-)convexity of energy functionals of the corresponding boundary value problem. As a result, the numerical simulation of those problems through energy minimisation poses a very challenging task because of the enforced high oscillatory character of the developed microstructure. Within the research group the projects either concern the modelling or the simulation. In contrast, the object of this project is the justification of simulations with an analysis of the discretization and the construction of powerful efficient algorithms.

Duration of project

Start date: 06/2007

End date: 12/2012

Research Areas