DFG Project "Optimal Control of Static Contact in Finite Strain Elasticity"
start of the project: 2016 , end of the project: 2019
contract number: SCHI 1379/2-1
DFG (Priority Programme 1962)
principal investigatorProf. Dr. Anton Schiela
aims of the project
Static contact problems in the regime of finite strain elasticity are an important class of mechanical problems with nonlinear, non-smooth behaviour. Finite strains occur if the considered materials are soft, for example rubber or biological soft tissue. Aim of this project is the development and analysis of algorithms for the optimal control of the problems.
We construct and analyse a regularization and homotopy approach; the non-penetration condition of the contact problem and the local injectivity condition of elasticity are relaxed. Properties of the regularized problems and convergence of the homotopy are studied.
The resulting regularized optimal control problems will still be non-smooth non-convex and will be solved by a function space oriented composite step method. This method will exploit the problem structure of finite strain elasticity particularly the variational structure of elasticity and the group structure of deformations. To finally approximate solutions of the original problem we will develop and analyse an affine invariant path-following method tailored for this class of problems.