Optimal Control of Static Contact in Finite Strain Elasticity

Description

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 for rubber or biological soft tissue. Aim of this project is the development and analysis of algorithms for the optimal control of these 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 problem and convergence of the homotopy are studied.

The resulting regularized optimal control problems will still be nonconvex and will be solved by a function space oriented composite step method. This method will exploit problem structure of finite strain, in particular 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.

Publications

No publications from this project yet.

Preprints

Anton Schiela, Matthias Stöcklein: Optimal Control of Static Contact in Finite Strain Elasticity (SPP1962-097, 10/2018, [bib])

Manuel Schaller, Anton Schiela, Matthias Stöcklein: A Composite Step Method with Inexact Step Computations for PDE Constrained Optimization (SPP1962-098, 10/2018, [bib])

Research Area

Modeling, problem analysis, algorithm design and convergence analysis

The focus of this area is on the development and analysis of genuinely non-smooth models in the sciences in order to properly capture real-world effects and to avoid comprising smoothing approaches. In simulation and optimization this requires to advance set-valued analysis and the design of robust algorithms for non-smooth problems.

Realization of algorithms, adaptive discretization and model reduction

As the target applications of this SPP involve non-smooth structures and partial differential operators, the discretization of the associated problems and robust error estimation are important issues to be address, and proper model-reduction techniques need to be developed.

Members

  • member's portrait

    Prof. Anton Schiela

    Universität Bayreuth
    Principal Investigator
  • member's portrait

    Matthias Stöcklein

    Universität Bayreuth
    Research Assistant

Project Related News

  • Oct 31, 2018 : New preprint submitted

    Matthias Stöcklein submitted the preprint SPP1962-097, Optimal Control of Static Contact in Finite Strain Elasticity

  • Oct 31, 2018 : New preprint submitted

    Matthias Stöcklein submitted the preprint SPP1962-098, A Composite Step Method with Inexact Step Computations for PDE Constrained Optimization

  • Oct 10, 2016 : Welcome to our new project member

    Matthias Stöcklein joins project 18.