Level set based multi-scale methods for large deformation contact problems

Authors:
Rolf Krause;Christina Mohr
Affiliations:
Institute of Computational Science, Faculty of Informatics, University of Lugano, Via Giuseppe Buffi 13, CH-6904 Lugano, Switzerland;Institute of Computational Science, Faculty of Informatics, University of Lugano, Via Giuseppe Buffi 13, CH-6904 Lugano, Switzerland
Venue:
Applied Numerical Mathematics
Year:
2011

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Abstract

We consider the numerical simulation of contact problems in elasticity with large deformations. The non-penetration condition is described by means of a signed distance function to the obstacle's boundary. Techniques from level set methods allow for an appropriate numerical approximation of the signed distance function preserving its non-smooth character. The emerging non-convex optimization problem subject to non-smooth inequality constraints is solved by a non-smooth multiscale SQP method in combination with a non-smooth multigrid method as interior solver. Several examples in three space dimensions including applications in biomechanics illustrate the capability of our methods.