A dissipative discretization for large deformation frictionless dynamic contact problems

Please always quote using this URN:urn:nbn:de:0296-matheon-11844
  • We present a discretization for dynamic large deformation contact problems without friction. Our model is based on Hamilton’s principle, which avoids the explicit appearance of the contact forces. The resulting differential inclusion is discretized in time using a modified midpoint rule. This modification, which concerns the evaluation of the generalized gradient, allows to achieve energy dissipativity. For the space discretization we use a dual-basis mortar method. The resulting spatial algebraic problems are nonconvex minimization problems with nonconvex inequality constraints. These can be solved efficiently using a trust-region SQP framework with a monotone multigrid inner solver.
Author:Jonathan William Youett, Oliver Sander
Referee:Ralf Kornhuber
Date of first Publication:2012/11/27
Institute:Research Center Matheon
Freie Universität Berlin
MSC-Classification:74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Hxx Dynamical problems / 74H15 Numerical approximation of solutions
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Mxx Special kinds of problems / 74M20 Impact
Preprint Number:990