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

• Published in: Applied numerical mathematics Vol. 61; no. 4; pp. 428 - 442
• Main Authors: Krause, Rolf, Mohr, Christina
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 01.04.2011; Elsevier
• Subjects: Approximation; Boundaries; Calculus of variations and optimal control; Contact; Contact problems; Deformation; Exact sciences and technology; Large deformations; Level set methods; Mathematical analysis; Mathematical models; Mathematics; Multigrid methods; Multiscale methods; Non-linear elasticity; Non-smooth optimization; Numerical analysis; Numerical analysis. Scientific computation; Numerical approximation; Numerical methods in mathematical programming, optimization and calculus of variations; Numerical methods in optimization and calculus of variations; Sciences and techniques of general use; Solvers; Contact problems; Non-linear elasticity; Level set methods; Multigrid methods; Non-smooth optimization; Large deformations; Three-dimensional calculations; Level set; Optimization method; Mechanical contact; Numerical approximation; Numerical analysis; Linear elasticity; Applied mathematics; Multiscale method; Inequality constraint; Smooth function; Variational calculus; Numerical simulation; Mathematical programming
• ISSN: 0168-9274; 1873-5460
• DOI: 10.1016/j.apnum.2010.11.007

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.