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

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...

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Vydané v:Applied numerical mathematics Ročník 61; číslo 4; s. 428 - 442
Hlavní autori: Krause, Rolf, Mohr, Christina
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Kidlington Elsevier B.V 01.04.2011
Elsevier
Predmet:
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
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Popis
Shrnutí: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.
Bibliografia:ObjectType-Article-1
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content type line 23
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2010.11.007