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Paper details
Number 1 - March 2002
Volume 12 - 2002
On finite element uniqueness studies for Coulomb's frictional contact model
Patrick Hild
Abstract
We are interested in the finite element approximation of Coulomb's frictional unilateral contact problem in linear elasticity. Using a mixed finite element method and an appropriate regularization, it becomes possible to prove existence and uniqueness when the friction coefficient is less than Cε2|log(h)|-1, where h and ε denote the discretization and regularization parameters, respectively. This bound converging very slowly towards 0 when h decreases (in comparison with the already known results of the non-regularized case) suggests a minor dependence of the mesh size on the uniqueness conditions, at least for practical engineering computations. Then we study the solutions of a simple finite element example in the non-regularized case. It can be shown that one, multiple or an infinity of solutions may occur and that, for a given loading, the number of solutions may eventually decrease when the friction coefficient increases.
Keywords
Coulomb's friction law, finite elements, mesh-size dependent uniqueness conditions, non-uniqueness example