Stress-based finite element methods for variational inequalities in contact mechanics
A stress-based mixed finite element method with reduced symmetry for Linear Elasticity featuring Raviart-Thomas elements is extended first to the frictionless Signorini problem and then to contact problems obeying Coulomb’s friction law. Different possible discretizations of the contact constraints are examined. The resulting (quasi-)variational inequalities with nonsmooth constraints are solved using Lagrange multipliers, a semi-smooth Newton method and, in case of Coulomb friction, a fixed point iteration. A reconstruction-based a-posteriori error estimator is derived. Its reliabilty is shown under certain regularity assumptions on the solution that correspond to a uniqueness criterion for the solution of Coulomb’s problem. The efficiency of the resulting adaptive refinement strategy is tested by a number of numerical experiments in two and three dimensions.