Consistent Finite Element Formulation of Nonlinear Frictional Contact Problems

摘要

A perturbed Lagrangian-based variational formulation is proposed for the finite element solution of fully nonlinear frictional contact problems. In the spirit of an operator splitting methodology, an analogy exists between the proposed treatment for the stick-slip motion and the corresponding treatment in elastoplasticity. Within the context of discrete formulations arising from a finite element approximation, explicit expressions for the frictional consistent contact tangent stiffness and residual are derived from variational equations by using a consistent linearization procedure for both the sliding and adhesion phases. The consistent tangent operator is always non-symmetric for the case of frictional sliding owing to the nature of the Coulomb's friction law employed. For two-dimensional applications, a three-node contact element is employed in the finite element discretization. Numerical examples are also presented that illustrate the performance of the proposed formulation. Keywords: structural mechanics.