Finite element solution of surface nonlinearities in structural mechanics with special emphasis to contact and fracture mechanics problems

Abstract

The paper presents a finite element solution of structural mechanics problems with surface nonlinearities. The nonlinearities arise for instance in contact problems. The contact surface between two interacting parts of a structure varies with the applied load and on the contact surface contact constitutive relations must be satisfied. Firstly, the paper presents incremental governing equations for linear elastic materials when small displacements and strains are assumed. As contact constitutive relation, i.e. relation between the contact stress increment vector and the slip increment vector in the contact surface, a general slip criterion with associated slip rule is included. Secondly, the governing equations are solved by means of the finite element displacement method. Only a few of the total number of degrees of freedoms are involved in the nonlinearities. In order to reduce the size of the problem degrees of freedom not involved in the nonlinearities are eliminated by using the superelement technique. Numerical results for several plane and axisymmetric problems are presented and compared with photoelastic experiments and other results known. A Coulomb type of slip criterion with associated slip hardening rule is assumed. The applicability of the method to crack closure problems is shown. Stress intensity factors are calculated and compared with known results.