The effects of anisotropic surface elasticity on the contact problem in an anisotropic material

Abstract

We study the contribution of surface elasticity to the two-dimensional contact problem in a generally anisotropic material using the Stroh sextic formalism. Surface elasticity is incorporated into the model of deformation using an anisotropic version of the continuum-based surface/interface model of Gurtin and Murdoch. Full-field analytic solutions are obtained in terms of exponential integrals for an anisotropic half-space when the contact surface is subjected to two particular types of loading: first, we consider the case of a uniform load (shearing and pressure) applied to an infinitely long strip of the contact surface and second, by reducing the strip to zero width, we deduce the corresponding result for a concentrated line force acting on the contact surface. The analysis indicates that the surface deformation gradient is finite in the first case of uniform loading of the strip and exhibits a weak logarithmic singularity at the location of the applied concentrated line force in the second case.