Indentation at a bimaterial interface: The line force solution

Abstract

The problem considered is that of a line force acting normal to the free surface of a bimaterial welded together at the bimaterial interface. The constitutive equations of each constituent of the bimaterial are such that the stress-strain relation is linear in one half but non-linear in the other. The case where both satisfy non-linear stress-strain relations can also be dealt with by the method of this paper. It is shown that in general, there is no separable solution, singular at the application of the line force, which satisfies the field equations of each medium. Instead asymptotic solutions are constructed for the cases where the non-linear medium is incompressible with power law stress-strain relation (i.e. σ ≈ εN, with N > 0) distinguishing between the cases where N is less or greater than unity. The characteristics of the asymptotic solutions are first illustrated by modelling non-linear potential problems, which can be viewed as anti-plane strain deformation. © 2001 Elsevier Science Ltd. All rights reserved.