Rapid sliding motion of a rigid frictionless indentor with a flat base over a thermoelastic half-space

The three-dimensional, rapid sliding indentation of a deformable half-space by a rigid indentor of a flat elliptical base is treated in this paper. The response of the material that fills the half-space is assumed to be governed by coupled thermoelasticity. The indentor translates without friction on the half-space surface at a constant sub-Rayleigh speed and the problem is treated as a steady-state one. An exact solution is obtained that is based on a Green’s function approach, integral equations, and Galin’s theorem. A closed-form expression for the distributed contact pressure under the elliptical base of the indentor is derived. Representative numerical results are given illustrating the effects of the indentor velocity, indentor geometry, and parameters of the thermoelastic solid on the contact displacement. Since there is an analogy between the steady-state theories of thermoelasticity and poroelasticity, the present results carry over to the latter case directly.