Transient thermoelastic contact problems for an elastic foundation

The paper presents a numerical solution of the problem of a hot rigid indenter sliding over a thermoelastic Winkler foundation at constant speed. It is shown analytically that no steady-state solution can exist for sufficiently high temperature or sufficiently small normal load or speed. The numerical solution shows that the steady-state solution, when it exists, is the final condition regardless of the initial conditions imposed. This suggests that the steady-state is also stable. When there is no steady-state, the predicted transient behavior involves regions of transient stationary contact interspersed with regions of separation. Initially, the system typically exhibits a small number of relatively large contact and separation regions, but as time progresses, larger and larger numbers of small contact areas are established, until eventually the accuracy of the algorithm is limited by the discretization used.