A rigid, cup-shaped die translates at constant subcritical speed on a thermoelastic
half-space that exhibits thermal relaxation and convection. The die surface is held at
a temperature different from ambient temperature, and sliding friction exists in a
contact zone that is not simply connected. A three-dimensional dynamic steady state
model is assumed and, based on an approximation for inversion of integral
transforms, a solution in analytic form is obtained. Auxiliary conditions for sliding
contact are satisfied; in particular, contact zone traction is stationary with respect to
compression force. Among other results, it is found that a dynamic steady
state is precluded if die-ambient temperature difference is too large. Similar
results are known, but only for die temperatures that exceed the ambient
value.
Keywords
thermoelasticity, 3D, relaxation, multiple connectivity,
critical temperature, convection, 3D dynamic, sliding,
transverse isotropy, contact zone geometry
