K. T. Andrews, M. Rochdi and M. Shillor,

The problem of thermoviscoelastic dynamic contact between a rod and a rigid
obstacle, when the material damage is taken into account, is modeled and analyzed.
The contact is modeled by the normal compliance condition and the stress-strain
constitutive equation is of Kelvin-Voigt type. The damage, which describes the reduction
of the load carrying capacity of the rod, evolves because of the opening of microcracks
as a result of tension or compression. When the damage reaches a criticalvalue at a point
on the rod the material cannot carry any load and the system breaks down. Mathematically,
this is expressed by the quenching of the solution. The existence of a local weak solution is
established using penalization and a priori estimates.