One-dimensional dynamic thermoviscoelastic contact with damage

AbstractThe 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 critical value 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