Abstract
We describe and analyse a model for a problem of thermoviscoelastic dynamic contact which allows for the general evolution of the material damage. The effects on the mechanical properties of the material due to crack expansion are described by a damage field, which measures the decrease in the load-bearing capacity of the material. The damage process is assumed to be reversible and the microcracks which develop as a result of tension or compression may grow or disappear. The geometric setting is that of a 1D rod which may contact a deformable obstacle. The contact is modelled by the normal compliance condition and the stress–strain constitutive equation is of Kelvin–Voigt type. The model consists of a coupled system of energy–elasticity equations together with a non-linear parabolic inclusion for the damage field. The existence of a local weak solution is established using penalization, a finite element algorithm for the solution is constructed and analysed and the results of numerical simulations based on this algorithm are presented. The simulations illustrate how the size of the normal compliance coefficients, the damage rate coefficients and the applied force affect the character of the evolution of the damage. In particular, cycles of bonding and debonding can occur.
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