Mathematical analysis of fully coupled approach to creep damage

We prove the existence and uniqueness of solution to a classical creep damage problem. We formulate a sufficient condition for the problem to have a unique smooth solution, locally in time. This condition is stated in terms of smoothness of given data, such as solid geometry, boundary conditions, applied loads, and initial conditions. Counterexamples with an arbitrary small lifetime of a structure are also given, showing the mechanical interpretation of imposed smoothness conditions. The proposed theory gives a rigorous framework for a strain localization analysis. The influence of the damage gradient on the strain localization process is characterized within this framework and a measure of the damage localization is proposed.