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Analytical results on a model for damaging in domains and interfaces. (English) Zbl 1230.35034
Summary: This paper deals with a model describing damage processes in a (nonlinear) elastic body which is in contact with adhesion with a rigid support. On the basis of phase transitions theory, we detail the derivation of the model written in terms of a PDE system, combined with suitable initial and boundary conditions. Some internal constraints on the variables are introduced in the equations and on the boundary, to get physical consistency. We prove the existence of global in time solutions (to a suitable variational formulation) of the related Cauchy problem by means of a Schauder fixed point argument, combined with monotonicity and compactness tools. We also perform an asymptotic analysis of the solutions as the interfacial damage energy (between the body and the contact surface) goes to \(+\infty\).

MSC:
35D30 Weak solutions to PDEs
74A15 Thermodynamics in solid mechanics
74M15 Contact in solid mechanics
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