We introduce a thermomechanical model describing dissipative phase transitions with thermal memory in terms of the entropy balance and the principle of virtual power written for microscopic movements. The thermodynamical consistence of this model is verified and existence of solutions is proved for a related initial and boundary value problem.
SUMMARYIn this paper, we analyze a contact problem with irreversible adhesion between a viscoelastic body and a rigid support. On the basis of Frémond's theory, we detail the derivation of the model and of the resulting partial differential equation system. Hence, we prove the existence of global in time solutions (to a suitable variational formulation) of the related Cauchy problem by means of an approximation procedure, combined with monotonicity and compactness tools, and with a prolongation argument. In fact the approximate problem (for which we prove a local well-posedness result) models a contact phenomenon in which the occurrence of repulsive dynamics is allowed for. We also show local uniqueness of the solutions, and a continuous dependence result under some additional assumptions.
We consider a model describing the evolution of damage in visco-elastic materials, where both the stiffness and the viscosity properties are assumed to degenerate as the damaging is complete. The equation of motion ruling the evolution of macroscopic displacement is hyperbolic. The evolution of the damage parameter is described by a doubly nonlinear parabolic variational inclusion, due to the presence of two maximal monotone graphs involving the phase parameter and its time derivative. Existence of a solution is proved in some subinterval of time in which the damage process is not complete. Uniqueness is established in the case when one of the two monotone graphs is assumed to be Lipschitz continuous.
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