A frictionless contact problem with adhesion and damage in elasto-viscoplasticity (Q957944)

The quasistatic, adhesive and frictionless contact problem is studied for an elasto-viscoplastic material with damate. The adhesion on the contact surface is modelled by an internal variable. A system of a variational inequality for the mechanical problem with unilateral contact, an includion of parabolic type for the damage field and an integro-differential equation for the bonding field is formulated. Existence of a weak solution is proved by means of monotonicity and fixed-point arguments. The model is of practical interest. The paper presents a mathematical investigation of the problem (existence of a solution). The studied model is based on nonsmooth thermomechanical theories and monotonicity arguments. Further material related to this study can be found in \textit{P.D. Panagiotopoulos} [Inequality problems in mechanics and applications. Convex and nonconvex energy functions. Boston - Basel - Stuttgart: Birkhäuser. (1985; Zbl 0579.73014)], \textit{M. Frémond} [Non-smooth thermomechanics. Berlin: Springer (2002; Zbl 0990.80001)] and \textit{M. Sofonea, W. Han, M. Shillor} [Analysis and approximation of contact problems with adhesion and damage. Pure and Applied Mathematics 276. Boca Raton, FL: Chapman \& Hall/ CRC.(2006; Zbl 1089.74004)]