Nonconvex Inequality Models for Contact Problems of Nonsmooth Mechanics

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This review paper deals with selected nonsmooth and nonconvex inequality problems for dynamic frictional contact between a viscoelastic body and a foundation. The process is modeled by general nonmonotone possibly multivalued multidimensional Clarke subdifferential contact boundary conditions. The problems of frictional contact with both short and long memory, thermoviscoelastic frictional contact, bilateral frictional contact and bilateral contact for piezoelectric materials with adhesion are considered. The formulations and results on existence, and uniqueness of solutions are presented.