A new class of quasistatic frictional contact problems governed by a variational–hemivariational inequality. (December 2019) - Migórski, Stanisław; Gamorski, Piotr
Abstract: A quasistatic nonsmooth frictional contact problem for a viscoelastic material is studied. The contact is modeled by a multivalued normal damped response condition with the Clarke generalized gradient of a locally Lipschitz superpotential and the friction is described by a version of the Coulomb law of dry friction with the friction bound depending on the regularized normal stress. The weak formulation of the contact problem is a history-dependent variational–hemivariational inequality coupled with an operator equation for the stress field. A result on the unique weak solvability to this coupled system is proved through a recent contribution on history-dependent subdifferential inclusions and a fixed point approach. Highlights: New model in contact mechanics. Multivalued contact conditions depending on each other. Existence and uniqueness of a local solution. Application of existence and uniqueness result to real world problems.