The Existence Problems of Solutions for a Class of Differential Variational–Hemivariational Inequality Problems

In this work, we used reflexive Banach spaces to study the differential variational—hemivariational inequality problems with constraints. We established a sequence of perturbed variational–hemivariational constraints and penalty coefficients. Then, for each inequality, proved unique solvability convergence solutions problems. Following that, proposed mathematical model viscoelastic rod in unilateral contact equilibrium, where unknowns were displacement field history deformation. abstract method analysis provided corresponding mechanical interpretations.