Abstract The aim of this work is to study a class of dynamic contact problems coupling adhesion and friction between two viscoelastic bodies with nonlinear viscosity operators. The boundary conditions concern relaxed unilateral contact, pointwise friction and adhesion including possible recoverable behavior. A mixed variational formulation of these problems is given as a five-field evolution implicit equation coupled with a differential inclusion describing the evolution of the intensity of adhesion. Based on several estimates and a classical fixed point theorem for multivalued functions, the existence of a strong variational solution is proved.

中文翻译：

---

具有粘附力和摩擦力的动态粘弹性问题的混合变分公式

摘要 这项工作的目的是研究一类具有非线性粘度算子的耦合两个粘弹性体之间的粘附和摩擦的动态接触问题。边界条件涉及松弛的单边接触、逐点摩擦和粘附，包括可能的可恢复行为。这些问题的混合变分公式被给出为一个五场演化隐式方程，加上一个描述粘附强度演化的微分包含。基于多值函数的若干估计和经典不动点定理，证明了强变分解的存在性。