Abstract The aim of this paper is to study a quasistatic frictional contact problem for viscoelastic materials with long-term memory. The contact boundary conditions are governed by Tresca’s law, involving a slip dependent coefficient of friction. We focus our attention on the weak solvability of the problem within the framework of variational inequalities. The existence of a solution is obtained under a smallness assumption on a normal stress prescribed on the contact surface and on the coefficient of friction. The proof is based on a time discretization method, compactness and lower semicontinuity arguments.

中文翻译：

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长记忆粘弹性材料的准静态摩擦接触问题

摘要 本文的目的是研究具有长时记忆的粘弹性材料的准静态摩擦接触问题。接触边界条件受 Tresca 定律约束，涉及滑动相关摩擦系数。我们将注意力集中在变分不等式框架内问题的弱可解性上。解的存在是在对接触表面规定的法向应力和摩擦系数的小假设下获得的。该证明基于时间离散化方法、紧凑性和下半连续性参数。