<p style='text-indent:20px;'>In this paper, we study a frictional contact model which takes into account the damage and the memory. The deformable body consists of a viscoelastic material and the process is assumed to be quasistatic. The mechanical damage of the material which caused by the tension or the compression is included in the constitutive law and the damage function is modelled by a nonlinear parabolic inclusion. Then the variational formulation of the model is governed by a coupled system consisting of a history-dependent hemivariational inequality and a nonlinear parabolic variational inequality. We introduce and study a fully discrete scheme of the problem and derive error estimates for numerical solutions. Under appropriate solution regularity assumptions, an optimal order error estimate is derived for the linear finite element method. Several numerical experiments for the contact problem are given for providing numerical evidence of the theoretical results.</p>

中文翻译：

---

带损伤记忆的摩擦接触问题的数值分析与模拟

<p style='text-indent:20px;'>本文研究了一种兼顾损伤和记忆的摩擦接触模型。可变形体由粘弹性材料组成，并且假定该过程是准静态的。由拉伸或压缩引起的材料的机械损伤包含在本构定律中，损伤函数采用非线性抛物线包含建模。然后模型的变分公式由一个耦合系统控制，该系统由一个与历史相关的半变分不等式和一个非线性抛物变分不等式组成。我们介绍并研究了该问题的完全离散方案，并得出数值解的误差估计。在适当的解规律性假设下，为线性有限元法导出了最优阶误差估计。给出了接触问题的几个数值实验，为理论结果提供了数值证据。</p>