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Analysis of a dynamic frictional contact problem with damage

机译：带有损伤的动摩擦接触问题分析

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This work studies variationally and numerically a dynamic problem which models the bilateral frictional contact between a viscoelastic body and a foundation. A regularized version of Tresca's law is employed to model the friction. Material damage, which results from tension or compression, is taken into account in the constitutive law and its evolution is described by a nonlinear parabolic partial differential equation. The problem is formulated as a coupled system of a nonlinear variational equation for the velocity field and an evolutionary nonlinear variational equation for the damage field. The existence of a unique solution is established. The proof uses a priori estimates and the theory of evolution equations for pseudomonotone operators. A fully discrete numerical scheme is introduced, by using the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. Error estimates are derived and. under suitable regularity assumptions, the linear convergence of the numerical scheme obtained. Finally, the results of simulations of three two-dimensional examples are presented.
机译：这项工作以变化和数值方式研究了一个动态问题，该问题模拟了粘弹性体与基础之间的双边摩擦接触。使用Tresca定律的正规化模型来模拟摩擦。在本构定律中考虑了由拉力或压缩引起的物质破坏，并通过非线性抛物线偏微分方程描述了其发展。该问题被表述为速度场的非线性变分方程和损伤场的演化非线性变分方程的耦合系统。建立了唯一解决方案的存在。证明使用先验估计和伪单调算子的演化方程理论。介绍了一种完全离散的数值方案，方法是使用有限元方法近似空间变量，并使用Euler方案离散时间导数。得出误差估计值。在适当的规律性假设下，数值方案的线性收敛。最后，给出了三个二维实例的仿真结果。

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