损伤粘弹性接触问题半变分不等式的数值研究
Numerical Studies of a Hemivariational Inequality for a Viscoelastic Contact Problem with Damage
摘要：
研究了粘弹性体与刚性地基间拟静态摩擦接触的半变分不等式。损伤效应通过损伤函数的抛物型微分包含引入到模型中。给出了解的存在唯一性结果.本文提出了一种全离散格式，损伤函数的时间导数用向后有限差分近似，空间导数用有限元近似。当速度和位移变量采用线性元，损伤函数采用分段常数时，导出了全离散格式的最优阶误差估计。数值例子的模拟结果显示的性能的全离散计划和理论预测的收敛阶。
英文摘要：
This paper is devoted to the study of a hemivariational inequality modeling the quasistatic bilateral frictional contact between a viscoelastic body and a rigid foundation. The damage effect is built into the model through a parabolic differential inclusion for the damage function. A solution existence and uniqueness result is presented. A fully discrete scheme is introduced with the time derivative of the damage function approximated by the backward finite different and the spatial derivatives approximated by finite elements. An optimal order error estimate is derived for the fully discrete scheme when linear elements are used for the velocity and displacement variables, and piecewise constants are used for the damage function. Simulation results on numerical examples are reported illustrating the performance of the fully discrete scheme and the theoretically predicted convergence orders.
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