In this work, we analyze a non-clamped dynamic viscoelastic contact problem involving thermal effect. The friction law is described by a non-monotone relation between the tangential stress and the tangential velocity. This leads to a system of second-order inclusion for displacement and a parabolic equation for temperature. We provide a fully discrete approximation of the problem and find optimal error estimates without any smallness assumption on the data. The theoretical result is illustrated by numerical simulations.

翻译：本文分析了一个涉及热效应的非夹持动态粘弹性接触问题。摩擦规律由切向应力与切向速度之间的非单调关系描述。这导致了一个关于位移的二阶包含系统和关于温度的抛物型方程。我们提供了该问题的全离散近似，并在无需数据小量假设的情况下得到了最优误差估计。数值模拟验证了理论结果。