Abstract A finite element model for the effect of wear on thermoelastic instability (TEI) is developed by combining the equations of thermoelasticity, the classical wear law, along with the conforming contact conditions. The method is based on a two-dimensional, frictional sliding model with a bimaterial interface and a simplified geometry of finite thickness. An assumption of the solution in the perturbation form leads to a quadratic eigenvalue problem. The existing analytical solutions for two half planes are employed to validate the numerical solutions for several representative scenarios, including a limiting case in the absence of wear. The analytical solutions are also sought for the special cases when one of the materials is a nonconductor and when the two materials are identical, for the purpose of comparison. In general, good agreements between the numerical and analytical approaches have been obtained. However, the discrepancies exist when the wear rates of the two materials are close to each other and when the wear rates are significantly greater than the critical rate. It is confirmed through this study that wear may suppress or amplify the effect of TEI depending on the thermomechanical properties of the materials, which is consistent with the recent research findings on the same topic via an analytical approach.

中文翻译：

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磨损对摩擦激发热弹性不稳定性的影响：一种有限元方法

摘要 通过结合热弹性方程、经典磨损定律以及符合的接触条件，建立了磨损对热弹性不稳定性 (TEI) 影响的有限元模型。该方法基于具有双材料界面和有限厚度的简化几何形状的二维摩擦滑动模型。扰动形式的解的假设导致二次特征值问题。两个半平面的现有解析解用于验证几种代表性场景的数值解，包括没有磨损的极限情况。当一种材料为非导体且两种材料相同时，也为特殊情况寻求解析解，以便进行比较。一般来说，数值方法和分析方法之间取得了良好的一致性。然而，当两种材料的磨损率彼此接近且磨损率显着大于临界率时，就会存在差异。通过这项研究证实，磨损可能会抑制或放大 TEI 的影响，具体取决于材料的热机械性能，这与最近通过分析方法对同一主题的研究结果一致。