三维幂律梯度弹性固体的切向接触：一般理论及其在部分滑移中的应用
Tangential contacts of three-dimensional power-law graded elastic solids: A general theory and application to partial slip
AI总结：
本文提出三维幂律梯度弹性固体切向接触的一般理论，基于Mossakovskii-Jäger过程推导闭式解，包含非轴对称位移分量，并应用于抛物线形接触，研究材料梯度和泊松比对耗散能量密度的影响。
摘要：
本文提出了一种求解任意几何形状的三维幂律梯度弹性固体之间切向接触的严格理论。对于多个接触，例如两个名义上平坦但粗糙的半空间之间发生的接触，建立了著名的Ciavarella-Jäger定理，并讨论了切向耦合问题。然而，本工作的重点是轴对称单接触在任意单向切向载荷下的情况，基于Mossakovskii-Jäger过程推导出了闭式解析解。与常见近似方法的结果相比，这些解包含了切向位移的非轴对称分量，这对于准确确定相对滑移分量以及部分滑移状态下摩擦能耗散的表面密度至关重要。尽管在计算耗散能量密度时采用了简化方法，但在均质材料极限情况下的结果与完整数值计算的结果非常吻合。作为应用实例，推导了抛物线形幂律梯度弹性固体在部分滑移状态下切向接触的完整解，并研究了材料梯度以及泊松比对耗散能量表面密度的影响。
英文摘要：
A rigorous theory for solving tangential contacts between three-dimensional power-law graded elastic solids of arbitrary geometry is presented. For multiple contacts such as those occurring between two nominally flat but rough half-spaces, the well-known Ciavarella-Jäger theorem is established accompanied by a discussion of tangential coupling. Nevertheless, the focus of the work is on axisymmetric single contacts under arbitrary unidirectional tangential loading, for which closed-form analytical solutions are derived based on the Mossakovskii-Jäger procedure. In comparison to the results of common approximate methods, the solutions include the non-axisymmetric components of tangential displacements, which are indispensable for the accurate determination of the relative slip components and thus the surface density of frictional energy dissipation in the partial slip regime. Although a simplified approach is used for the calculation of the dissipated energy density, the results in the limiting case of homogeneous material are in excellent agreement with those from a full numerical computation. As an application example, the complete solutions for the tangential contact of parabolically shaped power-law graded elastic solids in the partial slip regime are derived and the influence of the material gradient as well as Poisson's ratio on the surface density of dissipated energy is investigated.
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