论文标题
三维幂律分级弹性固体的切向接触：一种一般理论和对部分滑移的应用
Tangential contacts of three-dimensional power-law graded elastic solids: A general theory and application to partial slip
论文作者
论文摘要
提出了一种严格的理论，用于解决任意几何形状的三维幂律分级弹性固体之间的切向接触。对于多个触点，例如在两个名义上平坦但粗糙的半个空间之间发生的触点，众所周知的ciavarella-jäger定理伴随着对切向耦合的讨论。然而，这项工作的重点是在任意单向切向载荷下的轴对称单触点上，根据Mossakovskii-Jäger程序，为此得出了封闭形式的分析解决方案。与共同近似方法的结果相比，解决方案包括切向位移的非轴对称成分，对于准确确定相对滑移成分，因此是必不可少的，因此在部分滑移状态下摩擦能量耗散的表面密度是必不可少的。尽管一种简化的方法用于计算消散的能量密度，但同质材料的限制情况下的结果与完整的数值计算的结果非常吻合。作为一个应用示例，得出了部分滑移状态中抛物面幂律分级弹性固体的切向接触的完整解决方案，并研究了材料梯度以及泊松比对消散能的表面密度的影响。
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.
