Abstract

The contact problem of a cylindrical indenter and gradient medium is considered with allowance for adhesion forces between surfaces of contacting bodies. An analytical solution of the problem is found for the case of a gradient medium with a power dependence of the elastic modulus on the normal coordinate. The case of incompressible media with a Poisson ratio of 1/2 is described in detail. It is shown that the behavior of the system in this case can qualitatively differ from the case of homogeneous media. The influence of the surface roughness, which is modeled in the form of axisymmetric waviness is considered. Special attention is paid to the contact between a parabolic indenter and a gradient medium; the differences from the case of a cylinder are shown.

中文翻译：

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具有高梯度指数的不可压缩梯度介质的刚性压头和弹性半空间之间的粘附

摘要

考虑到圆柱体压头和梯度介质的接触问题，要考虑到接触体表面之间的粘附力。对于梯度介质具有弹性模量在法向坐标上具有幂依赖性的梯度介质，可以找到该问题的解析解。详细描述了泊松比为1/2的不可压缩介质的情况。结果表明，在这种情况下，系统的行为在质量上与均质介质的情况不同。考虑以轴对称波纹形式建模的表面粗糙度的影响。要特别注意抛物线压头和梯度介质之间的接触。显示了与圆柱体情况的区别。