周期性粗糙赫兹接触中的应力集中：赫兹到软平冲过渡
Stress concentration in periodically rough hertzian contact: Hertz to soft-flat-punch transition
摘要：
我们报告的弹性接触之间的球面透镜和图案化的基板，由一个六角形晶格的圆柱形支柱。通过数值方法（离散格林函数叠加法和迭代对分法）得到了应力场和接触区的大小。对于小的压痕，从赫兹到Boussinesq-Cerruti-like行为的过渡被观察到时，由支柱覆盖的基板的表面分数增加。特别是，我们提出了一个主曲线定义的两个无量纲参数，它允许预测的应力在接触区域的中心的支柱所占据的表面分数。极限接触制度之间的过渡，赫兹和Boussinesq-Cerruti的，很好地描述了一个合理的功能。此外，一个简单的模型来描述之间的Boussines-Cerruti接触的镜头和一个单一的弹性支柱，它考虑到支柱的几何形状和两个机构的弹性性能，提出。
英文摘要：
We report on the elastic contact between a spherical lens and a patterned substrate, composed of an hexagonal lattice of cylindrical pillars. The stress field and the size of the contact area are obtained by means of numerical methods (discrete Green's function superposition and iterative bisection-like methods). For small indentations, a transition from a Hertzian to a Boussinesq-Cerruti-like behavior is observed when the surface fraction of the substrate that is covered by pillars is increased. In particular, we present a master curve defined by two dimensionless parameters, which allows to predict the stress at the center of contact region in terms of the surface fraction occupied by pillars. The transition between the limiting contact regimes, Hertzian and Boussinesq-Cerruti-like, is well described by a rational function. Additionally, a simple model to describe the Boussines-Cerruti-like contact between the lens and a single elastic pillar, which takes into account the pillar geometry and the elastic properties of the two bodies, is presented.
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