Abstract This paper develops a simple theoretical model for the adhesive contact between a rigid sphere and a circular membrane radially stretched by constant tension. The adhesive stress between the surfaces in front of the contact edge is approximated by a constant value within a finite length. The mutual relations between net external force, contact radius, and contact displacement are obtained analytically. In particular, the critical contact responses at pull-off force and at zero external force are presented as functions of a dimensionless adhesion range parameter, respectively. It is demonstrated that the general solution can completely quantify the transition from the DMT-type limit to the JKR-type limit. These results might be helpful for the advancement of adhesion mechanics of thin membranes.

中文翻译：

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使用 Dugdale 模型的刚性球体和拉伸膜之间的粘附

摘要 本文开发了一个简单的理论模型，用于刚性球体和由恒定张力径向拉伸的圆形膜之间的粘附接触。接触边缘前表面之间的粘合应力近似为有限长度内的常数值。解析得到净外力、接触半径和接触位移之间的相互关系。特别是，在拉断力和零外力下的临界接触响应分别表示为无量纲粘附范围参数的函数。证明了通用解可以完全量化从 DMT 型极限到 JKR 型极限的转变。这些结果可能有助于薄膜粘附力学的进步。