The problem of a mode I crack having multiple contacts between the crack faces is considered. In the case of small contact islands of arbitrary shapes, which are arbitrarily located inside the crack, the first-order asymptotic model for the crack opening displacement is constructed using the method of matched asymptotic expansions. The case of a penny-shaped crack has been studied in detail. A scaling hypothesis for the compliance reduction factor is formulated.

中文翻译：

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一种在裂纹面之间具有多个理想接触岛的裂纹模式：渐近模型

考虑了裂纹面之间具有多个接触的模式 I 裂纹的问题。在裂纹内部任意形状的小接触岛情况下，采用匹配渐近展开法构建裂纹张开位移的一阶渐近模型。已经详细研究了便士形裂缝的情况。制定了合规性降低因子的缩放假设。