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On the contact of two plates one of which has a crack. (Russian) Zbl 0895.73060

The author investigates the contact of two plates one of which has a vertical crack up to the external boundary. The crack is described as a surface in \(\mathbb{R}^3\) by the relations \(y = \psi(x)\), \(x\in [0,1]\), \(-\varepsilon\leq z\leq \varepsilon\), \(2\varepsilon\) is the crack thickness, \(\psi\in H^3_0(0,1)\). The author proves solvability of the problem and studies a functional which describes the crack opening.

MSC:

74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
74K20 Plates