We obtain the solution of a plane problem of the theory of elasticity on the phenomenon of “healing” of a crack in an anisotropic body. By using the model of Winkler’s base, this problem is reduced to a singular integrodifferential equation for the displacements of points of the crack surface. In the case of a defect in the form of flattened ellipse, we obtain the exact analytic solution of the problem. The limit equilibrium state of the plate with a filled crack is estimated by using the energy criterion. We also determine the optimal strength of the injection material after hardening (maximizing the strength of the plate).

中文翻译：

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各向异性体中裂纹的修复

我们得到了弹性理论关于各向异性体裂纹“愈合”现象的平面问题的解。利用Winkler基模型，将该问题简化为裂纹表面点位移的奇异积分微分方程。对于扁平椭圆形式的缺陷，我们获得了问题的精确解析解。使用能量准则估计具有填充裂纹的板的极限平衡状态。我们还确定了硬化后注射材料的最佳强度（最大限度地提高板的强度）。