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<p>Within the framework of the three-dimensional linearized theory of stability of deformable bodies, a plane static problem of compression of a semibounded body (foundation) with a thin coating layer along a crack located in the foundation material parallel to the straight interface between two different materials for elastic potentials corresponding to the case of equal roots of the respective characteristic equations has been investigated. Analytical-numerical approach is proposed that allows reducing the original boundary-value problem stated in terms of potential harmonic functions to the eigenvalue problem for the system of the Fredholm integral equations of the first kind and the additional condition obtained in general form for a wide class of combinations of two different materials. For compressible materials with a harmonic-type potential, the critical values of the load parameter have been determined, and their dependence on the geometric, physical and mechanical parameters of the problem has been analyzed.</p>

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Fracture of Piecewise-Homogeneous Half-Plane Under Compression Along Crack not Located at Interface

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • O. L. Kipnis

摘要

Within the framework of the three-dimensional linearized theory of stability of deformable bodies, a plane static problem of compression of a semibounded body (foundation) with a thin coating layer along a crack located in the foundation material parallel to the straight interface between two different materials for elastic potentials corresponding to the case of equal roots of the respective characteristic equations has been investigated. Analytical-numerical approach is proposed that allows reducing the original boundary-value problem stated in terms of potential harmonic functions to the eigenvalue problem for the system of the Fredholm integral equations of the first kind and the additional condition obtained in general form for a wide class of combinations of two different materials. For compressible materials with a harmonic-type potential, the critical values of the load parameter have been determined, and their dependence on the geometric, physical and mechanical parameters of the problem has been analyzed.