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<p>A&#xa0;two-dimensional problem of fracture mechanics about the compression of a&#xa0;piecewise homogeneous semi-infinite body with a&#xa0;boundary fixed in a&#xa0;special way along a&#xa0;near-surface interface crack is studied. The analytical-numerical approach proposed within the framework of the three-dimensional linearized stability theory of deformable bodies consists of reducing the original boundary value problem to an eigenvalue problem for a&#xa0;system of Fredholm first-kind integral equations. For the case when the constituent materials of the body are described by the Bartenev–Khazanovich elastic potential and the ratio of their rigidities does not exceed a&#xa0;certain value, the value of the critical load parameters corresponding to the local loss of stability of the material in the vicinity of the crack at the initial stage of fracture is calculated.</p>

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Investigation of the compression of a piecewise homogeneous half-plane with a fixed boundary along the interface crack

  • 期刊论文

  • 发表日期：

    2025年5月1日

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  • A. L. Kipnis

摘要

A two-dimensional problem of fracture mechanics about the compression of a piecewise homogeneous semi-infinite body with a boundary fixed in a special way along a near-surface interface crack is studied. The analytical-numerical approach proposed within the framework of the three-dimensional linearized stability theory of deformable bodies consists of reducing the original boundary value problem to an eigenvalue problem for a system of Fredholm first-kind integral equations. For the case when the constituent materials of the body are described by the Bartenev–Khazanovich elastic potential and the ratio of their rigidities does not exceed a certain value, the value of the critical load parameters corresponding to the local loss of stability of the material in the vicinity of the crack at the initial stage of fracture is calculated.