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Abstract <p>The problem of a transverse displacement plane with two pairs of two-periodic (corresponding to the <i>X</i> and <i>Y</i> axes) cohesive cracks of unequal size, weakened by two-periodic round holes, is considered. The circular holes are filled with reinforcing fibers. Boundary problems between the filler and the matrix and along cohesive cracks are defined. The solution to the problem is sought in the form of an analytical function of a complex variable. A system of unequal algebraic equations is found along the holes, and singular integral equations are constructed along the cohesive cracks, which are reduced to a finite linear algebraic system of equations using mathematical transformations. Both systems are solved jointly by the Gaussian method, and crack growth is determined by the formulas for the stress intensity factor at the crack tips. The stress intensity factors are found by changing the crack length depending on the radius of the round holes. A 3D model has been constructed.</p>

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Transverse Shear of a Piecewise-Homogeneous Elastic Medium in the Case When the Binder and Inclusions Are Weakened by Cohesive Cracks

  • 期刊论文

  • 发表日期：

    2025年11月26日

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  • R. K. Mekhtiev,
  • Yu. A. Tanryverdiev

摘要

Abstract

The problem of a transverse displacement plane with two pairs of two-periodic (corresponding to the X and Y axes) cohesive cracks of unequal size, weakened by two-periodic round holes, is considered. The circular holes are filled with reinforcing fibers. Boundary problems between the filler and the matrix and along cohesive cracks are defined. The solution to the problem is sought in the form of an analytical function of a complex variable. A system of unequal algebraic equations is found along the holes, and singular integral equations are constructed along the cohesive cracks, which are reduced to a finite linear algebraic system of equations using mathematical transformations. Both systems are solved jointly by the Gaussian method, and crack growth is determined by the formulas for the stress intensity factor at the crack tips. The stress intensity factors are found by changing the crack length depending on the radius of the round holes. A 3D model has been constructed.