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<p>In this paper, a plane strain problem for an interface nano-sized crack located on a boundary between two semi-planes is studied. The boundaries of the crack possess surface energy in the Steigmann-Ogden form. Using the integral transforms of the stresses and the displacements, the problem is reduced to a system of four singular integro-differential equations with additional tip conditions. The system is further regularized by reduction to a system of Fredholm equations of the second kind, and the existence and uniqueness of the solution is discussed. The numerical solution is obtained by utilizing approximations of the unknown functions based on the Chebyshev polynomials. The computational examples are discussed and the comparison with known results is made.</p>

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An interface crack between two elastic semi-planes in the presence of surface energy

  • 期刊论文

  • 发表日期：

    2026年4月1日

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  • Anna Y. Zemlyanova

摘要

In this paper, a plane strain problem for an interface nano-sized crack located on a boundary between two semi-planes is studied. The boundaries of the crack possess surface energy in the Steigmann-Ogden form. Using the integral transforms of the stresses and the displacements, the problem is reduced to a system of four singular integro-differential equations with additional tip conditions. The system is further regularized by reduction to a system of Fredholm equations of the second kind, and the existence and uniqueness of the solution is discussed. The numerical solution is obtained by utilizing approximations of the unknown functions based on the Chebyshev polynomials. The computational examples are discussed and the comparison with known results is made.