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The stressed state in a neighborhood of a plane crack whose border has points of negative curvature

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Abstract

Using the example of a plane crack bounded by the limaçon of Pascal we study the influence of the points of negative curvature on the stressed state of a body in a neighborhood of border of the crack. It is shown that under tensile loads the damage of the body begins in a neighborhood of such points. In the case of shear loads prescribed on the edges of the crack damage of the body begins in a neighborhood of points of the border farthest from the points of negative curvature.

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Literature cited

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    G. C. Kit and M. V. Khai, “The integral equations of three-dimensional problems of thermoelasticity for bodies with cracks,”Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 12, 1108–1112 (1975).

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    M. V. Khai and I. V. Kalynyak, “On an approach to the numerical solution of problems of the mathematical theory of cracks,”Mat Met. i Fiz.-Mekh. Polya, No. 20, 38–42 (1984).

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    G. P. Cherepanov,The Mechanics of Brittle Breakage [in Russian], Nauka, Moscow (1974).

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Additional information

Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 33, 1991, pp. 83–90.

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Kalynyak, I.V. The stressed state in a neighborhood of a plane crack whose border has points of negative curvature. J Math Sci 65, 1893–1899 (1993). https://doi.org/10.1007/BF01097312

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Keywords

  • Stressed State
  • Tensile Load
  • Shear Load
  • Negative Curvature
  • Plane Crack