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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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).
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).
G. P. Cherepanov,The Mechanics of Brittle Breakage [in Russian], Nauka, Moscow (1974).
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
- Stressed State
- Tensile Load
- Shear Load
- Negative Curvature
- Plane Crack