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

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