On the construction of stress discontinuity lines for a two-dimensional plastic region
Автор: Evtikhov D.O., Yakhno A.N., Savostyanova I.L.
Журнал: Siberian Aerospace Journal @vestnik-sibsau-en
Рубрика: Informatics, computer technology and management
Статья в выпуске: 3 vol.23, 2022 года.
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The paper considers the plasticity equations in case of two dimensions and the construction of stress discontinuity lines. The construction of stress discontinuity lines is based on the fact that they are located at the intersection point of lines of the same family (characteristics) and are directed along the bisector of the angle formed by these characteristics. Therefore, to find these lines, we constructed characteristics. Such a problem is easier to solve in case of plastic torsion, then there is only one characteristic, it is directed along the normal to the outer contour, and finding the sliding lines and their intersection points is quite simple. Consequently, most of the works devoted to the construction of stress discontinuity lines solve the problem of plastic torsion for isotropic and anisotropic media. For problems of plane strain of plastic ma-terial, this method is not sufficiently developed. This is due to the complexity of constructing sliding lines for such problems and the presence of two families of sliding lines. In this paper, we construct a homotopy of two known exact solutions: that of Prandtl and of Nadai, that is, a continuous transformation of one solution into another. In this case, one can observe the evolution of characteristics that depend on the group parameter a: for a = 1, the characteristics of the Prandtl solution are obtained; at a = 0, the characteristics of the Nadai solution, at a = 0.5, the characteristics of one fami-ly begin to intersect and lines of stress discontinuity appear. These lines are constructed in this paper.
Stress discontinuity line, plasticity equations, homotopy of solutions
Короткий адрес: https://sciup.org/148329634
IDR: 148329634 | DOI: 10.31772/2712-8970-2022-23-3-364-371
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