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- W2740137584 abstract "In [5], a general approach is suggested for such problems. This approach to investigation of the initial stage of fracture within the linearized theory of deformable bodies currently seems to be most acceptable both because of its sufficient rigor and because of its generality for different models of materials. In [6, 7], a review is given of papers in which problems have been solved in the linearized formulation for different geometric schemes for the location of cracks, and values have been obtained for the breaking loads for different models of the materials. However, we should note that within the indicated approach, up to now only those problems have been investigated in which cracks in the material are located exclusively in planes along which compression of the material occurs [8]. In this paper, we investigate the question of fracture of an infinite material containing a crack of finite dimensions, located on a circular cylindrical surf.ace, under axial compression conditions. As an example, we consider such a crack in an incompressible hyperelastic body, i.e., in a body for which there exists an elastic potential which is specified as a function of the invariants �9 (11, 12) ~[ll(Ai, Az), I2(A,, A2)] = W(At, Az) [3]. We will model the crack, as in fracture mechanics, as a mathematical discontinuity. Furthermore, we will consider only the initial stage of fracture, and contact of the crack edges is not considered here. We also note that relatively few investigations have been carried out for the considered crack geometry even in the linear formulation [10-14]. 1. We will use a cylindrical coordinate system (r, 0, x3). In this coordinate system, let a circular cylindrical crack of radius b and length 2a occupy the region {r b, 0 < 0 < 2x, -a ~ x3 < a}. In the case of compression of the material along the directrixes of the cylindrical crack, a homogeneous subcritical stress-strain state arises in the material [4] 5~ S~=S~ (S~ u~ ,3j. (~/- 1 ) x; ~., cr ~, ~'2 ~ ~', 0.~ < 1 );" @default.
- W2740137584 created "2017-08-08" @default.
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- W2740137584 date "1996-01-01" @default.
- W2740137584 modified "2023-09-26" @default.
- W2740137584 title "FRACTURE OF AN INFINITE INCOMPRF.~SIBLE HYPER- ELASTIC MATERIAL UNDER COMPRESSION ALONG A CYLINDRICAL CRACK" @default.
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