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Spatial problem of crack theory for a prestressed incompressible elastic layer

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Abstract

The three-dimensional elasticity problem of loading the shores of an elliptic crack by normal pressure keeping the crack in the open state is considered. The crack is located in the midplane of a layer under the action of a preliminary finite deformation in the direction of the crack symmetry axes. The model of incompressible neo-Hookean material is considered. The two-dimensional integral Fourier transformis used to reduce the problem to a singular integro-differential equation of the first kind for the crack opening function. An asymptotic solution of the problem is constructed in the form of an expansion in two parameters characterizing the relative thickness of the layer and the difference between the coefficients of the preliminary finite deformation. It is shown that the initial stress does not change the order of the stress field singularity near the crack edge and influences only the normal stress intensity factor. The influence of the layer thickness and the preliminary stress parameters on the intensity of normal stresses in the crack plane is investigated.

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Authors and Affiliations

  1. Don State Technical University, pl. Gagarina 1, Rostov-on-Don, 344000, Russia

    I. M. Peshkhoev & B. V. Sobol

Authors
  1. I. M. Peshkhoev
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  2. B. V. Sobol
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Correspondence to I. M. Peshkhoev.

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Original Russian Text © I.M. Peshkhoev, B.V. Sobol, 2015, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2015, No. 3, pp. 136–145.

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Peshkhoev, I.M., Sobol, B.V. Spatial problem of crack theory for a prestressed incompressible elastic layer. Mech. Solids 50, 345–352 (2015). https://doi.org/10.3103/S0025654415030103

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