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The finite anti-plane shear field near the tip of a crack for a class of incompressible elastic solids

Knowles, James K. (1977) The finite anti-plane shear field near the tip of a crack for a class of incompressible elastic solids. International Journal of Fracture, 13 (5). pp. 611-639. ISSN 0376-9429.

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The present paper is concerned with an infinite slab containing a crack and deformed at infinity to a state of finite simple shear. The material of the slab is taken to be homogeneous, isotropic, elastic, and incompressible, and is further assumed to belong to a class of materials which admit nontrivial states of anti-plane shear. The analysis is carried out for the fully nonlinear equilibrium theory of finite elasticity. The stress field near the crack-tips is studied in detail; one of the special materials considered is such that the shear stresses near a crack tip remain bounded, despite the presence of unbounded displacement gradients. An analogy between the crack problem in finite anti-plane shear and the problem of transonic flow of a gas past a flat plate is pointed out and discussed.

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Additional Information:© 1977 Noordhoff International Publishing. Received July 30, 1976. The results communicated in this paper were obtained in the course of an investigation supported under Contract N00014-75-C-0196 between the California Institute of Technology and the Office of Naval Research. The author acknowledges the many helpful comments of Eli Sternberg during the preparation of the manuscript.
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Office of Naval Research (ONR)N00014-75-C-0196
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ID Code:59037
Deposited By: Tony Diaz
Deposited On:28 Jul 2015 18:17
Last Modified:28 Jul 2015 18:17

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