Localized shear discontinuities near the tip of a mode I crack |
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Authors: | Rohan Abeyaratne Jae-Sung Yang |
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Institution: | (1) Department of Mechanical Engineering, Massachusetts Institute of Technology, 02139 Cambridge, MA, USA;(2) College of Engineering, Michigan State University, 48824 East Lansing, MI, USA |
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Abstract: | In this paper we study the deformation and stress fields near the tip of a crack under plane strain mode I conditions. A fully nonlinear theory of finite deformations is used and the material, which is assumed to be homogeneous, isotropic, incompressible and elastic, is characterized by its stress-strain behavior in simple shear. For the class of materials considered the governing system of differential equations may lose ellipticity at sufficiently severe strains. The analysis is based on a direct asymptotic calculation. The results involve two curves, issuing from each crack-tip, across which the deformation gradient, the effective shear and the stresses are discontinuous. |
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