Non-elliptic deformation field near the tip of a mixed-mode crack in a compressible hyperelastic material |
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Authors: | CQ Ru |
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Institution: | Department of Mechanical Engineering, University of Alberta, Edmonton, Alta. Canada T6G 2G8 |
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Abstract: | This paper gives an asymptotic analysis of the deformation field near the tip of an arbitrary mixed-mode crack in a compressible hyperelastic harmonic material which loses ellipticity at sufficiently large deformations. It is found that the near-tip deformation field is characterized by a localized non-elliptic deformation band issuing from the crack-tip and bounded by two curves of discontinuous deformation gradient. Explicit expression for the near-tip deformation field is obtained both inside and outside the localized deformation band. In particular, a simple relation is derived that determines the orientation of the deformation band in terms of two complex governing parameters of the near-tip fields inside and outside the deformation band, respectively. |
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Keywords: | Ellipticity Finite elasticity Mixed-mode crack |
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