Mathematical aspects of non-linear fracture mechanics
Mathematical aspects of non-linear fracture mechanics
A mathematical analysis of the behaviour of the displacement field near the tip of a crack in a non-linear elastic material under antiplane strain deformation provides a criterion for the existence of a crack tip opening displacement. The theory is confirmed by the results of a conventional finite difference analysis of a finite cracked plate. The uneconomic nature of this numerical method prompts the question as to how the knowledge gained from the mathematics of the problem may be used to provide a more efficient process. This is obtained by removing the known singular behaviour of the stresses near a crack tip from the finite difference approximation. The resulting numerical solution is then an approximation to a continuous andd continuously differentiable function.
University of Southampton
1976
Tilley, David Ronald
(1976)
Mathematical aspects of non-linear fracture mechanics.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
A mathematical analysis of the behaviour of the displacement field near the tip of a crack in a non-linear elastic material under antiplane strain deformation provides a criterion for the existence of a crack tip opening displacement. The theory is confirmed by the results of a conventional finite difference analysis of a finite cracked plate. The uneconomic nature of this numerical method prompts the question as to how the knowledge gained from the mathematics of the problem may be used to provide a more efficient process. This is obtained by removing the known singular behaviour of the stresses near a crack tip from the finite difference approximation. The resulting numerical solution is then an approximation to a continuous andd continuously differentiable function.
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Published date: 1976
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Local EPrints ID: 458281
URI: http://eprints.soton.ac.uk/id/eprint/458281
PURE UUID: c5d8401f-76fb-4a82-85d2-bb7db81c7400
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Date deposited: 04 Jul 2022 16:46
Last modified: 04 Jul 2022 16:46
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Author:
David Ronald Tilley
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