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The penny-shaped crack problem for a finitely deformed incompressible elastic solid

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Abstract

In this paper the theory of small deformations superposed on large is used to examine the axisymmetric problem of a penny-shaped crack located in an incompressible elastic infinite solid which is subjected to a uniform finite radial stretch. The small axisymmetric deformations are due to a uniform stress applied in the axial direction. Formal integral expressions are derived for the displacements and stresses in the elastic solid. An exact expression is developed for critical stress necessary for the propagation of a penny-shaped crack in a finitely deformed elastic solid.

Résumé

Dans le mémoire, on utilise la théorie des petites déformations superposées à de larges déformations pour examiner le problètrique d'une fissure en disque noyée dans un solide élastique infini incompressible soumis à un étirement uniforme fini radial. Les déformations axisymétriques de faible amplitude sont dues à une contrainte uniforme appliquée suivant la direction axiale. Des expressions intégrales formelles sont déduites des déplacements et des contraintes dans le solide élastique. Une expression exacte relative à la contrainte critique nécessaire pour la propagation d'une fissure en forme de disque est développée dans le cas d'un solide élastique déformé de manière finie.

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Authors and Affiliations

  1. Department of Civil Engineering, Carleton University, Ottawa, Canada

    A. P. S. Selvadurai

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  1. A. P. S. Selvadurai
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Selvadurai, A.P.S. The penny-shaped crack problem for a finitely deformed incompressible elastic solid. Int J Fract 16, 327–333 (1980). https://doi.org/10.1007/BF00018237

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  • DOI: https://doi.org/10.1007/BF00018237

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