The numerical computation of the critical boundary displacement for radial cavitation

Reference:

Negron-Marrero, P. V. and Sivaloganathan, J., 2009. The numerical computation of the critical boundary displacement for radial cavitation. Mathematics and Mechanics of Solids, 14 (8), pp. 696-726.

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Official URL:

http://dx.doi.org/10.1177/1081286508089845

Abstract

We study radial solutions of the equations of isotropic elasticity in two dimensions (for a disc) and three dimensions (for a sphere). We describe a numerical scheme for computing the critical boundary displacement for cavitation based on the solution of a sequence of initial value problems for punctured domains. We give examples for specific materials and compare our numerical computations with some previous analytical results. A key observation in the formulation of the method is that the strong-ellipticity condition implies that the specification of the normal component of the Cauchy stress on an inner pre-existing but small cavity, leads to a relation for the radial strain as a function of the circumferential strain. To establish the convergence of the numerical scheme we prove a monotonicity property for the inner deformed radius for punctured balls.

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