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Mathematics and Mechanics of Solids
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The Numerical Computation of the Critical Boundary Displacement for Radial Cavitation

Pablo V. Negrón-Marrero

Department of Mathematics, University of Puerto Rico, Humacao, PR 00791-4300, Puerto Rico

Jeyabal Sivaloganathan

Department of Mathematical Sciences, University of Bath, Bath, UK

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.

Key Words: nonlinear elasticity • calculus of variations • cavitation • computation

This version was published on November 1, 2009

Mathematics and Mechanics of Solids, Vol. 14, No. 8, 696-726 (2009)
DOI: 10.1177/1081286508089845
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