TY - JOUR

T1 - The numerical computation of the critical boundary displacement for radial cavitation

AU - Negron-Marrero, P V

AU - Sivaloganathan, J

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=70350765155&partnerID=8YFLogxK

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

U2 - 10.1177/1081286508089845

DO - 10.1177/1081286508089845

M3 - Article

VL - 14

SP - 696

EP - 726

JO - Mathematics and Mechanics of Solids

JF - Mathematics and Mechanics of Solids

SN - 1081-2865

IS - 8

ER -