A Finite Strain Analysis of Cavity Formation at a Rigid Inhomogeneity |
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Authors: | Alan J Levy |
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Affiliation: | (1) Department of Mechanical, Aerospace and Manufacturing Engineering, Syracuse University, Syracuse, New York, U.S.A. |
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Abstract: | The formation of a cavity by inclusion-matrix interfacial separation is examined by analyzing the response of a plane rigid
inclusion embedded in an unbounded incompressible matrix subject to remote equibiaxial dead load traction. A vanishingly thin
interfacial cohesive zone, characterized by normal and tangential interface force-separation constitutive relations, is assumed
to govern separation behavior. Rotationally symmetric cavity shapes (circles) are shown to be solutions of an interfacial
integral equation depending on the strain energy density of the matrix, the interface force constitutive relation and the
remote loading. Nonsymmetrical cavity formation, under rotationally symmetric conditions of geometry and loading, is treated
within the theory of infinitesimal strain superimposed on a given finite strain state. Rotationally symmetric and nonsymmetric
bifurcations are analyzed and detailed results, for the Mooney–Rivlin strain energy density and for an exponential interface
force-separation law, are presented. For the nonsymmetric rigid body displacement mode, a simple formula for the critical
load is presented. The effect on bifurcation behavior of interfacial shear stiffness and other interface parameters is treated
as well. In particular we demonstrate that (i) for the smooth interface nonsymmetric bifurcation always precedes rotationally
symmetric bifurcation, (ii) unlike rotationally symmetric bifurcation, there is no threshold value of interface parameter
for which nonsymmetric bifurcation will not occur and (iii) interfacial shear may significantly delay the onset of nonsymmetric
bifurcation. Also discussed is the range of validity of a nonlinear infinitesimal strain theory previously presented by the
author (Levy 1]).
This revised version was published online in July 2006 with corrections to the Cover Date. |
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Keywords: | nonlinear elasticity cavity nucleation interfacial debonding and decohesion inclusion problem bifurcation problem |
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