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1.
Alan J. Levy 《Journal of Elasticity》2001,64(2-3):131-156
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. 相似文献
2.
This paper presents an analysis of the torsion of a solid or annular circular cylinder consisting of nonlinear material in the form of an elastic matrix with embedded unidirectional elastic fibers parallel to the cylinder axis. The specific class of composite considered is one for which nonlinear fiber-matrix interface slip is captured by uniform cohesive zones of vanishing thickness. Previous work on the effective antiplane shear response of this material leads to a stress–strain relation depending on the interface slip together with an integral equation governing its evolution. Here, we obtain an approximate single mode solution to the integral equation and utilize it to solve the torsion problem. Equations governing the radial distributions of shear stress and interface slip are obtained and formulae for torque–twist rate are presented. The existence of singular surfaces, i.e., surfaces across which the slip and the shear stress experience jump discontinuities are analyzed in detail. Specific results are presented for an interface force law that allows for interface failure in shear. 相似文献
3.
The purpose of this research is to investigate the effects of material inhomogeneity on the decay of Saint-Venant end effects
in linear isotropic elasticity. This question is addressed within the context of anti-plane shear deformations of an inhomogeneous
isotropic elastic solid. The mathematical issues involve the effects of spatial inhomogeneity on the decay rates of solutions
to Dirichlet or Neumann boundary-value problems for a second-order linear elliptic partial differential equation with variable
coefficients on a semi-infinite strip. The elastic coefficients are assumed to be smooth functions of the transverse coordinate.
The estimated rate of exponential decay with distance from the loaded end (a lower bound for the exact rate of decay) is characterized
in terms of the smallest positive eigenvalue of a Sturm–Liouville problem with variable coefficients. Analytic lower bounds
for this eigenvalue are used to obtain the desired estimated decay rates. Numerical techniques are also employed to assess
the accuracy of the analytic results. A related eigenvalue optimization question is discussed and its implications for the
issue of material tailoring is addressed. The results of this paper are applicable to continuously inhomogeneous materials
and, in particular, to functionally graded materials.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献