Cavitation, the incompressible limit, and material inhomogeneity
Author:
J. Sivaloganathan
Journal:
Quart. Appl. Math. 49 (1991), 521-541
MSC:
Primary 73G05; Secondary 73B27, 73C50, 73H99
DOI:
https://doi.org/10.1090/qam/1121684
MathSciNet review:
MR1121684
Full-text PDF Free Access
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Additional Information
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A. N. Gent and P. B. Lindley, Internal rupture of bonded rubber cylinders in tension, Proc. Roy. Soc. London Ser. A 249, 195–205 (1958)
- C. O. Horgan and R. Abeyaratne, A bifurcation problem for a compressible nonlinearly elastic medium: growth of a microvoid, J. Elasticity 16 (1986), no. 2, 189–200. MR 849671, DOI https://doi.org/10.1007/BF00043585
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J. Sivaloganathan, Cavitation in nonlinear elasticity and related problems, Ph.D. thesis, Heriot-Watt University, 1984
- Jeyabal Sivaloganathan, Uniqueness of regular and singular equilibria for spherically symmetric problems of nonlinear elasticity, Arch. Rational Mech. Anal. 96 (1986), no. 2, 97–136. MR 853969, DOI https://doi.org/10.1007/BF00251407
- J. Sivaloganathan, A field theory approach to stability of radial equilibria in nonlinear elasticity, Math. Proc. Cambridge Philos. Soc. 99 (1986), no. 3, 589–604. MR 830370, DOI https://doi.org/10.1017/S0305004100064513
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S. S. Antman and P. V. Negron-Marrero, The remarkable nature of radially symmetric equilibrium states of aelotropic nonlinearly elastic bodies, J. Elasticity 18, 131–164 (1987)
J. M. Ball, Discontinuous equilibrium solutions and cavitation in nonlinear elasticity, Philos. Trans. Roy. Soc. London Ser. A 306, 557–611 (1982)
A. N. Gent and P. B. Lindley, Internal rupture of bonded rubber cylinders in tension, Proc. Roy. Soc. London Ser. A 249, 195–205 (1958)
C. O. Horgan and R. Abeyaratne, A bifurcation problem for a compressible nonlinearly elastic medium: growth of a microvoid, J. Elasticity 16, 189–200 (1986)
C. O. Horgan and T. J. Pence, Cavity formation at the center of a composite incompressible nonlinearly elastic sphere, J. Appl. Mech. 56, 302–308 (1989)
C. O. Horgan and T. J. Pence, Void nucleation in tensile loading of a composite incompressible nonlinearly elastic sphere, J. Elasticity 21, 61–82 (1989)
R. D. James and S. J. Spector, The formation of filamentary voids in solids, IMA preprint, no. 572, University of Minnesota, 1989
R. J. Knops and C. A. Stuart, Quasiconvexity and uniqueness of equilibrium solutions in nonlinear elasticity, Arch. Rational Mech. Anal. 86, 233–249 (1984)
K. A. Pericak-Spector and S. J. Spector, Nonuniqueness for a hyperbolic system: cavitation in nonlinear elastodynamics, Arch. Rational Mech. Anal. 101, 293–317 (1988)
P. Podio-Guidugli, G. Vergara Caffarelli, and E. G. Virga, Discontinuous energy minimisers in nonlinear elastostatics: an example of J. Ball revisited, J. Elasticity 16, 75–96 (1986)
J. Sivaloganathan, Cavitation in nonlinear elasticity and related problems, Ph.D. thesis, Heriot-Watt University, 1984
J. Sivaloganathan, Uniqueness of regular and singular equilibria for spherically symmetric problems of nonlinear elasticity, Arch. Rational Mech. Anal. 96, 97–136 (1986)
J. Sivaloganathan, A field theory approach to stability of equilibria in radial elasticity, Math. Proc. Cambridge Philos. Soc. 99, 589–604 (1986)
J. Sivaloganathan, The generalised Hamilton-Jacobi inequality and the stability of equilibria in nonlinear elasticity, Arch. Rational Mech. Anal. 107, 347–369 (1989)
J. Sivaloganathan, Implications of rank-one convexity, Ann. Inst. H. Poincaré Anal. non linéaire 5, no. 4, 99–118 (1988)
C. A. Stuart, Radially symmetric cavitation for hyperelastic materials, Ann. Inst. H. Poincaré Anal. non linéaire 2, 33–66 (1985)
K. Zhang, Polyconvexity and stability of equilibria in nonlinear elasticity, Quart. Mech. Appl. Math. 43, 215–221 (1990)
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Article copyright:
© Copyright 1991
American Mathematical Society