Cavitation, the incompressible limit, and material inhomogeneity

Sivaloganathan, J.

doi:10.1090/qam/1121684

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

Stuart S. Antman and Pablo V. Negrón-Marrero, The remarkable nature of radially symmetric equilibrium states of aeolotropic nonlinearly elastic bodies, J. Elasticity 18 (1987), no. 2, 131–164. MR 905811, DOI https://doi.org/10.1007/BF00127554
J. M. Ball, Discontinuous equilibrium solutions and cavitation in nonlinear elasticity, Philos. Trans. Roy. Soc. London Ser. A 306 (1982), no. 1496, 557–611. MR 703623, DOI https://doi.org/10.1098/rsta.1982.0095

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
C. O. Horgan and T. J. Pence, Cavity formation at the center of a composite incompressible nonlinearly elastic sphere, Trans. ASME J. Appl. Mech. 56 (1989), no. 2, 302–308. MR 1001749, DOI https://doi.org/10.1115/1.3176084
C. O. Horgan and T. J. Pence, Void nucleation in tensile dead-loading of a composite incompressible nonlinearly elastic sphere, J. Elasticity 21 (1989), no. 1, 61–82. MR 995580, DOI https://doi.org/10.1007/BF00040934
Richard D. James and Scott J. Spector, The formation of filamentary voids in solids, J. Mech. Phys. Solids 39 (1991), no. 6, 783–813. MR 1120242, DOI https://doi.org/10.1016/0022-5096%2891%2990025-J
R. J. Knops and C. A. Stuart, Quasiconvexity and uniqueness of equilibrium solutions in nonlinear elasticity, Arch. Rational Mech. Anal. 86 (1984), no. 3, 233–249. MR 751508, DOI https://doi.org/10.1007/BF00281557
K. A. Pericak-Spector and Scott J. Spector, Nonuniqueness for a hyperbolic system: cavitation in nonlinear elastodynamics, Arch. Rational Mech. Anal. 101 (1988), no. 4, 293–317. MR 930330, DOI https://doi.org/10.1007/BF00251490
P. Podio-Guidugli, G. Vergara-Caffarelli, and E. G. Virga, Discontinuous energy minimizers in nonlinear elastostatics: an example of J. Ball revisited, J. Elasticity 16 (1986), no. 1, 75–96. MR 835366, DOI https://doi.org/10.1007/BF00041067

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
J. Sivaloganathan, The generalised Hamilton-Jacobi inequality and the stability of equilibria in nonlinear elasticity, Arch. Rational Mech. Anal. 107 (1989), no. 4, 347–369. MR 1004715, DOI https://doi.org/10.1007/BF00251554
J. Sivaloganathan, Implications of rank one convexity, Ann. Inst. H. Poincaré Anal. Non Linéaire 5 (1988), no. 2, 99–118 (English, with French summary). MR 954467
C. A. Stuart, Radially symmetric cavitation for hyperelastic materials, Ann. Inst. H. Poincaré Anal. Non Linéaire 2 (1985), no. 1, 33–66 (English, with French summary). MR 781591
Kewei Zhang, Polyconvexity and stability of equilibria in nonlinear elasticity, Quart. J. Mech. Appl. Math. 43 (1990), no. 2, 215–221. MR 1059004, DOI https://doi.org/10.1093/qjmam/43.2.215