On the stability of cavitating equilibria

Author:
J. Sivaloganathan

Journal:
Quart. Appl. Math. **53** (1995), 301-313

MSC:
Primary 73C50; Secondary 49J45, 73G05, 73H99, 73V25

DOI:
https://doi.org/10.1090/qam/1330654

MathSciNet review:
MR1330654

Full-text PDF Free Access

References | Similar Articles | Additional Information

**[1]**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)**[2]**J. M. Ball,*Constitutive inequalities and existence theorems in nonlinear elastostatics*, Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, Vol. 1 (R. J. Knops, ed.), Pitman, London, 1977, pp. 187-241**[3]**J. M. Ball,*Discontinuous equilibrium solutions and cavitation in nonlinear elasticity*, Philos. Trans. Roy. Soc. London Ser. A**306**, 557-611 (1982)**[4]**J. M. Ball, J. C. Currie, and P. J. Olver,*Null Lagrangians, weak continuity and variational problems of arbitrary order*, J. Funct. Anal.**41**, 135-174 (1981)**[5]**J. M. Ball and F. Murat,*-Quasiconvexity and variational problems for multiple integrals*, J. Funct. Anal.**58**, 225-253 (1984)**[6]**J. M. Ball and F. Murat,*Remarks on rank-one convexity and quasiconvexity*, Ordinary and Partial Differential Equations, Vol. III, Dundee, 1990; Pitman Research Notes Ser.**254**, 25-37 (1991)**[7]**P. G. Ciarlet,*Mathematical Elasticity, Vol*. 1:*Three-Dimensional Elasticity*, North Holland, Amsterdam, 1988**[8]**C. O. Horgan,*Void nucleation and growth for compressible nonlinearly elastic materials: an example*, Internat. J. Solids Structures**29**, 279-291 (1992)**[9]**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)**[10]**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)**[11]**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)**[12]**R. D. James and S. J. Spector,*The formation of filamentary voids in solids*, J. Mech. Phys. Sol.**39**, 783-813 (1991)**[13]**R. D. James and S. J. Spector,*Remarks on -quasiconvexity, interpenetration of matter, and function spaces for elasticity*, Ann. Inst. H. Poincaré-Anal. nonlinéaire**9**, 263-280 (1992)**[14]**C. B. Morrey,*Multiple Integrals in the Calculus of Variations*, Springer-Verlag, Berlin, 1965**[15]**F. Meynard,*Cavitation dans un milieu hyperelastique*, Thése de Doctorat, École Polytechnique Federale de Lausanne, 1990**[16]**F. Meynard,*Existence and nonexistence results on the radially symmetric cavitation problem*, Quart. Appl. Math.**50**, 201-226 (1992)**[17]**K. A. Pericak-Spector and S. J. Spector,*Nonuniqueness for a hyperbolic system: cavitation in nonlinear elastostatics*, Arch. Rational Mech. Anal.**101**, 293-317 (1988)**[18]**J. Sivaloganathan,*Cavitation, the incompressible limit, and material inhomogeneity*, Quart. Appl. Math.**49**, 521-541 (1991)**[19]**J. Sivaloganathan,*The generalised Hamilton-Jacobi inequality and the stability of equilibria in nonlinear elasticity*, Arch. Rational Mech. Anal.**107**, 347-369 (1989)**[20]**J. Sivaloganathan,*Implications of rank-one convexity*, Ann. Inst. H. Poincaré Anal. Non Linéaire**5**, 99-118 (1988)**[21]**J. Sivaloganathan,*Uniqueness of regular and singular equilibria for spherically symmetric problems of nonlinear elasticity*, Arch. Rational Mech. Anal.**96**, 96-136 (1986)**[22]**J. Sivaloganathan,*A field theory approach to stability of equilibria in radial elasticity*, Math. Proc. Cambridge Philos. Soc.**99**, 589-604 (1986)**[23]**C. A. Stuart,*Radially symmetric cavitation for hyperelastic materials*, Ann. Inst. H. Poincaré Anal. Non Linéaire**2**, 33-66 (1985)**[24]**C. Truesdell and W. Noll,*The non-linear field theories of mechanics*, Handbuch der Physik III/3, Springer-Verlag, Berlin, 1965

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Additional Information

DOI:
https://doi.org/10.1090/qam/1330654

Article copyright:
© Copyright 1995
American Mathematical Society