On the optimal location of singularities arising in variational problems of nonlinear elasticity

Journal of Elasticity

Volumn 58, Issue 3, 2000, Pages 191-224

  Sivaloganathan, Jeyabal ^a   Spector, Scott J ^b  

^a University of Bath   (United Kingdom)

^b Southern Illinois University Carbondale   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CAVITATION; DEFORMATION; ELASTICITY; FRACTURE; VARIATIONAL TECHNIQUES;

NONLINEAR ELASTICITY;

ELASTOMERS;

EID: 0034461032     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007629229174     Document Type: Article

References (17)

1. J.M. Ball, Discontinuous equilibrium solutions and cavitation in nonlinear elasticity. Phil. Trans. Roy. Soc. London A 306 (1982) 557-611.
2. J.M. Ball, Minimisers and the Euler-Lagrange equations. In: P.G. Ciarlet and M. Roseau (eds), Trends and Applications of Pure Mathematics to Mechanics, Springer, Berlin (1984) pp. 1-4.
3. P. Baumann, N.C. Owen and D. Phillips, Maximum principles and apriori estimates for a class of problems from nonlinear elasticity. Ann. Inst. H. Poincaré Anal. Nonlinéaire 8 (1991) 119-157.
4. G. DelPiero, Some properties of the set of fourth-order tensors, with application to elasticity. J. Elasticity 9 (1979) 245-261.
5. A.E. Green, On some general formulae in finite elastostatics. Arch. Rational Mech. Anal. 50 (1973) 73-80.
6. C.O. Horgan and D.A. Polignone, Cavitation in nonlinearly elastic solids: A review. Appl. Mech. Rev. 48 (1995) 471-485.
7. J.P. Jaric, On the representation of symmetric isotropic 4-tensors. J. Elasticity 51 (1998) 73-79.
8. R.J. Knops and C.A. Stuart, Quasiconvexity and uniqueness of equilibrium solutions in nonlinear elasticity. Arch. Rational Mech. Anal. 86 (1984) 233-249.
9. A.E.H. Love, A Treatise on the Mathematical Theory of Elasticity. Cambridge Univ. Press, 1927.
10. A.I. Lur'e, Three-Dimensional Problems of the Theory of Elasticity. Interscience, 1964.
11. F. Meynard, Existence and non-existence results on the radially symmetric cavitation problem. Quart. J. Appl. Math. 50 (1992) 201-226.
12. S. Müller and S.J. Spector, An existence theory for nonlinear elasticity that allows for cavitation. Arch. Rational Mech. Anal. 131 (1995) 1-66.
13. J. Sivaloganathan and S.J. Spector, On the existence of minimizers with prescribed singular points in nonlinear elasticity. J. Elasticity 59 (2000) 83-113.
14. J. Sivaloganathan, On the stability of cavitating equilibria. Quart. Appl. Math. 53 (1995) 301-313.
15. J. Sivaloganathan, Uniqueness of regular and singular equilibria for spherically symmetric problems of nonlinear elasticity. Arch. Rational Mech. Anal. 96 (1986) 96-136.
16. C.A. Stuart, Radially symmetric cavitation for hyperelastic materials. Ann. Inst. H. Poincaré Anal. Nonlinéaire 2 (1985) 33-66.
17. W. Thomson (Lord Kelvin), Dynamical problems regarding elastic spheroidal shells and spheroids of incompressible liquid. Phil. Trans. Roy. Soc. London 153 (1863) 583-616.