Estimating the critical radius for radially symmetric cavitation
Author:
C. A. Stuart
Journal:
Quart. Appl. Math. 51 (1993), 251-263
MSC:
Primary 73G05; Secondary 73C50
DOI:
https://doi.org/10.1090/qam/1218367
MathSciNet review:
MR1218367
Full-text PDF Free Access
References |
Similar Articles |
Additional Information
- 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
- C. A. Stuart, Special problems involving uniqueness and multiplicity in hyperelasticity, Nonlinear functional analysis and its applications (Maratea, 1985) NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 173, Reidel, Dordrecht, 1986, pp. 131–145. MR 852573
F. Meynard, Cavitation radiale d’un milieu hyperélastique isotrope et homogène, thèse No. 89, École Polytechnique Fédérale Lausanne, 1990
- François Meynard, Existence and nonexistence results on the radially symmetric cavitation problem, Quart. Appl. Math. 50 (1992), no. 2, 201–226. MR 1162272, DOI https://doi.org/10.1090/qam/1162272
- 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
- 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
- Paolo Marcellini, The stored-energy for some discontinuous deformations in nonlinear elasticity, Partial differential equations and the calculus of variations, Vol. II, Progr. Nonlinear Differential Equations Appl., vol. 2, Birkhäuser Boston, Boston, MA, 1989, pp. 767–786. MR 1034028
- Paolo Marcellini, Nonconvex integrals of the calculus of variations, Methods of nonconvex analysis (Varenna, 1989) Lecture Notes in Math., vol. 1446, Springer, Berlin, 1990, pp. 16–57. MR 1079758, DOI https://doi.org/10.1007/BFb0084930
J. E. Marsen, and T. J. R. Hughes, Mathematical Foundations of Elasticity, Prentice Hall, Englewood Cliffs, NJ, 1983
- 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. W. Ogden, Large deformation isotropic elasticity: on the correlation of theory and experiment for compressible rubberlike solids, Proc. Roy. Soc. London A328, 567–583 (1972)
- C. O. Horgan, Void nucleation and growth for compressible non-linearly elastic materials: an example, Internat. J. Solids Structures 29 (1992), no. 3, 279–291. MR 1138336, DOI https://doi.org/10.1016/0020-7683%2892%2990200-D
C. A. Stuart, Radially symmetric cavitation for hyperelastic materials, Ann. Inst. H. Poincaré 2, 33–66 (1985)
---, Special problems involving uniqueness and multiplicity in hyperelasticity, Nonlinear Functional Analysis and Its Applications, (S. P. Singh, ed.), Reidel, Dordrecht, 1986
F. Meynard, Cavitation radiale d’un milieu hyperélastique isotrope et homogène, thèse No. 89, École Polytechnique Fédérale Lausanne, 1990
---, Existence and nonexistence results on the radially symmetric cavitation problem, Quart. J. Appl. Math. 50, 201–226 (1992)
J. M. Ball, Discontinuous equilibrium solutions and cavitation in nonlinear elasticity, Philos. Trans. Roy Soc. London A306, 557–611 (1982)
J. Sivaloganathan, A field theory approach to stability of radial equilibria in nonlinear elasticity, Math. Proc. Cambridge Philos. Soc. 99, 586–604 (1986)
P. Marcellini, The stored-energy for some discontinuous deformations in nonlinear elasticity, Partial Differential Equations and the Calculus of Variation, Vol. II, (F. Colombini et al, eds.), Birkhäuser, Basel, 1989, pp. 767–786
---, Nonconvex integrals of the calculus of variations, Methods of Nonconvex Analysis, (A. Cellina, ed.), Lecture Notes in Math. vol. 1446, Springer-Verlag, 1990, pp. 16–57
J. E. Marsen, and T. J. R. Hughes, Mathematical Foundations of Elasticity, Prentice Hall, Englewood Cliffs, NJ, 1983
R. James and S. J. Spector, The formation of filamentary voids in solids, J. Mech. Phys. Solids 39, 783–813 (1991)
R. W. Ogden, Large deformation isotropic elasticity: on the correlation of theory and experiment for compressible rubberlike solids, Proc. Roy. Soc. London A328, 567–583 (1972)
C. O. Horgan, Void nucleation and growth for compressible non-linearly elastic materials: an example, Internat. J. Solids Structures 29, 279–291 (1992)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
73G05,
73C50
Retrieve articles in all journals
with MSC:
73G05,
73C50
Additional Information
Article copyright:
© Copyright 1993
American Mathematical Society
