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Asymmetric equilibrium configurations of hyperelastic cylindrical bodies under symmetric dead loads
Author(s):
Angelo
Marcello
Tarantino
Journal:
Quart. Appl. Math.
64
(2006),
605-615.
MSC (2000):
Primary 73G05, 73G10, 73H05
Posted:
November 13, 2006
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Abstract:
Homogeneous deformations provided by the nonlinear equilibrium problem of symmetrically loaded isotropic hyperelastic cylindrical bodies are investigated. Depending on the form of the stored energy function, the problem considered may admit asymmetric solutions, besides the expected symmetric solutions. For general compressible materials, the mathematical condition allowing the assessment of these asymmetric solutions, which describe the global path of equilibrium branches, is given. Explicit expressions for evaluating critical loads and bifurcation points are derived. Results and basic relations obtained for general isotropic materials are then specialized for a Mooney-Rivlin and a neo-Hookean material. A broad numerical analysis is performed and the qualitatively more interesting asymmetric equilibrium branches are shown. The influence of the constitutive parameters is discussed, and, using the energy criterion, a number of considerations are carried out concerning the stability of the equilibrium solutions.
References:
-
- 1.
- L.R.G. Treloar, Stress-strain data for vulcanized rubber under various type of deformation. Trans. Faraday Soc. 40, 59-70 (1944)
- 2.
- E.A. Kearsley, Asymmetric stretching of a symmetrically loaded elastic sheet. Int. J. Solid. Struct. 22, 111-119 (1986)
- 3.
- G.P. MacSithigh, Energy-minimal finite deformations of a symmetrically loaded elastic sheet. Quart. J. Mech. Appl. Math. 39, Pt 1, 111-123 (1986) MR 0827704 (87d:73036)
- 4.
- R.W. Ogden, On the stability of asymmetric deformations of a symmetrically-tensioned elastic sheet. Int. J. Engng. Sci. 25, 1305-1314 (1987) MR 0912604 (88i:73034)
- 5.
- Y.C. Chen, Stability of homogeneous deformations of an incompressible elastic body under dead-load surface tractions. J. Elasticity 17, 223-248 (1987) MR 0888317 (88d:73030)
- 6.
- Y.C. Chen, Bifurcation and stability of homogeneous deformations of an elastic body under dead-load tractions with
 symmetry. J. Elasticity 25, 117-136 (1991) MR 1111363 (92e:73023) - 7.
- H. W. Haslach Jr, Constitutive models and singularity types for an elastic biaxially loaded rubber sheet. Math. Mech. Solids 5, 41-73 (2000) MR 1740047 (2001h:74011)
- 8.
- A. M. Tarantino, Asymmetric Equilibrium Configurations of Symmetrically Loaded Isotropic Square Membranes. J. Elasticity 69, 73-97 (2002) MR 2020511 (2004i:74072)
- 9.
- R. W. Ogden, Local and global bifurcation phenomena in plane-strain finite elasticity. Int. J. Solid Struct. 21, 121-132 (1985)
- 10.
- R. W. Ogden, On nonuniqueness in the traction boundary-value problem for a compressible elastic solid. Quart. Appl. Math. 42, 337-344 (1984) MR 0757172 (85f:73058)
- 11.
- P. G. Ciarlet, Mathematical Elasticity. Vol. I: Three-Dimensional Elasticity. North-Holland, 1988 MR 0936420 (89e:73001)
- 12.
- R. S. Rivlin, Large elastic deformations of isotropic materials, IV. Further developments of the general theory. Phil. Trans. Roy. Soc. London A 241, 379-397 (1948) MR 0027674 (10:340b)
- 13.
- R. W. Ogden, Large deformation isotropic elasticity: On the correlation of theory and experiment for compressible rubberlike solids. Proc. Roy. Soc. London A 328, 567-583 (1972)
- 14.
- J. M. Ball, Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rational Mech. Anal. 63, 337-403 (1977) MR 0475169 (57:14788)
- 15.
- P. G. Ciarlet and G. Geymonat, Sur les lois de comportement en élasticité nonlinéaire compressible. C.R. Acad. Sci. Paris Sér. II 295, 423-426 (1982) MR 0695540 (84c:73013)
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Additional Information:
PII:
S0033-569X-06-01018-6
Keywords:
Finite elasticity,
bifurcation,
and stability.
Received by editor(s):
December 8, 2004
Posted:
November 13, 2006
Additional Notes:
Dipartimento di Ingegneria Meccanica e Civile, Università degli Studi di Modena e Reggio Emilia, via Vignolese 905 -- 41100 Modena, Italy
Copyright of article:
Copyright
2006,
Brown University
The copyright for this article reverts to public domain after 28 years from publication.
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