Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Asymmetric equilibrium configurations of hyperelastic cylindrical bodies under symmetric dead loads


Author: Angelo Marcello Tarantino
Journal: Quart. Appl. Math. 64 (2006), 605-615
MSC (2000): Primary 73G05, 73G10, 73H05
DOI: https://doi.org/10.1090/S0033-569X-06-01018-6
Published electronically: November 13, 2006
MathSciNet review: 2284462
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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.


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Additional Information

DOI: https://doi.org/10.1090/S0033-569X-06-01018-6
Keywords: Finite elasticity, bifurcation, and stability.
Received by editor(s): December 8, 2004
Published electronically: 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
Article copyright: © Copyright 2006 Brown University
The copyright for this article reverts to public domain 28 years after publication.


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