Asymmetric equilibrium configurations of hyperelastic cylindrical bodies under symmetric dead loads

Tarantino, Angelo

doi:10.1090/S0033-569X-06-01018-6

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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