Asymmetric equilibrium configurations of hyperelastic cylindrical bodies under symmetric dead loads. (English) Zbl 1115.74010

Tarantino, Angelo Marcello

Q. Appl. Math. 64, No. 4, 605-615 (2006).

Summary: We investigate homogeneous deformations provided by nonlinear equilibrium problems of symmetrically loaded isotropic hyperelastic cylindrical bodies. Depending on the form of the stored energy function, the problems considered may admit asymmetric solutions, besides the expected symmetric solutions. For general compressible materials, we give a mathematical condition allowing the assessment of these asymmetric solutions which describe the global path of equilibrium branches. Explicit expressions for evaluating critical loads and bifurcation points are derived. Results and basic relations obtained for general isotropic materials are then specialized for Mooney-Rivlin and neo-Hookean material. A broad numerical analysis is performed, and the qualitatively more interesting asymmetric equilibrium branches are shown. The influence of constitutive parameters is discussed, and, using the energy criterion, a number of considerations are carried out concerning the stability of the equilibrium solutions.

MSC:

74B20

Nonlinear elasticity

Keywords:

critical loads; bifurcation points; energy criterion

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