Abstract
In the theory of nonlinear elasticity of rubber-like materials, if a homogeneous isotropic compressible material is described by a strain–energy function that is a homogeneous function of the principal stretches, then the equations of equilibrium for axisymmetric deformations reduce to a separable first-order ordinary differential equation. For a particular class of such strain–energy functions, this property is used to obtain a general parametric solution to the equilibrium equation for plane strain bending of cylindrical sectors. Specification of the arbitrary function that appears in such strain–energy functions yields some parametric solutions. In some cases, the parameter can be eliminated to yield closed-form solutions in implicit or explicit form. Other possible forms for the arbitrary constitutive function that are likely to yield such solutions are also indicated.
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Horgan, C.O., Murphy, J.G. Plane Strain Bending of Cylindrical Sectors of Admissible Compressible Hyperelastic Materials. J Elasticity 81, 129–151 (2005). https://doi.org/10.1007/s10659-005-9010-8
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DOI: https://doi.org/10.1007/s10659-005-9010-8
Key words
- compressible isotropic nonlinearly elastic materials
- homogeneous strain-energy functions
- plane strain bending of cylindrical sectors
- parametric and closed-form solutions