On the behavior of rotating thick-walled cylinders made of hyperelastic materials

Abstract

This paper focuses on the behavior of rotating thick-walled cylinders made of the rubber-like materials. These materials are characterized by high deformability which their stress-stretch curves are arranged in the range of S-shaped to J-shaped forms. Here, it is considered an Ogden-type model with only integer powers to give a satisfactory correspondence with experimental results over wide ranges of different types of deformation. This type of constitutive model is mathematically simple and can provide the foundation of existence of a closed-form solution for the boundary value problems in the finite deformation elasticity. In this study, as an application, the Ogden-type strain energy density with only integer powers is applied to a rotating thick-walled cylinder made of the hyperelastic materials. It is shown that this constitutive model gives a closed-form solution, not involving the integral form, for the stress distribution through the wall thickness. Also, the results predicted from classic strain energy density models (Mooney-Rivlin, Neo-Hookean and Varga) and the Ogden-type model are compared for (i) a solid circular cylinder under rotation, (ii) a rotating circular cylinder with a concentric circular rigid inclusion, (iii) a rotating cylinder shrink-fitted to a rigid spindle and (iv) an unconstrained cylinder under rotation. These comparisons are done in order to investigate the accuracy of the simplification carried out by applying the well-known classic models instead of the Ogden-type model. It is concluded that this simplification is allowable if the classic models can follow the test data to some acceptable extent. While, the classic models are not capable to analyze an unconstrained rotating cylinder when experiences large deformations. Finally, influence of different parameters such as wall thickness, presence of the axial pre-stretch and form of mechanical behavior or strain-stiffening behavior of the rubber utilized in cylinders examined on stability of an unconstrained rotating cylinder.