An analytical temperature-dependent collocation model for preloaded rubber cylinders

Abstract

The non-linear temperature-dependent stiffness of an axially preloaded rubber cylinder is examined by an analytical collocation model, where influences of temperature, cylinder diameter and length, material parameters and prestrain are investigated. The rubber is assumed to be incompressible with the deviatoric response determined by an extended neo-Hookean free energy function, embodying a temperature shift function, being directly proportional to the temperature and to the temperature-dependent rubber density. The model is based on a semi-inverse method where the motion is split into two deformations: the first, a homogeneous temperature expansion, while the second, a preload deformation where material planes parallel to the bonded metal plate in the rubber cylinder are assumed to remain parallel, with the boundary conditions on the free rubber surface satisfied by collocation. The stiffness depends strongly on the preload—particularly for larger diameter-length ratios—and on the temperature covering —60 to + 60° C, where the shift function factor directly proportional to the temperature is found to play the greatest role. Contrary to other semi-inverse models, this model coincides at vanishing preloads with a well-known linear formula while extending the applicable shape factor range to cover shape factors typically found for vibration isolators.