On the Consequences of Limiting Chain Extensibility of Vulcanized Rubbers: Stiffening, Self-Homogenization, and Coupling of Strain Components

Abstract

Large deformation behavior of vulcanized rubbers is generally studied within the context of hyperelasticity. Various hyperelastic models have been proposed in the literature based either on continuum mechanics principles or on the molecular considerations of network chains of rubbers. As a phenomenological continuum-mechanical model with two well-defined parameters, Gent model has been shown to predict the large deformation of rubbers fairly well. Gent model constrains the first invariant of the left Cauchy—Green deformation tensor to a limiting maximum value and recovers the well-known neo-Hookean model as a subset. Albeit a phenomenological model, this feature of the Gent model accounts for the limiting or finite chain extensibility of network chains. In the last decade, various homogeneous and inhomogeneous deformation modes were analyzed using the Gent model. All these efforts mainly point to the stiffening effect of the limiting chain extensibility. In this article, helical shearing deformation of a homogeneous, isotropic, incompressible hollow rubber tube is analyzed with a view toward identifying other potential qualitative features of the Gent model predictions. This fundamental analysis has demonstrated that the presence of limiting chain extensibility in rubbers results in a homogenization of the strain field as well as in a coupling of various strain components, while stiffening the rubber and increasing the stresses.