Elastic behaviour of rubber cylinders under combined torsion and tension loading

Abstract

Rivlin derived an elastic solution for the problem of a rubber cylinder subjected to combinations of tension and torsion. The theory correctly predicts the experimentally observed behaviour where the length of the cylinder increases as a twist is applied and conversely there is a reduction in the moment resulting from the application of an additional tensile loading. This problem is of interest for two reasons. First, the reduction in axial force with twist is second order by virtue of the change in the axial force being a symmetric function of the square of the twist angle. Therefore, the problem makes a demanding test of the applicability of the finite element method at solving this large strain elasticity problem. Second, the Rivlin elasticity solution could in principle be applied to any form of stored energy function. As a result, it is a useful test of the validity of different stored energy functions. Also, this test geometry has been examined previously by the authors to investigate any anisotropic changes in the viscoelastic behaviour in rubber with prestrain and it is important to validate the elastic solutions for this work.

Modelling of elastomeric materials and products

“…Previous papers [9][10][11] have examined the elastic behaviour of rubber components and these have also identified the limitation when trying to predict the behaviour of real components. In this special edition Luo et al 12 have adopted these various approaches to give a practical guide on how to use a finite element design methodology to not only predict the behaviour of a component but also how to optimise the design.…”

The viscoelastic behavior of rubber under a complex loading. II. The effect large strains and the incorporation of carbon black

“…The method whereby a sample prestrained in tension has an additional small torsion oscillation superimposed has been adopted previously by several researchers17–21 and again recently by Suphadon et al3 A suitable schematic for the test is shown in Figure 1. The base of the rubber cylinder was fixed and the top was mounted to a torsion inertia bar.…”

Twisted Rubber Variable-Stiffness Artificial Muscles

“…36 Using a Neo-Hookean stored energy function (SEF), the axial force reduction F r is where r is the radius of the cylinder, C 10 is the Neo-Hookean material constant and c is the torsion defined as j/l, where j is the total twist angle and l is the rubber cylinder length. 37 Alternatively, using a Mooney SEF, the axial force reduction is…”

“…where k is the stretch ratio along the axis of the cylinder, and C 10 and C 01 are the Mooney SEF coefficients. 37 37 Although the variation in axial tensile force exhibited by rubber cord when twisted has been studied in detail from a materials perspective, 36,37 this phenomenon is yet to be investigated by the Soft Robotics community. Twisted rubber cord has extremely attractive qualities for use as artificial muscles: rubber cord is readily available, inexpensive, inherently compliant, and matches the typically desired artificial muscle form factor.…”