The Scaling Law for Finite Torsion of Elastic Cylinders

Abstract

The torque and forces normal to the end surfaces of cylinders of natural rubber were measured as a function of the angle of twist. The measurements were repeated on small cylinders cut from the larger cylinders to insure that the tests were on identical material. Plots of reduced torque and of reduced normal force versus reduced twist for the different sized cylinders coincide to within 1%. This result supports the simple material assumption of the classical theory of finite elastic deformations. An interesting instability was observed, and derivatives of the strain energy function were calculated.

Analysis of dynamic mechanical response in torsion

“…(8) with the approximated function g(u) in Eq. (9). The value of the ratio g(u)/g SV (u) is found to be 1 for all the aspect ratios u > 1.5, hence validating the above approximation of the de Saint-Venant prediction.…”

“…1 and 2(b)] have been performed extensively on rotational rheometers and are often considered as an industrial standard [1]. They provide characterization of the dynamic mechanical response of a wide variety of materials including glasses [2][3][4], filled and vulcanized systems [5][6][7][8][9][10][11][12][13], as well as soft gels [14,15]. They are particularly important in situations where the more common small amplitude oscillatory shear tests (performed with parallel plates or cone-plate geometries) are problematic or not possible at all (e.g., due to slip, transducer compliance or torque limitations).…”

Likely equilibria of the stochastic Rivlin cube

“…However, the general stability analysis developed there is applicable also to the case when µ 1 > 0 and µ 2 < 0, given that the shear modulus satisfies µ = µ 1 + µ 2 > 0. For rubber, some negative values of µ 2 were obtained in [43] from experimental data reported in [44]. More generally, we recall that, for a cube of Mooney-Rivlin material subject to simple shear, if µ 2 > 0, then the positive Poynting effect occurs, and if −µ 1 < µ 2 < 0, then the negative Poynting effect is obtained.…”

Asymptotic results for bifurcations in pure bending of rubber blocks

“…To fully explain this observation would require a nonlinear post-buckling analysis because the bifurcation involved is probably of subcritical type. We note in passing that Gent & Cho's creases are, to a certain extent, very similar to those encountered on the curved surface of severely torsioned stocky rubber cylinders [17]. These phenomena are likely to be related to the failure at the boundary of the complementing condition (see [18] and the reference therein), and they fall outside the scope of our study.…”