The circumferential shear of a nonlinear isotropic incompressible elastic annulus is studied using the neo-Hookean, Ogden constitutive relations in addition to a new constitutive relation for the Hencky strain in terms of the Cauchy stress. The predictions of the three constitutive relations to the specific boundary value problem are delineated. In view of the predictions being quite distinct between the new constitutive relation studied and that for the Ogden constitutive relation, it would be worthwhile to carry out an experiment to determine the efficacy of the models.
RajagopalKR.The elasticity of elasticity. Z Angew Math Phys2007; 58: 309–317.
3.
RajagopalKR.Conspectus of concepts of elasticity. Math Mech Solids2011; 16: 536–562.
4.
RajagopalKRSrinivasaAR.On the response of non-dissipative solids. Proc R Soc A2007; 463: 357–367.
5.
RajagopalKRSrinivasaAR.A Gibbs-potential-based formulation for obtaining the response functions for a class of viscoelastic materials. Proc R Soc A2011; 467: 39–58.
6.
BustamanteR.Some universal solutions for a class of incompressible elastic body that is not Green elastic. The case of large elastic deformations. Q J Mech Appl Math2020; 73: 177–199.
7.
BustamanteRRajagopalKR.A review of implicit constitutive theories to describe the response of elastic bodies. In: MerodioJOgdenRW (eds) Constitutive modelling of solid continua. Cham: Springer, 2020, pp. 187–230.
8.
GokulnathCRajagopalKRSaravananU.Representations for implicit constitutive relations describing non-dissipative response of implicit materials. Z Angew Math Phys2017; 68: 129–143.
9.
BustamanteRRajagopalKR.A new type of constitutive equation for nonlinear elastic bodies. Fitting with experimental data for rubber-like materials. Proc R Soc Lond A2021; 477: 20210330.
10.
OgdenRW.Large deformation isotropic elasticity—on the correlation of theory and experiment for incompressible rubberlike solids. Proc R Soc Lond A1972; 326: 565–584.
11.
TruesdellCANollW.The non-linear field theories of mechanics (ed SS Antman). 3rd ed.Berlin: Springer, 2004.
12.
TreloarLRG.The physics of rubber elasticity. 3rd ed.Oxford: Clarendon Press, 2005.
13.
GreenG.On the laws of reflexion and refraction of light at the common surface of two non-crystallized media. Trans Cambr Phil Soc1839; 7 (1839–1842): 1–24.
14.
GreenG.Mathematical papers of the late George Green (ed NM Ferris). London: Macmillan Publishers, 1871.
15.
MulianaARajagopalKRTscharnuterD, et al. Determining material properties of natural rubber using fewer material moduli in virtue of a novel constitutive approach for elastic bodies. Rubber Chem Technol2018; 91: 375–389.
16.
TruesdellCAToupinR. The classical field theories. In: FlüggeS (ed.) Principles of classical mechanics and field theory / Prinzipien der klassischen mechanik und feldtheorie (Handbuch der physik), vol. III/1. Berlin: Springer, 1960, pp. 226–858.
17.
PrušaVRajagopalKRTuŭmaK. Gibbs free energy based representation formula within the context of implicit constitutive relations for elastic solids. Int J Nonlin Mech2020; 121: 103433.
18.
OgdenRW.Non-linear elastic deformations. New York: Dover, 1997.
19.
RivlinRS. Large elastic deformations of isotropic materials VI. Further results in the theory of torsion shear and flexure. Phil Trans R Soc A1949; 242: 173–195.
20.
AdkinsJE.Some general results in the theory of large elastic deformations. Proc R Soc Lond A1955; 231: 75–90.
21.
JiangCOgdenRW.On azimuthal shear of a circular cylindrical tube of compressible elastic material. Q J Mech Appl Math1998; 51: 143–158.
HuntleyHEWinemanASRajagopalKR.Stress softening, strain localization and permanent set in the circumferential shear of an incompressible elastomeric cylinder. IMA J Appl Math1997; 59: 309–338.
25.
RajagopalKRHuangYN.Finite circumferential shearing of non-linear solids within the context of thermoelasticity. IMA J Appl Math1994; 50: 22–36.
26.
TaoLRajagopalKRWinemanAS.Circular shearing and torsion of generalized neo-Hookean materials. IMA J Appl Math1992; 48: 1–15.
