A kinematic model is proposed for materials whose polymeric molecular chains have a maximum achievable length. A widely used model for this effect which imposes a bound on the first strain invariant is examined and is shown that the difference between the models can be up to 23% for a limiting stretch value proposed in the literature. The closeness of fit is also examined for other limiting stretch values. A family of approximations is introduced and shown to converge to the proposed model. Convergence is shown to be fast for an important limiting stretch value.
[1] Horgan, C. O. and Saccomandi, G.Simple torsion of isotropic, hyperelastic, incompressible materials with limiting chain extensibility. Journal of Elasticity, 56, 159–170 (1999).
2.
[2] Horgan, C. O. and Saccomandi, G.Pure axial shear of isotropic incompressible nonlinearly elastic materials with limiting chain extensibility. Journal of Elasticity, 57, 307–319 (1999).
3.
[3] Horgan, C. O. and Saccomandi, G.Pure azimuthal shear of isotropic incompressible hyperelastic materials with limiting chain extensibility. International Journal of Nonlinear Mechanics, 36, 465–475 (2001).
4.
[4] Horgan, C. O. and Saccomandi, G.Large deformations of a rotating solid cylinder for non–Gaussian isotropic, incompressible, hyperelastic materials. Journal of Applied Mechanics, 68, 115–117 (2001).
5.
[5] Horgan, C. O. and Saccomandi, G.Antiplane shear deformations for non–Gaussian isotropic, incompressible, hyperelastic materials. Proceedings of the Royal Society of London, Series A, 457, 1999–2017 (2001).
6.
[6] Horgan, C. O. and Saccomandi, G.Constitutive modeling of rubber–like and biological materials with limiting chain extensibility. Mathematics and Mechanics of Solids, 7, 353–371 (2002).
7.
[7] Horgan, C. O. and Saccomandi, G.A molecular–statistical basis for the Gent constitutive model of rubber elasticity. Journal of Elasticity, 68, 167–176 (2002).
8.
[8] Horgan, C. O. and Saccomandi, G.A description of arterial wall mechanics using limiting chain extensibility constitutive models. Biomechanics and Modeling in Mechanobiology, 1, 251–266 (2003).
9.
[9] Horgan, C. O. and Saccomandi, G.Finite thermoelasticity with limiting chain extensibility. Journal of Mechanics and Physics of Solids, 51, 1127–1146 (2003)
10.
[10] Gent, A. N.A new constitutive relation for rubber. Rubber Chemistry and Technology, 69, 59–61 (1996).
11.
[11] Carroll, M. M.Elastic polymers with limiting chain extensibility. Preprint (2001).
12.
[12] Ogden, R. W.Nonlinear Elastic Deformations. Ellis Horwood, Chichester, 1984 (Reprinted by Dover, New York, 1997).
13.
[13] Currie, P. K.The attainable region of strain-invariant space for elastic materials. International Journal of Nonlinear Mechanics, 39, 833–842 (2004).
14.
[14] Chou-Wang, M. S. and Horgan C. O.Void nucleation and growth for a class of incompressible nonlinearly elastic materials. International Journal of Solids and Structures, 25, 1239–1254 (1989).
15.
[15] Horgan, C. O. and Saccomandi, G.Constitutive models for atactic elastomers, Proceedings of the Symposium on Waves and Stability in Continuous Media (WASCOM 2003), R. Monaco, S. Pennisi, S. Rionero and T. Ruggeri (Eds.), World Scientific, Singapore, 2004, pp. 281–293.
