Some remarks on kinematic modeling of limiting chain extensibility

Abstract: 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. Key Words: kinematic modeling, limiting chain extensibility, family of approximations 1