An 8-chain Model for Rubber-like Materials Accounting for Non-affine Chain Deformations and Topological Constraints

Abstract

Several industrial applications involve rubber and rubber-like materials, and it is important to be able to predict the constitutive response of these materials. In the present paper, a new constitutive model for rubber-like solids is proposed. The model is based on the 8-chain concept introduced by Arruda and Boyce (J. Mech. Phys. Solids 41, 389-412, 1993) to which two new components are added. Real polymer networks do not deform affinely, and in the proposed model this is accounted for by the inclusion of an elastic spring, acting in series with the representative polymer chain. Furthermore, real polymer chains are not completely free to move, which is modelled by imposing a topological constraint on the transverse motions of the representative polymer chain. The model contains five model parameters and these need to be determined on the basis of experimental data. Three experimental studies from the literature were used to assess the proposed model. The model was able to reproduce experimental data performed under conditions of uniaxial tension, generalised plane deformation, and biaxial tension with an excellent accuracy. The strong predictive abilities together with the numerically efficient structure of the model make it suitable for implementation in a finite element context.

Eight-chain and full-network models and their modified versions for rubber hyperelasticity: a comparative study

“…These materials are generally modeled by considering homogeneous, isotropic, incompressible or nearly incompressible, geometrically and physically nonlinear (visco) elastic solids. Such idealizations are also supported by experimental data [6,7].…”

“…(6)(7)(8). If one fits the UN, EB, and PS equations to the corresponding Treloar data, the optimal material parameters are found to be: …”

“…For the sake of modifications over the classical one, some models increase the number of parameters to fit the data, for example, Bechir model [20], whereas some remain with the two parameters, for example, the bootstrapped eightchain model [18]. Some well-known modified versions of the Arruda-Boyce model are the modified Flory-Erman model [8,21], Gornet-Desmorat (GD) model [19], bootstrapped eight-chain model [18], Bechir model [20], Meissner-Matejka model [22], and the Kroon model [6]. When a modified model is proposed aiming to show better results in contrast to the original eight-chain model, the modified version is usually compared with the original one but the comparison among the variants of the eightchain model are not demonstrated so far in the literature.…”

Mechanical behavior of porous polysiloxane with micropores interconnected by microchannels

“…The Arruda–Boyce Model was established based on an eight chain representation of the underlying macromolecular network structure of elastomer and non‐Gaussian behavior of the individual chains . The excellent fitting shown above indicated that the deformation behavior of a porous structure containing micropores interconnected by microchannels may be analogous to that of elastic networks.…”

Approximation of the inverse Langevin function revisited

“…In the paper by Hossain and Steinmann (2012), the authors summarized various micromechanical and phenomenological models. Other interesting review articles are written by Boyce and Arruda (2000), Elias-Zuniga and Beatty (2002), Böl and Reese (2006), Gillibert et al (2010), Kroon (2011), Linder et al (2011), Gloria et al (2012 and Jedynak (2013, 2014). These papers present also a significant contribution to the modeling of rubber-like materials.…”