A pseudo-compressible dual 4-chain model of polymer networks for exploring rubber elasticity

Rubber elasticity has been a subject of studies for an extended period of polymer physics. Currently, the advancement of rubbery polymers is proceeding at an accelerated pace, and the network structure is exceptionally complex. To comprehensively comprehend the mechanical behavior exhibited by these rubbery materials, it is imperative to further evolve the theoretical framework of rubber elasticity. To understanding this problem, this study introduces a pseudo-compressible dual four-chain model for analyzing polymer networks and rubber elasticity. To address the lack of periodicity in the 4-chain model, a pseudo-compressible dual four-chain model is constructed, which accounts for intrinsic moments and volume effects. The model assumes isotropic of the polymer and affine motion of crosslinking points, which changed the coordinate system, leading to a simplified 4-chain model. Due to the poor symmetry of the 4-chain model, the force balance caused by chain deformation is different from that of traditional Langevin statistics models. Based on the phantom network model, preliminary estimates of volume effects were made using phenomenology and scaling equations. The proposed model is validated against experimental data from literature on various mechanical tests, including compressibility, uniaxial tension, uniaxial compression, pure shear, equi-biaxial tension, and biaxial strain tests. Using uniaxial tensile data from literature, the fitting results of different models (proposed dual 4-chain model, p-chain model, Yeoh model, Anssari-Benam model) are also used to illustrate the characteristics of the proposed model. The proposed constitutive model provides a new dual 4-chain strategy for exploring rubber elasticity.