On rubber elasticity from a microscale structural mechanics representation of polymer chains

The search for a comprehensive strain-energy function for isotropic rubber elasticity has long been a central topic in continuum mechanics. Despite extensive effort and a variety of approaches, this problem remains open and continues to stimulate theoretical developments. In this contribution, we present a further attempt to address this longstanding challenge based on a microscale structural mechanics representation of polymer chains. Chain elasticity is derived from the strain energy associated with deformation of the (micro)structure, rather than from configurational entropy as in classical statistical mechanics approaches. The resulting force–extension response reflects two characteristic features: (i) progressive reduction of entanglement constraints at low-to-moderate stretches; and (ii) finite chain extensibility as the locking stretch is approached. By performing network-averaging, we derive the strain-energy function of the polymer network under both affine and non-affine kinematics. The model is assessed by fitting multiaxial experimental data from several rubbers with distinct behaviors, demonstrating consistent predictive capability. The proposed microscale nonlinear mechanics framework is entirely analytical and maintains connections with fundamental principles of non-Gaussian statistical mechanics, establishing a foundation for future theoretical developments in rubber elasticity.