A hybrid model of rubber elasticity in simple extension

A thermodynamically related continuum model developed for describing elastic rubber-like behavior of amorphous and crystallizing polymers is exemplified for simple extension. This model is based on a new concept of extendable dynamic segment (DS) whose unperturbed size is roughly evaluated for several polymers. The extension of the DS's hinders the cooperative rotations of monomer groups and contributes to the internal energy of chains. Therefore, in description of macroscopic elastic rubber deformation, this approach takes into account the motions of chains caused by both the entropy and internal energy. The model displays a continuous transition from entropy to energetic elasticity, without common singularity related to finite extensibility of polymer chains. A multi-scale molecular approach, based on the concept of extendable DS's, has been employed for evaluations of continuum parameters. In case of crystallizing polymers, a simple model is developed for the strain-induced crystallization based on local calculations of energetic gain caused by the formation of needle-like (NL) crystals. Then the strain-induced crystallization for a crystallizing rubber is described on continuum level taken into account the reinforcement effects of emerging NL crystals.