ABSTRACT
ABSTRACT: In this contribution, an attempt to bridge the gap between macroscopic and microscopic response of elastomers is made on the basis of statistical mechanics. The transition between macroscopic and mesoscopic deformation fields is carried out by means of an analytical network averaging concept. Accordingly, we assume the existence of a directional distribution function of polymer chains in the polymer network. The mean field mesoscopic deformations on the subnetwork level are computed by averagingthe macroscopic deformations over the unit sphere. The directional distribution of polymer chains introduces non-affine deformations, stress softening or strain hardening mechanisms into the model. Furthermore, the meso-micro bridging between the subnetwork and the single chain is done by the mesostretch amplification which is essential to capture the limited extension of the polymer network. In contrast to previous works, within the presented model the network averaging can be derived analytically. Furthermore, the free energy of polymer chains is developed from a closed-form of Rayleigh’s exact non-Gaussian distribution function based on quantum mechanics. Thus, the inverse Langevin function is entirely bypassed. Evolutions of the Mullins effect, hysteresis and crystallinity are also analytically evaluated. The model includes a few physically motivated material parameters and demonstrates good agreement with multi-dimensional experimental data of different elastomers.
