  In this study we have investigated into the entanglement effect and
crosslinking effect in long-chain SBR rubber polymer system to model the
mechanical hyperelastic behavior. The discussed methodologies are developed by
a dissipative particle dynamics (DPD) based multiscale modeling method. The DPD
interaction parameters are in turn obtained by all atomistic molecular dynamics
and subsequently utilized by the DPD simulations. In the DPD simulation boxes,
200 long polymer chains and 1600 vulcanizing sulphur beads were packed.
Vulcanization was achieved by random cross-linking among chains and
entanglement was detected by utilizing the M-coil estimator. The mechanical
effect of entanglement was modelled by extended tube model and the crosslinking
effect was modelled by the Arruda-Boyce model. The modelled stress-strain curve
is compared with the experimentally obtained curve for the qualitative and
quantitative aspects of mechanical properties. It was determined that for
strains up to 150%, the contribution of entanglement to the measured mechanical
properties can be even up to 50%.
