Mathematical Modeling of Rubber Elasticity

A mathematical modeling, the Finsler geometry (FG) technique, is applied to study the rubber elasticity. Existing experimental data of stress-strain (SS) diagrams, which are highly non-linear, are numerically reproduced. Moreover, the strain induced crystallization (SIC), typical of some rubbers like Natural Rubber (NR), which is known to play an important role in the mechanical property of rubbers, is partly implemented in the model. Indeed, experimentally observed hysteresis of SS curve can be reproduced if the parameter a of non-polar (or polar) interaction energy is increased for the unloading or shrinkage process in the Monte Carlo (MC) simulations, and at the same time we find that the order parameter M of the directional degrees of freedom σ of polymer show a hysteresis behavior which is compatible with that of the crystallization ratio. In addition, rupture phenomena, which are accompanied by a necking phenomenon observed in the plastic deformation region, can also be reproduced. Thus we find that the interaction implemented in the FG model via the Finsler metric is suitable in describing the mechanical property of rubbers.