Mathematical Modeling of Rubber Elasticity

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A mathematical modeling, the Finsler geometry (FG) technique, is applied to study the rubberelasticity. Existing experimental data of stress-strain (SS) diagrams, which are highly non-linear,are numerically reproduced. Moreover, the strain induced crystallization (SIC), typical of somerubbers like Natural Rubber (NR), which is known to play an important role in the mechanicalproperty of rubbers, is partly implemented in the model. Indeed, experimentally observedhysteresis of SS curve can be reproduced if the parameter aof non-polar (or polar) interactionenergy 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 Mof the directional degrees of freedom σof 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 observedin the plastic deformation region, can also be reproduced. Thus we find that the interactionimplemented in the FG model via the Finsler metric is suitable in describing the mechanicalproperty of rubbers.

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