Mathematical Modeling of Rubber Elasticity
Résumé
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 aof 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 Mof 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.
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