TY - JOUR
T1 - Mathematical Modeling of Rubber Elasticity
AU - Koibuchi, Hiroshi
AU - Bernard, Chrystelle
AU - Chenal, Jean Marc
AU - Diguet, Gildas
AU - Sebald, Gael
AU - Cavaille, Jean Yves
AU - Takagi, Toshiyuki
AU - Chazeau, Laurent
N1 - Funding Information:
This work is supported in part by JSPS KAKENHI Grant Number JP17K05149 and the Collaborative Research Project of the Institute of Fluid Science, Tohoku University.
Publisher Copyright:
© 2018 Institute of Physics Publishing. All rights reserved.
PY - 2018/12/21
Y1 - 2018/12/21
N2 - 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.
AB - 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.
KW - Finsler geometry
KW - Natural rubber
KW - Necking of rubber
KW - Rubber elasticity
KW - Strain induced crystallization
KW - Stress-strain diagram
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U2 - 10.1088/1742-6596/1141/1/012081
DO - 10.1088/1742-6596/1141/1/012081
M3 - Conference article
AN - SCOPUS:85059382246
VL - 1141
JO - Journal of Physics: Conference Series
JF - Journal of Physics: Conference Series
SN - 1742-6588
IS - 1
M1 - 012081
T2 - 7th International Conference on Mathematical Modeling in Physical Sciences, IC-MSQUARE 2018
Y2 - 27 August 2018 through 31 August 2018
ER -