Monte Carlo Study of Rubber Elasticity on the Basis of Finsler Geometry Modeling
Hiroshi Koibuchi,
Chrystelle Bernard,
Jean-Marc Chenal,
Gildas Diguet,
Gael Sebald,
Jean-Yves Cavaille,
Toshiyuki Takagi,
Laurent Chazeau
Affiliations
Hiroshi Koibuchi
National Institute of Technology (KOSEN), Sendai College, 48 Nodayama, Medeshima-Shiote, Natori-shi, Miyagi 981-1239, Japan
Chrystelle Bernard
ELyTMaX UMI 3757, CNRS-Universite de Lyon, Tohoku University, International Joint Unit, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
Jean-Marc Chenal
Materials Engineering and Science (MATEIS), CNRS, INSA Lyon UMR 5510, Université de Lyon Batiment B. Pascal, Avenue Jean Capelle, 69621 Villeurbanne, CEDEX, France
Gildas Diguet
ELyTMaX UMI 3757, CNRS-Universite de Lyon, Tohoku University, International Joint Unit, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
Gael Sebald
ELyTMaX UMI 3757, CNRS-Universite de Lyon, Tohoku University, International Joint Unit, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
Jean-Yves Cavaille
ELyTMaX UMI 3757, CNRS-Universite de Lyon, Tohoku University, International Joint Unit, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
Toshiyuki Takagi
ELyTMaX UMI 3757, CNRS-Universite de Lyon, Tohoku University, International Joint Unit, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
Laurent Chazeau
Materials Engineering and Science (MATEIS), CNRS, INSA Lyon UMR 5510, Université de Lyon Batiment B. Pascal, Avenue Jean Capelle, 69621 Villeurbanne, CEDEX, France
Configurations of the polymer state in rubbers, such as so-called isotropic (random) and anisotropic (almost aligned) states, are symmetric/asymmetric under space rotations. In this paper, we present numerical data obtained by Monte Carlo simulations of a model for rubber formulations to compare these predictions with the reported experimental stress−strain curves. The model is defined by extending the two-dimensional surface model of Helfrich−Polyakov based on the Finsler geometry description. In the Finsler geometry model, the directional degree of freedom σ → of the polymers and the polymer position r are assumed to be the dynamical variables, and these two variables play an important role in the modeling of rubber elasticity. We find that the simulated stresses τ sim are in good agreement with the reported experimental stresses τ exp for large strains of up to 1200 % . It should be emphasized that the stress−strain curves are directly calculated from the Finsler geometry model Hamiltonian and its partition function, and this technique is in sharp contrast to the standard technique in which affine deformation is assumed. It is also shown that the obtained results are qualitatively consistent with the experimental data as influenced by strain-induced crystallization and the presence of fillers, though the real strain-induced crystallization is a time-dependent phenomenon in general.