Abstract
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.
Highlights
Rubbers such as natural rubber are well known to support large recoverable strains in the elastic deformation process of stretching/recovery (Figure 1a,b)
The main purpose is to find that the Finsler geometry model can produce τsim comparable to τexp, and it is interesting to find the role of these parameters in the behavior of τsim and M
The τexp of this nano-composite of ethylene propylene diene terpolymer (EPDM) and layered double hydroxide (LDH), denoted by EL10, shows a standard shape of the stress–strain curve of rubbers, where the number at the end of EL indicates the amount of LDH in phr
Summary
Rubbers such as natural rubber are well known to support large recoverable strains in the elastic deformation process of stretching/recovery (Figure 1a,b). The affine transformation is assumed in this theory for polymer elongation using the deformation tensor In this framework, the free energy of the network is obtained, and the stress–strain curve becomes calculable [11,12,13,14,15,16]. Other than the properties of the extended and highly nonlinear behavior of the stress–strain curves, it is well known that the temperature of rubbers increases in the adiabatic extension process This property characteristic of rubbers is called entropy elasticity, which is reflected in the stress being proportional to the temperature. We show that experimentally observed and reported that stress–strain curves of rubbers are reproducible by the Finsler geometry modeling technique without the affine deformation assumption [26]. The expression of the 2D bending energy is described in Appendix B
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