| description abstract | Abstract. This paper explains the stress behavior of filled and vulcanized rubbers subject to large deformations by using the fractional derivatives proposed in a paper in this series (Fukunaga et al., 2025, “A Fractional Derivative Interpretation of Viscoelastic Rubbers. I. Thermodynamically Consistent Fractional-Derivative Models for Finite Strain,” ASME J. Comput. Nonlinear Dyn., 20(11), p. 111009, Paper I). The proposed rubber model consists of two fractional-derivative terms and one elastic term arranged in parallel. The orders of two fractional derivatives are α≃0.5 and β<α. Of the two fractional-derivative terms, the contribution from the term of order α (the α term) is small for low strain rates. Aside from the α term, the basic parameters are the order, β, the coefficient of the β term, and the shear modulus of the elastic term. Because the number parameters of fractional-derivative model is small, a deviation from the response of the fractional derivative can be directly interpreted as the effects of the ingredients or a change in state during the course of deformation. At large deformations, the influences of filler and vulcanization are represented by one parameter called the effective thickness, which is a measure of the effective volume fraction of the matrix. A method for decomposing these parameters is presented. The fractional-derivative model also suggests differences in the state of rubbers between the loading and unloading phases. The fractional-derivative term weakens or vanishes in the unloading phase. A model with β<0.2 is consistent with the stress data considered in this paper both in the loading and unloading phases. | |
