LINEAR RHEOLOGICAL SOLID MODEL WITH FRACTIONAL DERIVATIVE AND ITS APPLICATION

A linear rheological solid model with a fractional order derivative was obtained by replacing the dashpot in a standard linear solid model with a Koeller spring-pot unit. Its dynamic viscoelasticity characterized by a storage modulus, a loss modulus and a loss factor, and static viscoelasticity characterized by a creep compliance and a relaxation modulus, were derived. The stress relaxation characteristic of polypropylene (PP) was modeled using the fractional linear rheological solid model, a standard linear solid model and a five-element solid model. Moreover, the truncation error in the summation calculation of a Mittag-Leffler function was discussed. It is demonstrated that the fractional linear rheological solid model can more adequately reproduce the stress relaxation behavior of the PP sample than other two models.