Experimental validation of a simple fractional model for viscoelastic behavior of high filled polymer-based composites

The design for the reliability of high filled polymer-based composites requires accurate knowledge of their viscoelastic properties. With the increasing complexity in classic constitutive models to achieve an excellent description, however, the inadequacy of requiring too many parameters and the difficulty of describing complex dynamic viscoelastic behaviors has been noted. In this work, a version of the fractional derivative model (M-S model) is developed, which is composed of a fractional Maxwell element and a Maxwell element in parallel, in order to simultaneously describe complex dynamic and static viscoelastic behavior of soft high-filled polymer-based composites using fewer parameters. The performance of the fractional derivative model and four parallel Maxwell model is further compared. The two models can be used to describe the relaxation behaviors and storage modulus, but it is relevant to underline that our M-S model requires fewer parameters (five) than the latter model (eight). Meanwhile, our M-S model also can provide accurate descriptions of loss factor of soft high-filled polymer-based composites, which cannot be described by the latter model.