Fractional viscoplasticity

In this paper we generalize the Perzyna's type viscoplasticity using fractional calculus. We call such model fractional viscoplasticity. The main objective of this research is to propose a new way of description of permanent deformation in a material body, especially under extreme dynamic conditions. In this approach the fractional calculus can be understood as a tool enabling the introduction of material heterogeneity/multi-scale effects to the constitutive model.This newly developed phenomenological model is represented in the Euclidean space living more general setup for future work. The definition of the directions of a viscoplastic strains stated as a fractional gradient of plastic potential plays the fundamental role in the formulation. Moreover, the fractional gradient provides the non-associative plastic flow without necessity of additional potential assumption.