A generalized model for the uniaxial isothermal deformation of a viscoelastic body

Using the notion of a fractional derivative we formulate a new model for a uniaxial deformation of a visco-elastic body. The basic assumption is that all derivatives σ(γ) with respect to time of the stress depend (with specified weighting factor) on all derivatives ε(γ) with respect to time of the strain (multiplied with another weighting factor), for 0≤γ≤1. In this respect our model is a generalization of the Zener model, i.e., it is a Zener fractional model with infinitely many terms. The relation between stress and strain is given in explicit form. For two specific choices of parameters the behavior of the model under suddenly applied stress (creep) and suddenly applied strain (stress relaxation) are examined.