Fractional derivative models of viscoelastic materials for large extension

Dynamical properties of viscoelastic material are considered to be originated from the complex combination of elastic components and viscous components. From this idea, the time derivative of deviatoric part of the stress of elastic components have been integrated by fractional order. In this paper, several fractional derivative models for large extension are proposed based on this idea. The fractional derivative model depends on the energy function of the elastic components. It also depends on the type of stress tensor adopted for the stress-strain relation of elastic components. Numerical results are demonstrated for the description of the models.