Numerical application of fractional derivative model constitutive relations for viscoelastic materials

A differential equation describing the motion of a viscoelastic bar is developed and studied. The bar material is modeled using a fractional derivative based constitutive relationship. The three-dimensional Poisson tapering effect is included in the development of the differential equation, but is not included in the solution of the linearized system. Various numerical approaches and models for the representation of a fractional order derivative and for the solution of the differential equation are studied.