On the numerical handling of fractional viscoelastic material models in a FE analysis

The paper presents the finite element (FE) implementation of linear and nonlinear fractional viscoelasticity models. To this end, a short introduction on fractional calculus is given. In addition to the fractional operators, this includes analytical and numerical solution schemes for selected fractional integral and differential equations. The presented rheological model is based on state of the art approaches and has been adopted to model the strain rate dependent material behavior of polymers. To this end, two approaches with constant and overstress dependent viscous properties resulting in linear and nonlinear evolution equations are discussed. The uniaxial constitutive relations are generalized to the multiaxial case and processed to be implemented in a FE code. The model behavior of both approaches is demonstrated and compared for selected uniaxial and multiaxial load cases.