Fractional order models of viscoelastic polymeric solids undergoing large deformations

Abstract

We present a fractional order model for nonlinear visco-hyperelastic solids taking into account large deformations. A three-field form of the Hu-Washizu principle is introduced to create a stable finite element method in the context of nearly incompressible dynamics. The β-method (a generalized midpoint rule) for time discretization is implemented into a variational finite element framework for efficient computing of numerical approximations to the initial boundary-value problem for hyperbolic equation of motion. Finally, a 2-D cantilever beam problem with a step end load is considered in order to demonstrate the algorithm.

Keywords

• fractional viscoelasticity
• large deformations
• springpot
• fractional calculus
• finite element
• integration algorithm