Finite Element Formulation of Fractional Constitutive Laws Using the Reformulated Infinite State Representation

In this paper, we introduce a formulation of fractional constitutive equations for finite element analysis using the reformulated infinite state representation of fractional derivatives. Thereby, the fractional constitutive law is approximated by a high-dimensional set of ordinary differential and algebraic equations describing the relation of internal and external system states. The method is deduced for a three-dimensional linear viscoelastic continuum, for which the hydrostatic and deviatoric stress-strain relations are represented by a fractional Zener model. One- and two-dimensional finite elements are considered as benchmark problems with known closed form solutions in order to evaluate the performance of the scheme.

Automated summary

The paper introduces a formulation of fractional constitutive equations for finite element analysis using reformulated infinite state representation of fractional derivatives. The method approximates the fractional constitutive law with a high-dimensional set of ordinary differential and algebraic equations, and is applied to a three-dimensional linear viscoelastic continuum using a fractional Zener model. Performance evaluation is done on one- and two-dimensional finite elements with known closed form solutions.