Browsing by Author "Leine, Remco Ingmar"

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    Finite element formulation of fractional constitutive laws using the reformulated infinite state representation
    (2021) Hinze, Matthias; Schmidt, André; Leine, Remco Ingmar
    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.