Hinze, MatthiasSchmidt, AndréLeine, Remco Ingmar2022-08-252022-08-2520212504-31101819372529http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-123447http://elib.uni-stuttgart.de/handle/11682/12344http://dx.doi.org/10.18419/opus-12325In 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.eninfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/4.0620article2021-10-01