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.
%0 Journal Article
%1 Hinze&Schmidt&Leine2021
%A Hinze, M.
%A Schmidt, A.
%A Leine, R. I.
%D 2021
%J Fractal Fractional
%K imported journal inm leine from:rleine project_hinze
%N 132
%P 1--22
%T Finite element formulation of fractional constitutive laws using the reformulated infinite state representation
%U https://doi.org/10.3390/fractalfract5030132
%V 5
%X 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.
@article{Hinze&Schmidt&Leine2021,
abstract = {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.},
added-at = {2022-03-22T14:39:07.000+0100},
author = {Hinze, M. and Schmidt, A. and Leine, R. I.},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2ee458b481fda12382a9f3cc84ab77b3f/inm},
interhash = {71dfbbed00ac97307150600d795e20e8},
intrahash = {ee458b481fda12382a9f3cc84ab77b3f},
journal = {Fractal Fractional},
keywords = {imported journal inm leine from:rleine project_hinze},
number = 132,
pages = {1--22},
timestamp = {2023-03-24T07:39:11.000+0100},
title = {Finite element formulation of fractional constitutive laws using the reformulated infinite state representation},
url = {https://doi.org/10.3390/fractalfract5030132},
volume = 5,
year = 2021
}
