Fractal and fractional, 2021-09, Vol.5 (3), p.132
2021
Details
- Autor(en) / Beteiligte
- Titel
- Finite Element Formulation of Fractional Constitutive Laws Using the Reformulated Infinite State Representation
- Ist Teil von
- Fractal and fractional, 2021-09, Vol.5 (3), p.132
- Ort / Verlag
- Basel: MDPI AG
- Erscheinungsjahr
- 2021
- Link zum Volltext
- Quelle
- EZB Electronic Journals Library
- Beschreibungen/Notizen
- 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.
- Sprache
- Englisch
- Identifikatoren
- ISSN: 2504-3110eISSN: 2504-3110DOI: 10.3390/fractalfract5030132Titel-ID: cdi_doaj_primary_oai_doaj_org_article_a64b27f61c13476f8f87d9db8ef6fe6c
- Format
- –
- Schlagworte
- Approximation, Calculus, Constitutive equations, Constitutive relationships, Differential equations, Finite element analysis, Finite element method, fractional viscoelasticity, fractional Zener model, infinite state representation, Integrals, Mathematical functions, Ordinary differential equations, Representations, Rheology, Stress-strain relationships, Two dimensional models, Viscoelasticity