Theory and Applications of 3D Fractional Models

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: closed (30 September 2021) | Viewed by 3718

Special Issue Editors


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Guest Editor
Department of Engineering Science, Oxford Brookes University, Oxford, UK

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Co-Guest Editor
Department of Civil, Environmental, Energy and Materials Engineering (DICEAM), University “Mediterranea” of Reggio Calabria, 89124 Reggio Calabria, Italy
Interests: fractional viscoelaticity; fractional calculus; solid and structural mechanics; dynamics of structures; nonlocal mechanics; metamaterials; dynamics of fixed and floating wind turbine; finite element method; seismic engineering; biomechanics; constitutive behavior of innovative and biomedical materials

Special Issue Information

Dear Colleagues,

Fractional order models are becoming more and more popular among engineers when it is essential to capture the real behavior of complex materials such as viscoelasticity, non-local mechanics, thermal and fluid transport, and/or diffusion. In recent literature, such phenomena are often represented mathematically with fractional PDEs. Furthermore, recent advances in three-dimensional fractional viscoelasticity, non-local mechanics, poroelasticity, as well as anomalous diffusion models have attracted the attention of many researchers.

This Special Issue aims to collect recent theoretical perspectives in models based on fractional PDEs, solution of boundary value problems, and application of such models in all fields of science, engineering applications, and other applied fields.

Dr. Olga Barrera
Dr. Gioacchino Alotta
Guest Editors

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Keywords

  • Fractional PDEs 
  • Fractional viscoelasticity 
  • Fractional poroelasticity 
  • Non-local mechanics 
  • Anomalous transport phenomena

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Published Papers (1 paper)

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Research

22 pages, 521 KiB  
Article
Finite Element Formulation of Fractional Constitutive Laws Using the Reformulated Infinite State Representation
by Matthias Hinze, André Schmidt and Remco I. Leine
Fractal Fract. 2021, 5(3), 132; https://doi.org/10.3390/fractalfract5030132 - 21 Sep 2021
Cited by 2 | Viewed by 2522
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Theory and Applications of 3D Fractional Models)
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