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Mathematical Methods in the Applied Sciences
Article . 2022 . Peer-reviewed
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zbMATH Open
Article . 2023
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https://dx.doi.org/10.48550/ar...
Article . 2022
License: arXiv Non-Exclusive Distribution
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A generalised distributed‐order Maxwell model

A generalised distributed-order Maxwell model
Authors: Luís L. Ferrás; M. Luísa Morgado; Magda Rebelo;

A generalised distributed‐order Maxwell model

Abstract

In this work, we present a generalised viscoelastic model using distributed‐order derivatives. The model consists of two distributed‐order elements (distributed springpots) connected in series, as in the Maxwell model. The new model generalises the fractional viscoelastic model presented by Schiessel and Blumen and allows for a more broad and accurate description of complex fluids when a proper weighting function of the order of the derivatives is chosen. We discuss the connection between classical, fractional and viscoelastic models of distributed order and highlight the fundamental concepts that support these constitutive equations. We also derive the relaxation modulus, the storage and loss modulus and the creep compliance for specific weighting functions.

Keywords

Laplace transform, Classical Physics (physics.class-ph), FOS: Physical sciences, Physics - Classical Physics, fractional calculus, 26A33, 42A38, 76P05, 76-10, Maxwell model, Mathematics - Analysis of PDEs, FOS: Mathematics, Viscoelastic fluids, distributed order fractional derivatives, viscoelasticity, Analysis of PDEs (math.AP)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
4
Top 10%
Average
Top 10%
Green