Next Article in Journal
Effective Heat and Mass Transport Properties of Anisotropic Porous Ceria for Solar Thermochemical Fuel Generation
Next Article in Special Issue
Stresses and Displacements in Functionally Graded Materials of Semi-Infinite Extent Induced by Rectangular Loadings
Previous Article in Journal
Preparation and Thermal Characterization of Annealed Gold Coated Porous Silicon
Previous Article in Special Issue
Novel Concept to Detect an Optimum Thixoforming Condition of Al-Al3Ni Functionally Graded Material by Wavelet Analysis for Online Operation
Materials 2012, 5(1), 169-191; doi:10.3390/ma5010169
Article

Generalized Fractional Derivative Anisotropic Viscoelastic Characterization

Received: 11 November 2011 / Revised: 30 December 2011 / Accepted: 30 December 2011 / Published: 18 January 2012
(This article belongs to the Special Issue Advances in Functionally Graded Materials)
Download PDF [543 KB, uploaded 18 January 2012]
Abstract: Isotropic linear and nonlinear fractional derivative constitutive relations are formulated and examined in terms of many parameter generalized Kelvin models and are analytically extended to cover general anisotropic homogeneous or non-homogeneous as well as functionally graded viscoelastic material behavior. Equivalent integral constitutive relations, which are computationally more powerful, are derived from fractional differential ones and the associated anisotropic temperature-moisture-degree-of-cure shift functions and reduced times are established. Approximate Fourier transform inversions for fractional derivative relations are formulated and their accuracy is evaluated. The efficacy of integer and fractional derivative constitutive relations is compared and the preferential use of either characterization in analyzing isotropic and anisotropic real materials must be examined on a case-by-case basis. Approximate protocols for curve fitting analytical fractional derivative results to experimental data are formulated and evaluated.
Keywords: anisotropic non-homogeneous viscoelasticity; error analysis; fractional derivatives; functionally graded materials; generalized Kelvin models; master relaxation curves; material characterization; nonlinear viscoelastic properties; shift functions anisotropic non-homogeneous viscoelasticity; error analysis; fractional derivatives; functionally graded materials; generalized Kelvin models; master relaxation curves; material characterization; nonlinear viscoelastic properties; shift functions
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Export to BibTeX |
EndNote


MDPI and ACS Style

Hilton, H.H. Generalized Fractional Derivative Anisotropic Viscoelastic Characterization. Materials 2012, 5, 169-191.

AMA Style

Hilton HH. Generalized Fractional Derivative Anisotropic Viscoelastic Characterization. Materials. 2012; 5(1):169-191.

Chicago/Turabian Style

Hilton, Harry H. 2012. "Generalized Fractional Derivative Anisotropic Viscoelastic Characterization." Materials 5, no. 1: 169-191.


Materials EISSN 1996-1944 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert