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Generalized Fractional Derivative Anisotropic Viscoelastic Characterization
Aerospace Engineering Department, College of Engineering and Private Sector Program Division,National Center for Supercomputing Applications (NCSA), University of Illinois at Urbana-Champaign (UIUC), 104 S. Wright Street, MC-236, Urbana, IL 61801–2935, USA
Received: 11 November 2011; in revised form: 30 December 2011 / Accepted: 30 December 2011 / Published: 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
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MDPI and ACS Style
Hilton, H.H. Generalized Fractional Derivative Anisotropic Viscoelastic Characterization. Materials 2012, 5, 169-191.
Hilton HH. Generalized Fractional Derivative Anisotropic Viscoelastic Characterization. Materials. 2012; 5(1):169-191.
Hilton, Harry H. 2012. "Generalized Fractional Derivative Anisotropic Viscoelastic Characterization." Materials 5, no. 1: 169-191.