Generalized Fractional Derivative Anisotropic Viscoelastic Characterization

Materials

关键词: anisotropic non-homogeneous viscoelasticity;    error analysis;    fractional derivatives;    functionally graded materials;    generalized Kelvin models;    master relaxation curves;    material characterization;    nonlinear viscoelastic properties;    shift functions;   

DOI  :  10.3390/ma5010169

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2012 by the author; licensee MDPI, Basel, Switzerland.