Hilton Harry H
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.
Materials (Basel). 2012 Jan 18;5(1):169-191. doi: 10.3390/ma5010169.
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.
各向同性线性和非线性分数阶导数本构关系是根据多参数广义开尔文模型建立并研究的，并进行了分析扩展，以涵盖一般各向异性均匀或非均匀以及功能梯度粘弹性材料行为。从分数阶微分本构关系导出了计算能力更强的等效积分本构关系，并建立了相关的各向异性温度 - 湿度 - 固化度移位函数和缩减时间。推导了分数阶导数关系的近似傅里叶变换反演，并评估了其精度。比较了整数阶和分数阶导数本构关系的有效性，在分析各向同性和各向异性实际材料时优先使用哪种表征必须逐案进行研究。制定并评估了将分数阶导数分析结果拟合到实验数据的近似曲线拟合方案。
