期刊
CHAOS SOLITONS & FRACTALS
卷 102, 期 -, 页码 333-338出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.chaos.2017.03.032
关键词
Linear viscoelasticity; Creep; Relaxation; Hadamard fractional derivative; Fractional calculus; Volterra integral equations; Ultra slow kinetics
资金
- Department of Pure and Applied Sciences (DiSPeA) of the Urbino University Carlo Bo [CUP H32I160000000005]
We present a new approach based on linear integro-differential operators with logarithmic kernel related to the Hadamard fractional calculus in order to generalize, by a parameter nu epsilon (0, 1], the logarithmic creep law known in rheology as Lomnitz law (obtained for nu = 1). We derive the constitutive stress-strain relation of this generalized model in a form that couples memory effects and time-varying viscosity. Then, based on the hereditary theory of linear viscoelasticity, we also derive the corresponding relaxation function by solving numerically a Volterra integral equation of the second kind. So doing we provide a full characterization of the new model both in creep and in relaxation representation, where the slow varying functions of logarithmic type play a fundamental role as required in processes of ultra slow kinetics. (C) 2017 Elsevier Ltd. All rights reserved.
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