A generalization of the Lomnitz logarithmic creep law via Hadamard fractional calculus

Roberto Garra, Francesco Mainardi and Giorgio Spada

Chaos, Solitons & Fractals, 2017, vol. 102, issue C, 333-338

Abstract: 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 ν ∈ (0, 1], the logarithmic creep law known in rheology as Lomnitz law (obtained for ν=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.

Keywords: Linear viscoelasticity; Creep; Relaxation; Hadamard fractional derivative; Fractional calculus; Volterra integral equations; Ultra slow kinetics (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:102:y:2017:i:c:p:333-338

DOI: 10.1016/j.chaos.2017.03.032

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