Fractional Burgers models in creep and stress relaxation tests

Abstract

Classical and thermodynamically consistent fractional Burgers models are examined in creep and stress relaxation tests. Using the Laplace transform method, the creep compliance and relaxation modulus are obtained in integral form, that yielded, when compared to the thermodynamical requirements, the narrower range of model parameters in which the creep compliance is a Bernstein function while the relaxation modulus is completely monotonic. Moreover, the relaxation modulus may even be oscillatory function with decreasing amplitude. The asymptotic analysis of the creep compliance and relaxation modulus is performed near the initial time-instant and for large time as well.

arXiv commentThe manuscript is submitted to the Applied Mathematical Modelling on 25-02-2019

References in corpus (4)

• Fractional Calculus: Integral and Differential Equations of Fractional Order
• Creep, Relaxation and Viscosity Properties for Basic Fractional Models in Rheology
• Distributed-order fractional wave equation on a finite domain. Stress relaxation in a rod
• The Frequency Response Function of the Creep Compliance

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• Wave propagation in three-dimensional fractional viscoelastic infinite solid body
• Stress and power as a response to harmonic excitation of a fractional anti-Zener and Zener type viscoelastic body
• Fractional Burgers wave equation on a finite domain