Formulation and integration of the standard linear viscoelastic solid with fractional order rate laws

Enelund, Mikael; Mähler, Lennart; Runesson, Kenneth; Josefson, B. L.

doi:10.1016/s0020-7683(98)00111-5

Cited by 77 publications

(28 citation statements)

References 11 publications

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“…Because the strain rate c is included in Equations (13) and (14), it is very clear that the FOCM can be used to consider the problem of rate sensitivity. Moreover, it can be shown that Equation (14) is a power law function, which can also be seen in Equations (11), (12), and (13). Such result is conducive to explain numerous power law phenomena in nature.…”

Section: Formula Of a Constant-strain-rate Loadingmentioning

confidence: 71%

Fractional order constitutive model of geomaterials under the condition of triaxial test

Yin

Chen

et al. 2012

Num Anal Meth Geomechanics

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SUMMARYFractional calculus has been successfully applied to characterize the rheological property of viscoelastic materials; however, geomaterials were seldom involved in fractional order constitutive models (FOCM), and the topic of first loading and then unloading is rarely discussed through fractional calculus. In this paper, mechanical properties are considered as a ‘spectrum’, both ends of which are elasticity and viscosity, and the fractional order can be utilized to describe such properties quantitatively. In addition to conditions such as creep, stress‐relaxation, and constant‐strain‐rate loading, stress‐strain relationship under the condition of first loading and then unloading was also derived using FOCM. FOCM is then adopted to simulate triaxial tests of geomaterials under corresponding conditions. A comparison of test and numerical results demonstrates that FOCM can reasonably describe the mechanical characteristics of geomaterials.Copyright © 2012 John Wiley & Sons, Ltd.

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Section: Formula Of a Constant-strain-rate Loadingmentioning

confidence: 71%

Fractional order constitutive model of geomaterials under the condition of triaxial test

Yin

Chen

et al. 2012

Num Anal Meth Geomechanics

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“…This finite difference approximation is applied to Eq. (2), and integrated over time, using the General Midpoint Rule (Enelund et al, 1999).…”

Section: Numerical Integration Of Constitutive Responsementioning

confidence: 99%

A fractional order rate approach for modeling concrete structures subjected to creep and fracture

Barpi

Valente

2004

International Journal of Solids and Structures

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“…According to the extended Riemann-Liouville deÿnition [16,19,20], the fractional -order derivative of the function f(t) is deÿned as…”

Section: Equations Of Motion With Fractional Dampingmentioning

confidence: 99%

Computation of the Laplace inverse transform by application of the wavelet theory

Wang

Zhou

Gao

2003

Commun. Numer. Meth. Engng.

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SUMMARYAn e cient and robust method of solving Laplace inverse transform is proposed based on the wavelet theory. The inverse function is expressed as a wavelet expansion with rapid convergence. Several examples are provided to demonstrate the methodology. As an example of application, the proposed inversion method is applied to the dynamic analysis of a single-degree-of-freedom spring-mass-damper system whose damping is described by a stress-strain relation containing fractional derivatives. The results are compared with previous studies.

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Formulation and integration of the standard linear viscoelastic solid with fractional order rate laws

Cited by 77 publications

References 11 publications

Fractional order constitutive model of geomaterials under the condition of triaxial test

Fractional order constitutive model of geomaterials under the condition of triaxial test

A fractional order rate approach for modeling concrete structures subjected to creep and fracture

Computation of the Laplace inverse transform by application of the wavelet theory

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