A fractional calculus approach to modeling rheological behavior of soft magnetic elastomers

Nadzharyan, T.A.; Сорокін, В. В.; Степанов, Г. В.; Bogolyubov, A. N.; Kramarenko, Elena Yu.

doi:10.1016/j.polymer.2016.03.075

Cited by 38 publications

(16 citation statements)

References 46 publications

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“…Bouc-Wen model and Ramberg-Osgood model were employed in parallel with viscoelastic model to describe the hysteresis behavior [23,24] ; and the disadvantage of classical viscoelastic model can be also remedied with fractional elements, in which the stress-strain relation is expressed by fractional derivatives [25,26,27] . Recently, an optimal fractional rheological model was constructed for MREs, and the interaction between the viscoelastic properties and the magnetic field was analysed in terms of fractional element order parameters [28,29] . Such constitutive models can be further developed by integrating the MR effect [30,31,32] .…”

Section: Introductionmentioning

confidence: 99%

A fractional-order model on the dynamic mechanical behavior of magnetorheological elastomers

Zhu¹,

Xiong²,

Li³

et al. 2020

Smart Mater. Struct.

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In order to describe the dynamic behavior of magnetorheological elastomers (MREs) for the realization of vibration control, this study proposes a constitutive model containing a fractional element and nonlinear springs attributed to the viscoelastic and the rheological properties, respectively. The viscoelastic behavior in various magnetic fields was studied experimentally to develop this fractional-order nonlinear model, and the model parameters were identified through experimental data fitting of dynamic modulus in frequency domain. The model predictions were subsequently obtained with the predictor-corrector approach to validate the proposed model by comparing with the experimental results on the stress-strain hysteresis. In addition, the efficiency of the proposed model of MRE was also evaluated by comparing the numerical solution with the results of the revised Bouc-Wen model.

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Section: Introductionmentioning

confidence: 99%

A fractional-order model on the dynamic mechanical behavior of magnetorheological elastomers

Zhu¹,

Xiong²,

Li³

et al. 2020

Smart Mater. Struct.

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show abstract

“…Therefore, modeling the frequency and amplitude dependence of MS rubber is also needed in additional to the magnetic dependence. The magnetic and frequency dependence of MS rubber can be depicted by the model developed by Kou et al [ 26 ], Brancati et al [ 27 ] and models based on the fractional derivative operator [ 28 , 29 ]. However, the amplitude dependence of MS rubber was not taken into account.…”

Section: Introductionmentioning

confidence: 99%

Constitutive Model of Isotropic Magneto-Sensitive Rubber with Amplitude, Frequency, Magnetic and Temperature Dependence under a Continuum Mechanics Basis

Wang

Kari

2021

Polymers

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A three-dimensional nonlinear constitutive model of the amplitude, frequency, magnetic and temperature dependent mechanical property of isotropic magneto-sensitive (MS) rubber is developed. The main components of MS rubber are an elastomer matrix and magnetizable particles. When a magnetic field is applied, the modulus of MS rubber increases, which is known as the magnetic dependence of MS rubber. In addition to the magnetic dependence, there are frequency, amplitude and temperature dependencies of the dynamic modulus of MS rubber. A continuum mechanical framework-based constitutive model consisting of a fractional standard linear solid (SLS) element, an elastoplastic element and a magnetic stress term of MS rubber is developed to depict the mechanical behavior of MS rubber. The novelty is that the amplitude, frequency, magnetic and temperature dependent mechancial properties of MS rubber are integrated into a whole constitutive model under the continuum mechanics frame. Comparison between the simulation and measurement results shows that the fitting effect of the developed model is very good. Therefore, the constitutive model proposed enables the prediction of the mechanical properties of MS rubber under various operating conditions with a high accuracy, which will drive MS rubber’s application in engineering problems, especially in the area of MS rubber-based anti-vibration devices.

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“…These phenomenological models can be used to predict the MRE behavior under complex loading conditions, even to solve the frequency- and strain-amplitude-dependent problems [ 16 ]. However, none of those models had strict microscopic justification or established the explicit functional relationship between the model parameters and the magnetic property [ 18 ]. Therefore, it is necessary to develop new phenomenological models to predict the magneto-mechanical coupling behaviors of MRE, which considers such magnetic property and the magnetic field dependence of model parameters.…”

Section: Introductionmentioning

confidence: 99%

A Magneto-Hyperelastic Model for Silicone Rubber-Based Isotropic Magnetorheological Elastomer under Quasi-Static Compressive Loading

Qiao

Zhang

et al. 2020

Polymers

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A new magneto-hyperelastic model was developed to describe the quasi-static compression behavior of silicone rubber-based isotropic magnetorheological elastomer (MRE) in this work. The magnetization property of MRE was characterized by a vibrating sample magnetometer (VSM), and the quasi-static compression property under different magnetic fields was tested by using a universal testing machine equipped with a magnetic field accessory. Experimental results suggested that the stiffness of the isotropic MRE increased with the magnetic flux density within the tested range. Based on experimental results, a new magneto-hyperelastic model was established by coupling the Ogden hyperelastic model, the magnetization model and the magneto-induced modulus model based on a magnetic dipole theory. The results show that the proposed new model can accurately predict the quasi-static compression property of the isotropic MRE under the tested magnetic flux density and strain ranges using only three model parameters.

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A fractional calculus approach to modeling rheological behavior of soft magnetic elastomers

Cited by 38 publications

References 46 publications

A fractional-order model on the dynamic mechanical behavior of magnetorheological elastomers

A fractional-order model on the dynamic mechanical behavior of magnetorheological elastomers

Constitutive Model of Isotropic Magneto-Sensitive Rubber with Amplitude, Frequency, Magnetic and Temperature Dependence under a Continuum Mechanics Basis

A Magneto-Hyperelastic Model for Silicone Rubber-Based Isotropic Magnetorheological Elastomer under Quasi-Static Compressive Loading

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