Laws of mechanical relaxation processes in polymers

Slonimsky, G. L.

doi:10.1002/polc.5070160342

Cited by 39 publications

(12 citation statements)

References 7 publications

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“…Viscoelastic models based on fractional derivatives (FD) were introduced by Sloninsky in 1967 [25] to find a parsimonious representation for complex media. The mechanical responses predicted by such models were found to be consistent with the molecular theory of polymers by Bagley and Torvik [26].…”

Section: Introductionmentioning

confidence: 99%

Fractional derivative models for ultrasonic characterization of polymer and breast tissue viscoelasticity

Coussot

Kalyanam

Yapp

et al. 2009

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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The viscoelastic response of hydropolymers, which include glandular breast tissues, may be accurately characterized for some applications with as few as 3 rheological parameters by applying the Kelvin-Voigt fractional derivative (KVFD) modeling approach. We describe a technique for ultrasonic imaging of KVFD parameters in media undergoing unconfined, quasi-static, uniaxial compression. We analyze the KVFD parameter values in simulated and experimental echo data acquired from phantoms and show that the KVFD parameters may concisely characterize the viscoelastic properties of hydropolymers. We then interpret the KVFD parameter values for normal and cancerous breast tissues and hypothesize that this modeling approach may ultimately be applied to tumor differentiation.

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Section: Introductionmentioning

confidence: 99%

Fractional derivative models for ultrasonic characterization of polymer and breast tissue viscoelasticity

Coussot

Kalyanam

Yapp

et al. 2009

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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“…On the other hand Nutting (1921) observed that the creep or the relaxation test performed on any real material follow a power law kernel instead of an exponential one. Based on this observation the constitutive law of any real material, including rubber, glass, asphalt mixture, is ruled by a fractional operator (Koeller 1984;Bagley, Torvik 1983, 1986Slonimsky 1967;Smit, de Vrie 1970;Soczkiewicz 2002;Di Paola et al 2011). The characterization of the real material by means of fractional derivative and integrals of real order produces strong variations on the response with respect to the characterization involving derivatives (or integrals) of integer order.…”

Section: Introductionmentioning

confidence: 99%

Linear and Nonlinear Fractional Hereditary Constitutive Laws of Asphalt Mixtures

Mino

Airey

Paola

et al. 2016

Journal of Civil Engineering and Management

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Abstract. The aim of this paper is to propose a fractional viscoelastic and viscoplastic model of asphalt mixtures using experimental data of several tests such as creep and creep recovery performed at different temperatures and at different stress levels. From a best fitting procedure it is shown that both the creep one and recovery curve follow a power law model. It is shown that the suitable model for asphalt mixtures is a dashpot and a fractional element arranged in series. The proposed model is also available outside of the linear domain but in this case the parameters of the model depend on the stress level.

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“…(1.1) can be obtained from a fractional vibration equation for viscoelastic damped structures with a springpot component. The springpot, also known as the Scott Blair element, is an intermediate body between the purely elastic (Hookean element) and the perfectly viscous liquid (Newtonian element), see [32,33]. In 1967, Slonimsky [32] introduced the viscous element in studying the laws of mechanical relaxation processes in polymers.…”

Section: Introductionmentioning

confidence: 99%

Analytical solution of the generalized Bagley–Torvik equation

Pang

Wei

et al. 2019

Adv Differ Equ

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In this paper, we investigate the generalized Bagley-Torvik equation with the fractional order (0, 2). With a novel max-metric containing a Caputo derivative, the existence and uniqueness of the solution to the initial value problem are derived. We obtain the analytical solutions in terms of the Prabhakar function and the Wiman function, and they expand the well-known results about the general Bagley-Torvik equation. Two examples are presented to illustrate the validity of our main results.

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Laws of mechanical relaxation processes in polymers

Cited by 39 publications

References 7 publications

Fractional derivative models for ultrasonic characterization of polymer and breast tissue viscoelasticity

Fractional derivative models for ultrasonic characterization of polymer and breast tissue viscoelasticity

Linear and Nonlinear Fractional Hereditary Constitutive Laws of Asphalt Mixtures

Analytical solution of the generalized Bagley–Torvik equation

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