An equivalence between generalized Maxwell model and fractional Zener model

Xiao, Rui; Sun, HongGuang; Chen, Wen

doi:10.1016/j.mechmat.2016.06.016

Cited by 72 publications

(43 citation statements)

References 29 publications

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“…Despite this drawback, this generalized viscoelastic model is adopted in our study as it is more convenient within finite element simulations, e.g., [16,17,18]. A comparison of the performance of the generalized Maxwell model and a fractional (Zener) model in [19] shows that both models are quantitatively equivalent. Finally, the physical meaning of some fractional derivative models is less intuitive.…”

Section: Materials Modelmentioning

confidence: 99%

Experimental and Numerical Study of Viscoelastic Properties of Polymeric Interlayers Used for Laminated Glass: Determination of Material Parameters

et al. 2019

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An accurate material representation of polymeric interlayers in laminated glass panes has proved fundamental for a reliable prediction of their response in both static and dynamic loading regimes. This issue is addressed in the present contribution by examining the time–temperature sensitivity of the shear stiffness of two widely used interlayers made of polyvinyl butyral (TROSIFOL BG R20) and ethylene-vinyl acetate (EVALAM 80-120). To that end, an experimental program has been executed to compare the applicability of two experimental techniques, (i) dynamic torsional tests and (ii) dynamic single-lap shear tests, in providing data needed in a subsequent calibration of a suitable material model. Herein, attention is limited to the identification of material parameters of the generalized Maxwell chain model through the combination of linear regression and the Nelder–Mead method. The choice of the viscoelastic material model has also been supported experimentally. The resulting model parameters confirmed a strong material variability of both interlayers with temperature and time. While higher initial shear stiffness was observed for the polyvinyl butyral interlayer in general, the ethylene-vinyl acetate interlayer exhibited a less pronounced decay of stiffness over time and a stiffer response in long-term loading.

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Section: Materials Modelmentioning

confidence: 99%

Experimental and Numerical Study of Viscoelastic Properties of Polymeric Interlayers Used for Laminated Glass: Determination of Material Parameters

et al. 2019

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“…With the development of fractional order methods, scholars begin to use fractional order to describe the constitutive equation of viscoelasticity. For example, the fractional derivative model [3][4][5], each model can also be converted to each other [6][7][8]. Since fractional order equations have good memory and can be used to describe material properties more accurately with fewer parameters, they are considered to be good mathematical models for describing the dynamic mechanical behavior of materials.…”

Section: Introductionmentioning

confidence: 99%

A numerical method for solving fractional-order viscoelastic Euler–Bernoulli beams

Zhang

Chen

et al. 2019

Chaos, Solitons & Fractals

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In this paper, a new method is presented for solving the constitutive equations of fractional-order viscoelastic Euler-Bernoulli beams. Firstly, the constitutive equation of the Euler-Bernoulli beam is established by analyzing the constitutive relation between the fractional viscoelastic materials. Secondly, the constitutive equation of the beam is transformed into a matrix equation by using a Quasi-Legendre polynomial in the time domain. Then the matrix equation is discretized and solved, and the numerical solution is obtained for the constitutive equation of the beam. Finally, numerical analysis of two different fractional viscoelastic materials is carried out by numerical experiments. Displacements under different external loads are obtained for the polybutadiene beam and butyl B252 beam. With the change of time and position, the change law of displacements is found. And the performance of the two materials is compared and analyzed.

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“…The standard linear solid model is a special case of the generalized Maxwell model (Figure 2), in which a spring and an arbitrary number of Maxwell bodies are connected in parallel. The standard linear solid model is much simpler compared to other more general models like the generalized Maxwell model and fractional-order viscoelastic model (Xiao et al, 2016). Nevertheless, the standard linear solid model is still useful for analyzing viscoelastic behaviors of many biomaterials like polycaprolactone scaffolds (Sethuraman et al, 2013) and hydrogels (Shazly et al, 2008;Feng et al, 2010;Tirella et al, 2014;Cacopardo et al, 2019).…”

Section: Introductionmentioning

confidence: 99%

Alternative Form of Standard Linear Solid Model for Characterizing Stress Relaxation and Creep: Including a Novel Parameter for Quantifying the Ratio of Fluids to Solids of a Viscoelastic Solid

Lin

2020

Front. Mater.

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The standard linear solid model (SLSM) is a typical and useful model for analyzing stress relaxation and creep behaviors of viscoelastic solids for obtaining the corresponding viscoelastic properties. However, the analysis results cannot be directly compared to the parameters commonly adopted for defining the mechanical properties of viscoelastic solids in the finite element simulation package such as the modulus of elasticity (E e) and the two parameters in the dimensionless form of the relaxation modulus (g and τ 1). The purpose of this paper is to introduce an alternative form of SLSM in terms of E e , g, and τ 1 for characterizing stress relaxation and creep behaviors. A series of stress relaxation and creep curves with different E e , g, and τ 1 was simulated by finite element simulation. The derived alternative form of SLSM was used to curve fit the simulated stress relaxation and creep curves to obtain the corresponding values of E e , g, and τ 1. The results showed that the values of E e , g, and τ 1 obtained from the simulation were approximately equal to the theoretical ones (i.e., those set in the simulation), showing that the alternative form of SLSM can accurately evaluate the corresponding E e , g, and τ 1. In conclusion, the alternative form is formulated in terms of the parameters used to define the mechanical properties in the finite element simulation package, so that the parameters obtained by curve fitting can be directly compared to those set in the finite element simulation package. It was also found that the physical meaning of g is associated with the ratio of viscous fluids to solids of a viscoelastic solid.

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An equivalence between generalized Maxwell model and fractional Zener model

Cited by 72 publications

References 29 publications

Experimental and Numerical Study of Viscoelastic Properties of Polymeric Interlayers Used for Laminated Glass: Determination of Material Parameters

Experimental and Numerical Study of Viscoelastic Properties of Polymeric Interlayers Used for Laminated Glass: Determination of Material Parameters

A numerical method for solving fractional-order viscoelastic Euler–Bernoulli beams

Alternative Form of Standard Linear Solid Model for Characterizing Stress Relaxation and Creep: Including a Novel Parameter for Quantifying the Ratio of Fluids to Solids of a Viscoelastic Solid

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