A Simplified Nonlinear Generalized Maxwell Model for Predicting the Time Dependent Behavior of Viscoelastic Materials

Monsia, M. D.

doi:10.4236/wjm.2011.13021

Cited by 28 publications

(18 citation statements)

References 3 publications

(9 reference statements)

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“…In this model, several Maxwell elements are assembled in parallel. It takes into account that the relaxation which occurs in a set of times and not in a single time (Chotard-Ghodsnia & Verdier, 2007;Monsia, 2011;Roylance, 2001…”

Section: Theoretical Consideration: Stress Relaxationmentioning

confidence: 99%

“…In this model, several Maxwell elements are assembled in parallel. It takes into account that the relaxation which occurs in a set of times and not in a single time (Chotard‐Ghodsnia & Verdier, ; Monsia, ; Roylance, ). The stress relaxation elements τ i (relaxation time [s]), E i (primary compressive stress), and E e (residual modulus at the end of test) were used for analyzing results.…”

Section: Introductionmentioning

confidence: 99%

Structural changes and stress relaxation behavior of κ‐carrageenan cold‐processed gels: Effects of ultrasonication time and power

Zendeboodi¹,

Farahnaky

Gholian

2019

Journal of Texture Studies

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Ultrasound has been used for cold gelation of κ‐carrageenan hydrocolloid. In this work, the effect of ultrasound conditions such as power (50–150 W) and time (20–240 s) of sonication has been investigated. The application of ultrasound to hydrocolloid dispersion caused an increase in water solubility. The texture profile analysis test was used in order to evaluate the mechanical properties of gels. Textural parameters of κ‐carrageenan gels, enhanced with increasing sonication time and power up to a certain level (usually 2.5 min) and longer sonication times had negative effects. In addition, intrinsic viscosities of sonicated specimens were measured to investigate the molecular characteristics of all samples. An increase in the process time and power reduced the intrinsic viscosity. The microstructural observation by scanning electron microscope determined that applying power ultrasound on κ‐carrageenan dispersions influenced the formation of gel networks significantly.

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“…The distribution has a variety of areas that range from statistics to physics, particularly in statistical mechanics. Some recent examples of this are: constructing fractional rheological constitutive equations (Schiessel et al, 1995); be friction model suitable for quick simulation and control (Farid et al, 2005); forecasting the temporal change of opening angle in multiple time scales and electroscalar wave (Zhang et al, 2008;Arbab and Satti, 2009); project of the time related to behavior of viscoelastic materials (Monsia, 2011). The properties of it also have been studied in some literature, see Liu and Fu (2013) and .…”

Section: Introductionmentioning

confidence: 99%

Tail behavior of the generalized Maxwell distribution

Huang

Chen

Tuo³

2016

Communications in Statistics - Theory and Methods

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Abstract. In this paper, we investigate the tail properties of the generalized Maxwell distribution and gain an asymptotic behavior of Mills-type ratio. Meanwhile, We show two applications. The first application thinks about the asymptotic property of the ratio of density functions and the ratio of the tails of the generalized Maxwell and classical Maxwell distributions. Another application obtains the asymptotic distribution of the partial maximum of an independent and identically distributed sequence from the distribution.

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“…In (Monsia, 2011d), the author formulated a nonlinear four-parameter rheological Voigt model made of a nonlinear Voigt element arranged in series with a classical linear Voigt element with constant material coefficients for representing the nonlinear stiffening response of the initial low-load portion and the softening, that is to say, the S-shaped mechanical behavior of some viscoelastic materials. Recently, Monsia (2011e) developed a simple nonlinear generalized Maxwell fluid model composed of nonlinear spring connected with a nonlinear dashpot in series obeying a power-law with constant material coefficients for representing accurately the time-dependent behavior of some viscoelastic materials. However, in many viscoelastic models, such as the models mentioned previously, in exception of the model (Monsia, 2011a), the inertia of the system under study is neglected.…”

Section: Introductionmentioning

confidence: 99%

A Theoretical Characterization of Time Dependent Materials by Using a Hyperlogistic-Type Model

Monsia¹,

Kpomahou²

2012

MER

Self Cite

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In this work, the classical mechanical Voigt model is modified and extended to finite deformations by using a rational elastic spring force function to describe accurately the nonlinear time-dependent deformation response of some viscoelastic materials. As theoretical results, a hyperlogistic-type function has been found as the deformation versus time relationship. This growth model appeared powerful to reproduce mathematically as shown by numerical works, any S-shaped experimental data. Compared with some previous models, the present one-dimensional formulation gives the advantage to assure or to control via an explicit material parameter, to speak, via the coefficient of inertia, the nonlinearity of the model. The proposed model demonstrated then the importance to consider in the material modeling the inertial coefficient.

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“…The nonlinear viscoelastic models have also been proposed for simulating materials with large deformation or properties that change with deformation or time 23,24 . For example, Schapery's model has considered the spring's elastic modulus as a nonlinear function of time 25 , and some other models have presented the dashpot's stress in a nonlinear function dependent on the strain rate 26,27 or relaxation time 28 . Please note that our literature review doesn't cover fluid models.…”

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confidence: 99%

A new nonlinear viscoelastic model and mathematical solution of solids for improving prediction accuracy

Engquist

Solaimanian

et al. 2020

Sci Rep

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We developed an innovative material nonlinear viscoelastic model with physical mechanism and mathematical solution to improve existing ones. the relaxation modulus transits from the glassy stage to the rubbery stage through a time-dependent viscosity in a continuous spectrum considering the nonlinear strain hardening. Experimental results of differential solid materials including asphalt concrete, agarose gel, vaginal tissue, polymer, agar, bone, spider silk, and hydrogel demonstrate that the developed model is superior to generalized Maxwell model or Prony series for more accurate prediction outside of the range for data fitting while using much less model parameters. Numerical simulation results indicate that the new model has improved accuracy. It is stable numerically, and does not reduce computation speed. Therefore, the model may be used to simulate a broad range of viscoelastic solids for predicting experimental data and responses with improved accuracy.

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A Simplified Nonlinear Generalized Maxwell Model for Predicting the Time Dependent Behavior of Viscoelastic Materials

Cited by 28 publications

References 3 publications

Structural changes and stress relaxation behavior of κ‐carrageenan cold‐processed gels: Effects of ultrasonication time and power

Tail behavior of the generalized Maxwell distribution

A Theoretical Characterization of Time Dependent Materials by Using a Hyperlogistic-Type Model

A new nonlinear viscoelastic model and mathematical solution of solids for improving prediction accuracy

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