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Статті в журналах з теми "Generalised Maxwell Model"

Автор: Grafiati

Опубліковано: 12 квітня 2025

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1

Karner, Timi, Rok Belšak, and Janez Gotlih. "Using a Fully Fractional Generalised Maxwell Model for Describing the Time Dependent Sinusoidal Creep of a Dielectric Elastomer Actuator." Fractal and Fractional 6, no. 12 (December 4, 2022): 720. http://dx.doi.org/10.3390/fractalfract6120720.

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Анотація:

Actuators made of dielectric elastomers are used in soft robotics for a variety of applications. However, due to their mechanical properties, they exhibit viscoelastic behaviour, especially in the initial phase of their performance, which can be observed in the first cycles of dynamic excitation. A fully fractional generalised Maxwell model was derived and used for the first time to capture the viscoelastic effect of dielectric elastomer actuators. The Laplace transform was used to derive the fully fractional generalised Maxwell model. The Laplace transform has proven to be very useful and practical in deriving fractional viscoelastic constitutive models. Using the global optimisation procedure called Pattern Search, the optimal parameters, as well as the number of branches of the fully fractional generalised Maxwell model, were derived from the experimental results. For the fully fractional generalised Maxwell model, the optimal number of branches was determined considering the derivation order of each element of the branch. The derived model can readily be implemented in the simulation of a dielectric elastomer actuator control, and can also easily be used for different viscoelastic materials.

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2

Fabris, Júlio C. "Cosmological model from generalised Maxwell-Einstein system in higher dimensions." Physics Letters B 267, no. 1 (September 1991): 30–32. http://dx.doi.org/10.1016/0370-2693(91)90519-v.

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3

Zhao, Yanqing, Yuanbao Ni, and Weiqiao Zeng. "A consistent approach for characterising asphalt concrete based on generalised Maxwell or Kelvin model." Road Materials and Pavement Design 15, no. 3 (February 26, 2014): 674–90. http://dx.doi.org/10.1080/14680629.2014.889030.

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4

Liu, Zizhen, and Lynne Bilston. "On the viscoelastic character of liver tissue: experiments and modelling of the linear behaviour." Biorheology: The Official Journal of the International Society of Biorheology 37, no. 3 (May 2000): 191–201. http://dx.doi.org/10.1177/0006355x2000037003002.

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This paper presents the results of recent investigations into the viscoelastic character of liver tissue, especially the linear response. The linear domain of liver tissue has been determined by a strain sweep oscillation test. The fluid‐like viscoelastic behaviour of liver tissue was confirmed by stress relaxation experiments. To demonstrate the consistency and quality of the experimental data, the relaxation spectrum was used to reconstruct the relaxation modulus, as well as the storage and loss moduli. The generalised Maxwell model was successfully employed to model the mechanical behaviour in the linear viscoelastic domain.

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5

Long, Le Dinh, Bahman Moradi, Omid Nikan, Zakieh Avazzadeh, and António M. Lopes. "Numerical Approximation of the Fractional Rayleigh–Stokes Problem Arising in a Generalised Maxwell Fluid." Fractal and Fractional 6, no. 7 (July 2, 2022): 377. http://dx.doi.org/10.3390/fractalfract6070377.

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This paper presents a numerical technique to approximate the Rayleigh–Stokes model for a generalised Maxwell fluid formulated in the Riemann–Liouville sense. The proposed method consists of two stages. First, the time discretization of the problem is accomplished by using the finite difference. Second, the space discretization is obtained by means of the predictor–corrector method. The unconditional stability result and convergence analysis are analysed theoretically. Numerical examples are provided to verify the feasibility and accuracy of the proposed method.

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6

Yang, X. S. "Nonlinear viscoelastic compaction in sedimentary basins." Nonlinear Processes in Geophysics 7, no. 1/2 (June 30, 2000): 1–8. http://dx.doi.org/10.5194/npg-7-1-2000.

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Abstract. In the mathematical modelling of sediment compaction and porous media flow, the rheological behaviour of sediments is typically modelled in terms of a nonlinear relationship between effective pressure pe and porosity Φ, that is pe = pe (Φ). The compaction law is essentially a poroelastic one. However, viscous compaction due to pressure solution becomes important at larger depths and causes this relationship to become more akin to a viscous rheology. A generalised viscoelastic compaction model of Maxwell type is formulated, and different styles of nonlinear behaviour are asymptotically analysed and compared in this paper.

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7

Schiffmann, Kirsten Ingolf. "Nanoindentation creep and stress relaxation tests of polycarbonate: Analysis of viscoelastic properties by different rheological models." International Journal of Materials Research 97, no. 9 (September 1, 2006): 1199–211. http://dx.doi.org/10.1515/ijmr-2006-0189.

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Abstract Feedback-controlled nanoindentation with a Berkovich diamond tip has been used to perform creep and stress relaxation tests on polycarbonate at room temperature for a wide range of loads (10 – 30000 μN) and indentation depths (30 – 3000 nm). The creep compliance J(t) and relaxation modulus G(t) have been calculated from experimental data as a function of time in the range t = 0.1 – 100 (1000) s. The data are analysed by different rheological models which are compared: (1) the Burgers model, (2) the generalised Maxwell/generalised Kelvin model, and two empirical approaches: (3) a logarithmic model, and (4) a power law model. The Burgers model gives a poor description of the material behaviour since it assumes a steady-state flow of material which is not observed in the experimental time range. The generalised models yield a set of discrete relaxation- and retardation time constants. It is shown that these time constants do not correlate with specific molecular moving processes in the polymer, but are only one of several possible parameterisations of the creep and relaxation curves. Numerical differentiation of G(t) and J(t) shows that polycarbonate has continuous relaxation- and retardation time spectra, respectively, and the dynamic viscosity η(t) of the material increases linearly with time. The behaviour of polycarbonate is best represented by the empirical power law model, which allows optimum fit of creep/relaxation curves, relaxation and retardation time spectra and time-dependent viscosity.

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8

Naveena Kumara, A., Shreyas Punacha, and Md Sabir Ali. "Lyapunov exponents and phase structure of Lifshitz and hyperscaling violating black holes." Journal of Cosmology and Astroparticle Physics 2024, no. 07 (July 1, 2024): 061. http://dx.doi.org/10.1088/1475-7516/2024/07/061.

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Abstract We study the phase structure of Lifshitz and hyperscaling violating (HSV) black holes using Lyapunov exponents. For describing hyperscaling violating system, we chose a particular gravity model constructed from generalized Einstein-Maxwell-Dilaton action which includes the Lifshitz cases at appropriate limits. We study the relationship between Lyapunov exponents and black hole phase transitions considering both the timelike and null geodesics. We observe that, the black hole phase transiton properties are reflected in Lyapunov exponent where its multiple branches correspond to the distinct phases of the black hole. The discontinuos change of the Lyapunov exponent during the phase transition serve as an order parameter with critical exponent 1/2 near the critical point. Our numerical study reveals that the correlation between the Lyapunov exponent and black hole thermodynamic properties can be generalised beyond the AdS spacetime. We find that it is independent of the HSV parameter as well as the Lifshitz exponent.

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9

Gerritzen, Johannes, Michael Müller-Pabel, Jonas Müller, Benjamin Gröger, Niklas Lorenz, Christian Hopmann, and Maik Gude. "Development of a High-Fidelity Framework to Describe the Process-Dependent Viscoelasticity of a Fast-Curing Epoxy Matrix Resin including Testing, Modelling, Calibration and Validation." Polymers 14, no. 17 (September 2, 2022): 3647. http://dx.doi.org/10.3390/polym14173647.

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Fast-curing epoxy resins enable substantial reduction of cycle times during production of thermoset polymer matrix composites. Due to the snap-cure behaviour, both characterisation and processing of these resins are associated with high complexity which motivates the development of a high-fidelity framework for the prediction of the process-dependent behaviour ranging from experiment to model validation. In order to determine influence of time, temperature, and degree of cure, a multitude of rheometer and dynamic mechanical analysis experiments are conducted and evaluated. Building on the experimental results, a material model based on a generalised Maxwell model is developed. It is calibrated on the results obtained in the tests and shown to describe the material’s behaviour with high accuracy under all investigated conditions. The model’s predictive capabilities are further tested by applying it to a dynamic mechanical analysis, exposing the model to previously unknown loading and temperature conditions. It is demonstrated that the model is capable of predicting such changing boundary conditions with high accuracy.

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10

Parodi, Pietro, and Peter Watson. "PROPERTY GRAPHS – A STATISTICAL MODEL FOR FIRE AND EXPLOSION LOSSES BASED ON GRAPH THEORY." ASTIN Bulletin 49, no. 2 (March 27, 2019): 263–97. http://dx.doi.org/10.1017/asb.2019.4.

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AbstractIt is rare that the severity loss distribution for a specific line of business can be derived from first principles. One such example is the use of generalised Pareto distribution for losses above a large threshold (or more accurately: asymptotically), which is dictated by extreme value theory. Most popular distributions, such as the lognormal distribution or the Maxwell-Boltzmann-Bose-Einstein-Fermi-Dirac (MBBEFD), are convenient heuristics with no underlying theory to back them. This paper presents a way to derive a severity distribution for property losses based on modelling a property as a weighted graph, that is, a collection of nodes and weighted arcs connecting these nodes. Each node v (to which a value can also be assigned) corresponds to a room or a unit of the property where a fire can occur, while an arc (v, v′; p) between vertices v and v′ signals that the probability of the fire propagating from v to v′ is p. The paper presents two simple models for fire propagation (the random graph approach and the random time approach) and a model for explosion risk that allow one to calculate the loss distribution for a given property from first principles. The MBBEFD model is shown to be a good approximation for the simulated distribution of losses based on property graphs for both the random graph and the random time approach.

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11

Câmara, Gustavo, Rui Micaelo, Nuno Monteiro Azevedo, and Hugo Silva. "Incremental Viscoelastic Damage Contact Models for Asphalt Mixture Fracture Assessment." Infrastructures 9, no. 7 (July 22, 2024): 118. http://dx.doi.org/10.3390/infrastructures9070118.

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Asphalt mixtures are widely used as a surfacing material for pavements due to their several advantages. For this reason, robust numerical models still need to be developed to improve the understanding of their fracture behaviour. Recently, an incremental generalised Kelvin (GK) contact model that relates increments in contact displacements with increments in contact forces was proposed to assess the viscoelastic behaviour of asphalt mixtures within a discrete element method (DEM) framework. In this work, the contact model is extended to allow its application to asphalt mixture fracture studies. Two damage models—a brittle and a bilinear softening—coupled with the GK contact model are proposed to consider damage initiation and propagation. A parametric study is presented that assesses the impact of the GK-Damage parameters, showing a sensitivity to the loading velocity and the Maxwell elements, particularly its viscosity element, on the stress–strain response of a single contact. A reduced-size numerical mastic is initially used to speed up the calibration process of the GK-Damage contact parameters, with subsequent validation on a specimen with real experimental dimensions. It is shown that the proposed calibrated damage models can successfully reproduce the time-dependent behaviour, peak stress, and crack path observed in experimental results, highlighting the benefits of the adopted methodology. For the GK-Bilinear model, the fracture energy and maximum contact tensile stress are shown to adjust both the peak stress and softening response. Uniaxial tensile tests on asphalt mixtures indicate that the GK-Bilinear model provides a more realistic characterisation of fracture development. A higher susceptibility to damage at aggregate-to-mastic contacts compared to contacts within the mastic phase is identified.

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12

Castro-Palacio, Juan Carlos, J. M. Isidro, Esperanza Navarro-Pardo, Luisberis Velázquez-Abad, and Pedro Fernández-de-Córdoba. "Monte Carlo Simulation of a Modified Chi Distribution with Unequal Variances in the Generating Gaussians. A Discrete Methodology to Study Collective Response Times." Mathematics 9, no. 1 (December 31, 2020): 77. http://dx.doi.org/10.3390/math9010077.

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The Chi distribution is a continuous probability distribution of a random variable obtained from the positive square root of the sum of k squared variables, each coming from a standard Normal distribution (mean = 0 and variance = 1). The variable k indicates the degrees of freedom. The usual expression for the Chi distribution can be generalised to include a parameter which is the variance (which can take any value) of the generating Gaussians. For instance, for k = 3, we have the case of the Maxwell-Boltzmann (MB) distribution of the particle velocities in the Ideal Gas model of Physics. In this work, we analyse the case of unequal variances in the generating Gaussians whose distribution we will still represent approximately in terms of a Chi distribution. We perform a Monte Carlo simulation to generate a random variable which is obtained from the positive square root of the sum of k squared variables, but this time coming from non-standard Normal distributions, where the variances can take any positive value. Then, we determine the boundaries of what to expect when we start from a set of unequal variances in the generating Gaussians. In the second part of the article, we present a discrete model to calculate the parameter of the Chi distribution in an approximate way for this case (unequal variances). We also comment on the application of this simple discrete model to calculate the parameter of the MB distribution (Chi of k = 3) when it is used to represent the reaction times to visual stimuli of a collective of individuals in the framework of a Physics inspired model we have published in a previous work.

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13

ZHU, ChangSheng, HaiJun ZHANG, Qin YANG, and ZhiXian ZHONG. "Generalized maxwell velocity slip boundary model." SCIENTIA SINICA Physica, Mechanica & Astronomica 43, no. 5 (May 1, 2013): 662–69. http://dx.doi.org/10.1360/132011-827.

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14

Hu, H. "On the Nonlinear Generalized Maxwell Fluid Model." Journal of Applied Mechanics 70, no. 2 (March 1, 2003): 309–10. http://dx.doi.org/10.1115/1.1544538.

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An equation describing a nonlinear generalized Maxwell fluid model is presented. Model behavior, for constant rate elongations, is investigated. A comparison of the results in this study with those in the literature has been given. The conclusion of Corr et al. that the model has two solutions is questionable.

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15

Wang, Ping, Jin-Ling Liu, and Fang Wang. "The first solution for the helical flows of generalized Maxwell fluid with longitudinal time dependent shear stresses on the boundary." Thermal Science 26, no. 2 Part A (2022): 1113–21. http://dx.doi.org/10.2298/tsci2202113w.

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Helical flows of generalized Maxwell fluid is researched between two infinite co-axial circular cylinders. The velocity field and the adequate shear stress corresponding to the flow of a Maxwell fluid with fractional derivative model, between two infinite coaxial cylinders, are determined by means of the Laplace and finite Hankel transforms. The first solutions that have been obtained, presented under integral and series form in terms of the generalized G- and R-functions, satisfy all imposed initial and boundary conditions. The similar solutions for ordinary Maxwell and Newtonian fluid can be also obtained as the limit of the solution of generalized Maxwell fluid.

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16

Rehman, Aziz Ur, Fahd Jarad, Muhammad Bilal Riaz, and Zaheer Hussain Shah. "Generalized Mittag-Leffler Kernel Form Solutions of Free Convection Heat and Mass Transfer Flow of Maxwell Fluid with Newtonian Heating: Prabhakar Fractional Derivative Approach." Fractal and Fractional 6, no. 2 (February 10, 2022): 98. http://dx.doi.org/10.3390/fractalfract6020098.

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In this article, the effects of Newtonian heating along with wall slip condition on temperature is critically examined on unsteady magnetohydrodynamic (MHD) flows of Prabhakar-like non integer Maxwell fluid near an infinitely vertical plate under constant concentration. For the sake of generalized memory effects, a new mathematical fractional model is formulated based on a newly introduced Prabhakar fractional operator with generalized Fourier’s law and Fick’s law. This fractional model has been solved analytically and exact solutions for dimensionless velocity, concentration, and energy equations are calculated in terms of Mittag-Leffler functions by employing the Laplace transformation method. Physical impacts of different parameters such as α, Pr, β, Sc, Gr, γ, and Gm are studied and demonstrated graphically by Mathcad software. Furthermore, to validate our current results, some limiting models such as classical Maxwell model, classical Newtonian model, and fractional Newtonian model are recovered from Prabhakar fractional Maxwell fluid. Moreover, we compare the results between Maxwell and Newtonian fluids for both fractional and classical cases with and without slip conditions, showing that the movement of the Maxwell fluid is faster than viscous fluid. Additionally, it is visualized that both classical Maxwell and viscous fluid have relatively higher velocity as compared to fractional Maxwell and viscous fluid.

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17

Nguyen, ST, M.-H. Vu, MN Vu, and TN Nguyen. "Generalized Maxwell model for micro-cracked viscoelastic materials." International Journal of Damage Mechanics 26, no. 5 (October 7, 2015): 697–710. http://dx.doi.org/10.1177/1056789515608231.

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18

Hess, Siegfried, Bastian Arlt, Sebastian eidenreich, Patrick Ilg, Chris Goddard, and Ortwin Hess. "Flow Properties Inferred from Generalized Maxwell Models." Zeitschrift für Naturforschung A 64, no. 1-2 (February 1, 2009): 81–95. http://dx.doi.org/10.1515/zna-2009-1-213.

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Анотація:

The generalized Maxwell model is formulated as a nonlinear relaxation equation for the symmetric traceless stress tensor. The relaxation term of the equation involves the derivative of a potential function with respect to the stress tensor. Two special cases for this potential referred to as “isotropic” and “anisotropic” are considered. In the first case, the potential solely depends on the second scalar invariant, viz. the norm of the tensor. In the second case, also a dependence on the third scalar invariant, essentially the determinant, is taken into account in analogy to the Landau-de Gennes potential of nematic liquid crystals. Rheological consequences of the model are presented for a plane Couette flow with an imposed shear rate. The non-Newtonian viscosity and the normal stress differences are analyzed for stationary solutions. The dependence on the model parameters is discussed in detail. In particular, the occurrence of a shear-thickening behaviour is studied. The possibility to describe substances with yield stress and the existence of non-stationary, stick-slip-like solutions are pointed out. The extension of the model to magneto-rheological fluids is indicated.

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19

Xiao, Rui, Hongguang Sun, and Wen Chen. "An equivalence between generalized Maxwell model and fractional Zener model." Mechanics of Materials 100 (September 2016): 148–53. http://dx.doi.org/10.1016/j.mechmat.2016.06.016.

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20

Yenilmez, Bekir, Baris Caglar, and E. Murat Sozer. "Viscoelastic modeling of fiber preform compaction in vacuum infusion process." Journal of Composite Materials 51, no. 30 (March 27, 2017): 4189–203. http://dx.doi.org/10.1177/0021998317699983.

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A woven fabric’s compaction was modeled by using five viscoelastic models – Maxwell, Kelvin-Voigt, Zener, Burgers, and Generalized Maxwell – to reveal the capabilities and limitations of the models. The model parameters were optimized by minimizing the deviation between the model results and experimental data collected in our previous material characterization study mimicking different compaction stages (loading, fiber settling, wetting, unloading, and fiber relaxation) that a fiber structure undergoes during vacuum infusion process. Although Burgers and Generalized Maxwell models have the highest performance due to their almost equal coefficient of determination values, they have diverse characteristics in terms of modeling different stages of compaction. Burgers model allowed modeling the permanent deformation in relaxation stage, but failed in modeling permanent deformation in settling stage. Generalized Maxwell model could do the opposite, i.e. failed in the former and could handle the latter. This study’s major contribution is a holistic numerical approach and its conclusions by modeling all stages of the vacuum infusion process instead of one stage at a time, and thus optimizing only one set of model parameters (constants of springs and dampers) since they do not change with time. The numerical results of different models were fit to the results of a specially designed compaction characterization experiments conducted in our complementary study.

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21

Zhang, Chao, Jinhao Qiu, Yuansheng Chen, and Hongli Ji. "Modeling hysteresis and creep behavior of macrofiber composite–based piezoelectric bimorph actuator." Journal of Intelligent Material Systems and Structures 24, no. 3 (September 21, 2012): 369–77. http://dx.doi.org/10.1177/1045389x12460337.

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Macrofiber composite–based bimorph actuators inherit the nonlinear properties of hysteresis and creep of piezoelectric materials, which limit the accuracy in real-time control. Many hysteresis models have been proposed, and generalized Maxwell slip model consisting of a series of nonlinear elements is one of the simplest and most efficient operators to describe symmetrical hysteresis. However, these hysteresis operators do not contain the creep behavior of piezoelectric materials. In this study, a hybrid model including a generalized Maxwell slip operator, a creep operator, and a dynamic model is developed to characterize a macrofiber composite–based piezoelectric bimorph actuator. The generalized Maxwell slip operator is used to describe the hysteresis, the creep operator is used to describe the creep behavior, and a transfer function is used to describe the dynamic model. Each nonlinear element in the creep operator is made up of a diode, a resistance, and a capacitance. The experiment results show that the proposed model can accurately predict the hysteresis, creep, and dynamic behaviors of the macrofiber composite–based piezoelectric bimorph actuator.

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22

Cheng, Gang, Jean Claude Gelin, and Thierry Barrière. "Physical Modelling and Identification of Polymer Viscoelastic Behaviour above Glass Transition Temperature and Application to the Numerical Simulation of the Hot Embossing Process." Key Engineering Materials 554-557 (June 2013): 1763–76. http://dx.doi.org/10.4028/www.scientific.net/kem.554-557.1763.

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Анотація:

The experimental processing parameters, such as applied pressure and forming temperature have been analysed during polymer hot embossing of micro-cavities. The viscoelastic characteristics of polymer above the glass transition temperature have been investigated with the classical viscoelastic models. Generalized Maxwell Model has been used to describe polymer behaviours in the glass transition temperature range. The parameters include relaxation time, storage modulus and loss modulus of the Generalized Maxwell Model that have been introduced. The identification of polymer characteristics has been carried out through Dynamic Mechanical Analysis (DMA). The storage modulus, the loss modulus and the damping factor of the selected polymer have been obtained with different imposed frequencies. The master curve of complex modulus has been obtained by applying the time temperature superposition principle. The experimental data has been identified with optimized fitting parameters of Generalized Maxwell Model. A proper agreement between the experimental measurement and the identification of viscoelastic model is observed. The resulting constitutive equations have been implemented in finite element software in order to achieve the numerical simulation of the hot embossing process.

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23

Guemmadi, M., and A. Ouibrahim. "Generalized Maxwell Model as Viscoelastic Lubricant in Journal Bearing." Key Engineering Materials 478 (April 2011): 64–69. http://dx.doi.org/10.4028/www.scientific.net/kem.478.64.

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Анотація:

The hydrodynamic lubrication interest is still of great importance, so that more and more elaborated lubricants are considered. They, however, involve consequently more and more hydrodynamic complexity as a result of the rheological properties of the additives. In our case, we consider lubricants having viscoelastic properties described by a generalized Maxwell model used in the case of journal bearing lubrication. The complexity of the coupled associated equations (momentum and constitutive) to describe the hydrodynamic prevailing in such a geometry requires numerical solutions. Using the commercial Finite Volume software Fluent 6.3 together with an appropriate developed computational code, via UDF (User Defined Functions), we determine the pressure distribution as well as the flow velocity profile and the stress field in the core, the load bearing capacity developed and the attitude angle; all together with the effects of the viscoelastic lubricant parameters (relaxation time and shear viscosity).

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24

Kapteijn, F., J. A. Moulijn, and R. Krishna. "The generalized Maxwell–Stefan model for diffusion in zeolites:." Chemical Engineering Science 55, no. 15 (August 2000): 2923–30. http://dx.doi.org/10.1016/s0009-2509(99)00564-3.

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25

Corr, D. T., M. J. Starr, R. Vanderby,, and T. M. Best. "A Nonlinear Generalized Maxwell Fluid Model for Viscoelastic Materials." Journal of Applied Mechanics 68, no. 5 (April 26, 2001): 787–90. http://dx.doi.org/10.1115/1.1388615.

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Анотація:

A nonlinear Maxwell fluid model consisting of a linear dashpot in series with a parallel arrangement of a linear spring and a second-order nonlinear spring, was developed. This configuration provides the flexibility necessary to describe both the stiffening and the softening responses of some viscoelastic materials. A noteworthy feature of the model is that under constant rate displacement, the force equation can be solved in closed form, thereby providing a continuous, exact general solution.

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26

Luo, Dan, and Hong-Shan Chen. "A new generalized fractional Maxwell model of dielectric relaxation." Chinese Journal of Physics 55, no. 5 (October 2017): 1998–2004. http://dx.doi.org/10.1016/j.cjph.2017.08.020.

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27

Petera, Jerzy, Kamil Kaminski, and Monika Kotynia. "A generalized viscoelastic Maxwell model for semisolid thixotropic alloys." International Journal of Material Forming 3, S1 (April 2010): 775–78. http://dx.doi.org/10.1007/s12289-010-0885-y.

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28

Orekhov, A. A., L. N. Rabinskiy, and G. V. Fedotenkov. "Fundamental Solutions of the Equations of Classical and Generalized Heat Conduction Models." Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki 165, no. 4 (February 18, 2024): 404–14. http://dx.doi.org/10.26907/2541-7746.2023.4.404-414.

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Анотація:

This article presents the mathematical formulations of transient heat conduction problems corresponding to the models of classical heat conduction using the Fourier law and generalized heat conduction based on the Cattaneo–Vernotta–Lykov law (Maxwell–Cattaneo model), as well as the generalized Green–Nagdy type II and III models. The Fourier transforms in spatial coordinates and the Laplace transforms in time were used to obtain the fundamental solutions of the equations of the Maxwell–Cattaneo and Green–Nagdy type II and III models of classical and generalized heat conduction. The results were displayed graphically and analyzed. Differences between the considered heat conduction models were shown, and suggestions for their practical application were given.

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29

Kryvko, Andriy, Claudia del C. Gutiérrez-Torres, José Alfredo Jiménez-Bernal, Orlando Susarrey-Huerta, Eduardo Reyes de Luna, and Didier Samayoa. "Fractal Continuum Maxwell Creep Model." Axioms 14, no. 1 (January 2, 2025): 33. https://doi.org/10.3390/axioms14010033.

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In this work, the fractal continuum Maxwell law for the creep phenomenon is introduced. By mapping standard integer space-time into fractal continuum space-time using the well-known Balankin’s approach to variable-order fractal calculus, the fractal version of Maxwell model is developed. This methodology employs local fractional differential operators on discontinuous properties of fractal sets embedded in the integer space-time so that they behave as analytic envelopes of non-analytic functions in the fractal continuum space-time. Then, creep strain ε(t), creep modulus J(t), and relaxation compliance G(t) in materials with fractal linear viscoelasticity can be described by their generalized forms, εβ(t),Jβ(t) and Gβ(t), where β=dimS/dimH represents the time fractal dimension, and it implies the variable-order of fractality of the self-similar domain under study, which are dimS and dimH for their spectral and Hausdorff dimensions, respectively. The creep behavior depends on beta, which is characterized by its geometry and fractal topology: as beta approaches one, the fractal creep behavior approaches its standard behavior. To illustrate some physical implications of the suggested fractal Maxwell creep model, graphs that showcase the specific details and outcomes of our results are included in this study.

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30

Wang, Zhao Jing, Ling Luo, Yu Xi Jia, Jun Peng Gao, and Xiao Su Yi. "Predicting Polyurethane Shape Memory Behaviors in Stress-Controlled Situations Using a Viscoelastic Model." Key Engineering Materials 575-576 (September 2013): 101–6. http://dx.doi.org/10.4028/www.scientific.net/kem.575-576.101.

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As an outstanding class in smart materials of particular interest, shape memory polymers (SMPs) and their composites are drawing more and more attentions due to their potential applications in fields like biomedical and spacecraft industry. In this paper, shape memory behaviors of polyurethane (PU) in stress-controlled situations are simulated on the basis of the generalized Maxwell model and the time-temperature superposition principle. The free recovery cycles under three different imposed stresses and the influence on shape memory behaviors caused by changing heating rate are discussed. As the results reveal, the generalized Maxwell model can be used to describe the PU shape memory performance, and the shape recovery temperature increases with the increase of heating rate.

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31

Bách, Phạm Tiến, Võ Đại Nhật, Nguyễn Việt Kỳ, and Lê Quân. "Maxwell model geotextile encased stone column in soft soil improvement." Science & Technology Development Journal - Engineering and Technology 4, no. 1 (April 9, 2021): first. http://dx.doi.org/10.32508/stdjet.v4i1.772.

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In the field of geotechnical – soft soil improvement, the mathematical model or mechanical model is one of the important input parameters for the design calculations or studies. The determination of the appropriateness of the models has a great influence on the accuracy results of design and calculation as well as the sustainable stability of soft ground after improvement. On the contrary, the selection of inadequate calculation models will lead to increased costs of soft soil improvement, possibly even leading to the destabilization of the work and causing immense loss of people and property. Recently, many projects major highway after construction design in use has not meet the requirements of the standard, leading to wasted money and time of individuals, organizations, and the state of post-treatment. Therefore, the research and application of using mathematical or mechanical models in accordance with the new soft soil improvement method will greatly help as well as add additional options for soft soil improvement in Vietnam. The soft soil deformation is not only related to load but also to load time. The change in stress and deformation of weak soil over time is called rheology, and in this study is the viscoelastic behavior. From the above reasons, we try to apply a generalized Maxwell model to explain the viscoelastic behavior of a soft soil. In particular, the time-dependent behavior of a viscoelastic soft soil was represented by using the Maxwell rheological model. The Matlab programming code helps to solve numerically all the equation of the mathematical exhibition of the generalized Maxwell model results. We acknowledge that the generalized Maxwell model is superior in demonstrating the time-dependent behavior of soft soil. The results probably show that this is one of the effective models to predict the behavior of soft soils in ground improvement with GEC.

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32

BANERJEE, N., and R. BANERJEE. "GENERALIZED HAMILTONIAN EMBEDDING OF THE PROCA MODEL." Modern Physics Letters A 11, no. 24 (August 10, 1996): 1919–27. http://dx.doi.org/10.1142/s0217732396001922.

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We convert the second-class Proca model into a first-class theory by using the generalized prescription of Batalin, Fradkin and Tyutin. We then show how a basic set of gauge-invariant fields in the embedded model can be identified with the fundamental fields in the Proca model as well as with the observables in the Stückelberg model or in the model involving the interaction of an Abelian two-form field with the Maxwell field. The connection of these models with the massive Kalb–Ramond model is also elucidated within a path integral approach.

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33

Brandt, F. T., J. Frenkel, and D. G. C. McKeon. "Dual symmetry in a generalized Maxwell theory." Modern Physics Letters A 31, no. 32 (October 5, 2016): 1650184. http://dx.doi.org/10.1142/s0217732316501844.

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We examine Podolsky’s electrodynamics, which is non-invariant under the usual duality transformation. We deduce a generalization of Hodge’s star duality, which leads to a dual gauge field and restores to a certain extent the dual symmetry. The model becomes fully dual symmetric asymptotically, when it reduces to the Maxwell theory. We argue that this strict dual symmetry directly implies the existence of the basic invariants of the electromagnetic fields.

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34

Kibaroğlu, Salih, Oktay Cebecioğlu, and Ahmet Saban. "Gauging the Maxwell Extended GLn,R and SLn+1,R Algebras." Symmetry 15, no. 2 (February 9, 2023): 464. http://dx.doi.org/10.3390/sym15020464.

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We consider the extension of the general-linear and special-linear algebras by employing the Maxwell symmetry in D space-time dimensions. We show how various Maxwell extensions of the ordinary space-time algebras can be obtained by a suitable contraction of generalized algebras. The extended Lie algebras could be useful in the construction of generalized gravity theories and the objects that couple to them. We also consider the gravitational dynamics of these algebras in the framework of the gauge theories of gravity. By adopting the symmetry-breaking mechanism of the Stelle–West model, we present some modified gravity models that contain the generalized cosmological constant term in four dimensions.

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35

Basagiannis, Christos A., and Martin S. Williams. "Modified Generalized Maxwell Model for Hysteresis Behavior of Elastomeric Dampers." Journal of Engineering Mechanics 146, no. 8 (August 2020): 04020083. http://dx.doi.org/10.1061/(asce)em.1943-7889.0001801.

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36

Wang, Fan, Wang-Cheng Shen, Jin-Ling Liu, and Ping Wang. "The analytic solutions for the unsteady rotating flows of the generalized Maxwell fluid between coaxial cylinders." Thermal Science 24, no. 6 Part B (2020): 4041–48. http://dx.doi.org/10.2298/tsci2006041w.

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In this paper, we consider the unsteady rotating flow of the generalized Maxwell fluid with fractional derivative model between two infinite straight circular cylinders, where the flow is due to an infinite straight circular cylinder rotating and oscillating pressure gradient. The velocity field is determined by means of the combine of the Laplace and finite Hankel transforms. The analytic solutions of the velocity and the shear stress are presented by series form in terms of the generalized G and R functions. The similar solutions can be also obtained for ordinary Maxwell and Newtonian fluids as limiting cases.

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37

Stropek, Zbigniew, Zbigniew Stropek, Krzysztof Golacki, and Krzysztof Golacki. "Stress Relaxation of Apples at Different Deformation Velocities and Temperatures." Transactions of the ASABE 62, no. 1 (2019): 115–21. http://dx.doi.org/10.13031/trans.12993.

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ABSTRACT. Stress relaxation tests on apples (‘Beni Shogun’ variety) were performed at different velocities in the range of 0.0002 to 1 m s-1 and at three temperatures (2°C, 10°C, and 20°C). The generalized Maxwell model was used to describe the experimental stress relaxation curves. The two relaxation times of the model decreased with an increase in the deformation velocity. The relaxation times were related to the processes of gas and liquid flows in the intercellular spaces. This research showed the critical velocity associated with the weakness of the apple structure to lie between deformation velocities of 0.0002 and 0.002 m s-1, where a rapid decrease in the two relaxation times occurred. An increase in the peak force response with increasing deformation velocity showed the viscoelastic behavior of apple flesh. The equilibrium modulus describing the material condition after deformation was much larger under the quasi-static loading condition than the impact loading condition at all deformation velocities. The temperature did not seem to affect the Maxwell model parameters and peak force response for all deformation velocities under both loading conditions. Keywords: Apple, Generalized Maxwell model, Impact loading, Quasi-static loading, Stress relaxation, Viscoelasticity.

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38

Montenegro, David, and B. M. Pimentel. "Planar generalized electrodynamics for one-loop amplitude in the Heisenberg picture." International Journal of Modern Physics A 36, no. 19 (July 5, 2021): 2150142. http://dx.doi.org/10.1142/s0217751x21501426.

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We examine the generalized quantum electrodynamics as a natural extension of the Maxwell electrodynamics to cure the one-loop divergence. We establish a precise scenario to discuss the underlying features between photon and fermion where the perturbative Maxwell electrodynamics fails. Our quantum model combines stability, unitarity, and gauge invariance as the central properties. To interpret the quantum fluctuations without suffering from the physical conflicts proved by Haag’s theorem, we construct the covariant quantization in the Heisenberg picture instead of the Interaction one. Furthermore, we discuss the absence of anomalous magnetic moment and mass-shell singularity.

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39

Xue, Changfeng, and Junxiang Nie. "Exact Solutions of Rayleigh-Stokes Problem for Heated Generalized Maxwell Fluid in a Porous Half-Space." Mathematical Problems in Engineering 2008 (2008): 1–10. http://dx.doi.org/10.1155/2008/641431.

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The Rayleigh-Stokes problem for a generalized Maxwell fluid in a porous half-space with a heated flat plate is investigated. For the description of such a viscoelastic fluid, a fractional calculus approach in the constitutive relationship model is used. By using the Fourier sine transform and the fractional Laplace transform, exact solutions of the velocity and the temperature are obtained. Some classical results can be regarded as particular cases of our results, such as the classical solutions of the first problem of Stokes for Newtonian viscous fluids, Maxwell fluids, and Maxwell fluids in a porous half-space.

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40

Al-Bender, F., V. Lampaert, and J. Swevers. "The generalized Maxwell-slip model: a novel model for friction Simulation and compensation." IEEE Transactions on Automatic Control 50, no. 11 (November 2005): 1883–87. http://dx.doi.org/10.1109/tac.2005.858676.

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41

Hu Jun, 胡军, 许凯乐 Xu Kaile, 马壮壮 Ma Zhuangzhuang, and 马强 Ma Qiang. "Simulation Analysis of Aspherical Lens Molding Based on Generalized Maxwell Model." Laser & Optoelectronics Progress 57, no. 9 (2020): 092201. http://dx.doi.org/10.3788/lop57.092201.

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42

Nguyen, TuanDung, Jin Li, Lijie Sun, DanhQuang Tran, and Fuzhen Xuan. "Viscoelasticity Modeling of Dielectric Elastomers by Kelvin Voigt-Generalized Maxwell Model." Polymers 13, no. 13 (July 2, 2021): 2203. http://dx.doi.org/10.3390/polym13132203.

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Dielectric elastomers (DEs) are polymer materials consisting of a network of polymer chains connected by covalent cross-links. This type of structural feature allows DEs to generate large displacement outputs owing to the nonlinear electromechanical coupling and time-dependent viscoelastic behavior. The major challenge is to properly actuate the nonlinear soft materials in applications of robotic manipulations. To characterize the complex time-dependent viscoelasticity of the DEs, a nonlinear rheological model is proposed to describe the time-dependent viscoelastic behaviors of DEs by combining the advantages of the Kelvin–Voigt model and the generalized Maxwell model. We adopt a Monte Carlo statistical simulation method as an auxiliary method, to the best knowledge of the author which has never reportedly been used in this field, to improve the quantitative prediction ability of the generalized model. The proposed model can simultaneously describe the DE deformation processes under step voltage and alternating voltage excitation. Comparisons between the numerical simulation results and experimental data demonstrate the effectiveness of the proposed generalized rheological model with a maximum prediction error of 3.762% and root-mean-square prediction error of 9.03%. The results presented herein can provide theoretical guidance for the design of viscoelastic DE actuators and serve as a basis for manipulation control to suppress the viscoelastic creep and increase the speed response of the dielectric elastomer actuators (DEA).

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43

Kamenar, Ervin, and Saša Zelenika. "Issues in validation of pre-sliding friction models for ultra-high precision positioning." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 3 (February 14, 2018): 997–1006. http://dx.doi.org/10.1177/0954406218758797.

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Friction is one of the main disturbances in nanometric positioning. Recently, it was shown that ultra-high precision positioning typically happens in the pre-sliding motion regime where friction is characterized by an elasto-plastic nonlinear hysteretic behavior with a marked stochastic variability. With the aim of providing the tools for the development of robust control typologies for ultra-high precision mechatronics devices, different pre-sliding friction models are thus considered in this work. The most relevant ones are hence experimentally validated, as well as compared in terms of the complexity of identifying their characteristic parameters and of simulating the factual dynamic response. It is hence shown that the generalized Maxwell-slip model can account for all the important pre-sliding frictional effects in nanometric positioning applications. A thorough sensitivity analysis of the parameters of the generalized Maxwell-slip model model is therefore performed allowing to establish that three Maxwell-slip blocks are the minimum needed to approximate the behavior of the real precision positioning systems, six blocks allow representing excellently the real behavior, while the slower dynamics, which induces a difficult real-time implementation, with a very limited gain in terms of model accuracy, does not justify the usage of a larger number of elements.

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44

IKEDA, Kohsuke, Ryo OMURA, Toshikatsu NOHARA, Kazunori KUGA, Ryoji OKABE, Satoshi ISHIKAWA, and Masaki FUJIKAWA. "Applicability of Generalized Maxwell Model to Creep Deformation Behavior of Thermoplastics." Proceedings of Mechanical Engineering Congress, Japan 2021 (2021): J122–18. http://dx.doi.org/10.1299/jsmemecj.2021.j122-18.

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45

Niekamp, R., E. Stein, and A. Idesman. "Finite elements in space and time for generalized viscoelastic maxwell model." Computational Mechanics 27, no. 1 (January 29, 2001): 49–60. http://dx.doi.org/10.1007/s004660000213.

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46

Francis, Royce A., Srinivas Reddy Geedipally, Seth D. Guikema, Soma Sekhar Dhavala, Dominique Lord, and Sarah LaRocca. "Characterizing the Performance of the Conway-Maxwell Poisson Generalized Linear Model." Risk Analysis 32, no. 1 (July 30, 2011): 167–83. http://dx.doi.org/10.1111/j.1539-6924.2011.01659.x.

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47

Li, Chuangdi, Xuefeng Yang, Yuxiang Li, and Xinguang Ge. "Wind vibration responses of structure with generalized Maxwell model viscoelastic dampers." Structures 47 (January 2023): 425–33. http://dx.doi.org/10.1016/j.istruc.2022.10.127.

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48

Cao, Limei, Cong Li, Botong Li, Xinhui Si, and Jing Zhu. "Electro-osmotic flow of generalized Maxwell fluids in triangular microchannels based on distributed order time fractional constitutive model." AIP Advances 13, no. 2 (February 1, 2023): 025146. http://dx.doi.org/10.1063/5.0138004.

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Based on the linearized Poisson–Boltzmann equation, the electro-osmotic flow of a generalized Maxwell fluid under an alternating field in an isosceles right triangle microchannel is studied. The finite volume method and L2 interpolation method are used to obtain the numerical solution. An analytical solution is constructed to verify the accuracy of the numerical solution. Under the alternating current, the velocity will oscillate periodically. The velocity amplitude of the Maxwell fluid with the distributed order time fractional derivative is larger than that of Newtonian fluids and fractional Maxwell fluids, which indicates that its elastic characteristics further promote fluid flow. However, oscillation of the velocity does not achieve synchronization with the oscillation of the electric fields. Furthermore, due to the existence of the angle effect, the velocity will develop at acute angles and form a larger value of velocity first. The numerical results show that the relaxation time, electrokinetic width, zeta potential, and angular Reynolds number play important roles in determining the velocity and amplitude of electro-osmosis.

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49

Frolova, A. A. "Numerical Comparison of the Generalized Maxwell and Cercignani–Lampis Models." Computational Mathematics and Mathematical Physics 60, no. 12 (December 2020): 2094–107. http://dx.doi.org/10.1134/s0965542520120040.

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50

Jalocha, D., A. Constantinescu, and R. Neviere. "Revisiting the identification of generalized Maxwell models from experimental results." International Journal of Solids and Structures 67-68 (August 2015): 169–81. http://dx.doi.org/10.1016/j.ijsolstr.2015.04.018.

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