Fractional Operator Viscoelastic Models in Dynamic Problems of Mechanics of Solids: A Review

Shitikova, Marina V.

doi:10.3103/s0025654422010022

Cited by 49 publications

(12 citation statements)

References 155 publications

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“…In contrast, the literature on viscoelastic constitutive relations and applications is immense. Indeed, in the past two years there have been several review papers on constitutive relations, which are either general or specific to a research area such as biomechanics [4,5]. Papers expanding these modeling frameworks are also very common to the current day [6,7].…”

Section: Introductionmentioning

confidence: 99%

A generalized time-domain constitutive finite element approach for viscoelastic materials

Abercrombie,

Gregory McDaniel,

Walsh

2024

Modelling Simul. Mater. Sci. Eng.

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Despite the existence of time domain finite element formulations forviscoelastic materials, there are still substantial ways to improve the analysis. Tothe authors’ knowledge, the formulation of the problem is always done with respectto a single constitutive relation and so limits the implementer to a single scheme withwhich to model relaxation. Furthermore, all current constitutive relations involvethe finding of fitting parameters for an analytical function, which is a sufficientlypainful process to warrant the study of best fitting procedures to this day. Incontrast, this effort is the first full derivation of the two dimensional problem fromfundamental principles. It is also the first generalization of the problem, which freesusers to select constitutive relations without re-derivation or re-expression of theproblem. This approach is also the first approach to the problem that could leadto the elimination of constitutive relations for representing relaxation in viscoelasticmaterials. Following, the full derivation, several common constitutive relations areoutlined with analysis of how they may best be implemented in the generalized form.Several expressions for viscoelastic terms are also provided given linear, quadratic, andexponential interpolation assumptions.

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Section: Introductionmentioning

confidence: 99%

A generalized time-domain constitutive finite element approach for viscoelastic materials

Abercrombie,

Gregory McDaniel,

Walsh

2024

Modelling Simul. Mater. Sci. Eng.

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“…Varying derivatives of fractional operators have now been used to help create the model of viscoelastic material behavior [39]. An extensive review of the fractional operator viscoelastic models in dynamic problems and their applications is done by Shitikova [40]. Mokhtari et al [41] examined the dynamic behavior of a sandwich circular cylindrical shell with a fractional viscoelastic core using the Donnell-Moshtari theory.…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis of sandwich cylindrical shells made of graphene platelet polymer–viscoelastic–ceramic/metal FG layers

Permoon

Farsadi

Askarian

2023

Funct. Compos. Struct.

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In this paper, natural frequencies and loss factors of cylindrical sandwich shells composed of the viscoelastic core layer, surrounded by functionally graded graphene-platelet reinforced polymer composite (FG-GPLRPC) and ceramic/metal (FG-ceramic/metal) are investigated. The viscoelastic layer is expressed using the fourth parameter fractional viscoelastic model, and the functionally graded ceramic/metal layer is theoretically modeled using a power-law function. The uniform, symmetric and un-symmetric patterns are considered for simulating the graphene platelet (GPL) nanofillers distributions along with the thickness direction. The classical shell theory is used for functionally graded layers and properties of the effective materials of GPLRPC multilayers are determined by using a modified Halpin–Tsai micromechanics model and the rule of mixture. The governing equations of motion are extracted by applying the Lagrange equation and the Rayleigh-Ritz method. The determinant of the coefficient matrix of the characteristic equation is calculated, and the natural frequencies and loss factors of the system are extracted. A study of the interactions of materials and geometrical factors such as the ratio of radius to length, the properties of functionally graded materials, and GPL weight fractions for patterns of proposed distributions is presented and some conclusions have been formed.

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“…Several applications take advantage of fractional models. A review regarding the application of fractional calculus in the models of linear viscoelasticity utilized in dynamic problems of mechanics of solids has been conducted by Shitikova [ 13 ]. Abouelregal [ 14 ] proposed a methodology to study thermoelastic vibrations in a homogeneous isotropic three-dimensional solid based on a fractional derivative Kelvin–Voigt model.…”

Section: Introductionmentioning

confidence: 99%

Fractional Calculus Approach to Reproduce Material Viscoelastic Behavior, including the Time–Temperature Superposition Phenomenon

2022

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The design of modern products and processes cannot prescind from the usage of viscoelastic materials that provide extreme design freedoms at relatively low cost. Correct and reliable modeling of these materials allows effective use that involves the design, maintenance, and monitoring phase and the possibility of reuse and recycling. Fractional models are becoming more and more popular in the reproduction of viscoelastic phenomena because of their capability to describe the behavior of such materials using a limited number of parameters with an acceptable accuracy over a vast range of excitation frequencies. A particularly reliable model parametrization procedure, using the poles–zeros formulation, allows researchers to considerably reduce the computational cost of the calibration process and avoid convergence issues typically occurring for rheological models. The aim of the presented work is to demonstrate that the poles–zeros identification methodology can be employed not only to identify the viscoelastic master curves but also the material parameters characterizing the time–temperature superposition phenomenon. The proposed technique, starting from the data concerning the isothermal experimental curves, makes use of the fractional derivative generalized model to reconstruct the master curves in the frequency domain and correctly identify the coefficients of the WLF function. To validate the methodology, three different viscoelastic materials have been employed, highlighting the potential of the material parameters’ global identification. Furthermore, the paper points out a further possibility to employ only a limited number of the experimental curves to feed the identification methodology and predict the complete viscoelastic material behavior.

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Fractional Operator Viscoelastic Models in Dynamic Problems of Mechanics of Solids: A Review

Cited by 49 publications

References 155 publications

A generalized time-domain constitutive finite element approach for viscoelastic materials

A generalized time-domain constitutive finite element approach for viscoelastic materials

Vibration analysis of sandwich cylindrical shells made of graphene platelet polymer–viscoelastic–ceramic/metal FG layers

Fractional Calculus Approach to Reproduce Material Viscoelastic Behavior, including the Time–Temperature Superposition Phenomenon

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