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    Wyświetlanie 1-4 z 4
    Tytuł:
    Parallel Scott-Blair fractional model of viscoelastic biological materials
    Autorzy:
    Stankiewicz, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/411389.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Oddział w Lublinie PAN
    Tematy:
    fractional calculus
    viscoelasticity
    relaxation modulus
    Scott-Blair fractional model
    Opis:
    Fractional calculus is a mathematical approach dealing with derivatives and integrals of arbitrary and also complex orders. Therefore, it adds a new means to understand and describe the nature and behavior of complex dynamical systems. Here we use the fractional calculus for modeling mechanical viscoelastic properties of materials. In the present work, after reviewing some of the main viscoelastic fractional models, a new parallel model is employed, connecting in parallel two Scott-Blair models with additional multiplicative weight functions. The model is presented in terms of two power functions weighted by Debye-type functions extend representation, understanding and description of complex systems viscoelastic properties. Monotonicity of the model relaxation modulus is studied and some upper bounds for the minimal time value, above which the model relaxation modulus is monotonically decreasing are given and compared both analytically and numerically. The comparison with the results of relaxation tests executed on some real phenomena has shown that the parallel Scott-Blair model involving fractional derivatives has been in a good agreement.
    Źródło:
    ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes; 2018, 7, 1; 107-115
    2084-5715
    Pojawia się w:
    ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Two-stage scheme for identification of parallel Scott-Blair fractional model of viscoelastic biological materials
    Autorzy:
    Stankiewicz, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/411463.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Oddział w Lublinie PAN
    Tematy:
    fractional calculus
    viscoelasticity
    relaxation modulus
    parallel Scott-Blair fractional model
    model identification
    Opis:
    Fractional calculus considers derivatives and integrals of an arbitrary order. This article focuses on fractional parallel Scott-Blair model of viscoelastic biological materials, which is a generalization of classic Kelvin-Voight model to non-integer order derivatives suggested in the previous paper. The parallel Scott-Blair model admit the closed form of analytical solution in terms of two power functions multiplied by Debye type weight function. To build a parallel Scott-Blair model when only discrete-time measurements of the relaxation modulus are accessible for identification is a basic concern. Based on asymptotic models a two-stage approach is proposed for fitting the measurement data, which means that in the first stage the data are fitted by solving two dependent, but simple, linear least-squares problems in two separate time intervals. Next, at the second stage of the identification procedure the exact parallel Scott-Blair model optimal in the least-squares sense is computed. The log-transformed relaxation modulus data is used in the first stage of identification scheme, while the original relaxation modulus data is applied for the second stage identification. A complete identification procedure is presented. The usability of the method to find the parallel Scott-Blair fractional model of real biological material is demonstrated. The parameters of the parallel Scott-Blair model of a sample of sugar beet root, which very closely approximate the experimental relaxation modulus data, are given.
    Źródło:
    ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes; 2018, 7, 1; 87-96
    2084-5715
    Pojawia się w:
    ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the monotonicity of the relaxation spectrum of fractional Maxwell model of viscoelastic materials
    Autorzy:
    Stankiewicz, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/411420.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Oddział w Lublinie PAN
    Tematy:
    fractional calculus
    viscoelasticity
    fractional Maxwell model
    relaxation spectrum
    maximum of relaxation spectrum
    Opis:
    This article focuses on the relaxation spectrum of fractional Maxwell model, which is a generalization of classic viscoelastic Maxwell model to non-integer order derivatives. The analytical formula for the spectrum of relaxation frequencies is derived. Theoretical analysis of the relaxation spectrum monotonicity is conducted by using simple analytical methods and illustrated by means of numerical examples. The necessary and sufficient conditions for the existence and uniqueness of the maximum of relaxation spectrum are stated and proved. The analytical formulas for minimum and maximum of the relaxation spectrum are derived. Also, a few useful properties concerning the relaxation spectrum monotonicity and concavity are given in the mathematical form of simple inequalities expressed directly in terms of the fractional Maxwell model parameters, which can be used to simplify the calculations and analysis.
    Źródło:
    ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes; 2018, 7, 1; 117-125
    2084-5715
    Pojawia się w:
    ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Non-integer viscoelastic constitutive law to model soft biological tissues to in-vivo indentation
    Autorzy:
    Demirci, N.
    Tönük, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/307448.pdf
    Data publikacji:
    2014
    Wydawca:
    Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
    Tematy:
    rachunek niecałkowitego rzędu
    tkanka miękka
    lepkosprężystość
    fractional calculus
    indentation tests
    inverse finite element analysis
    soft tissue constitutive relation
    viscoelasticity
    Opis:
    Purpose: During the last decades, derivatives and integrals of non-integer orders are being more commonly used for the description of constitutive behavior of various viscoelastic materials including soft biological tissues. Compared to integer order constitutive relations, non-integer order viscoelastic material models of soft biological tissues are capable of capturing a wider range of viscoelastic behavior obtained from experiments. Although integer order models may yield comparably accurate results, non-integer order material models have less number of parameters to be identified in addition to description of an intermediate material that can monotonically and continuously be adjusted in between an ideal elastic solid and an ideal viscous fluid.Methods: In this work, starting with some preliminaries on non-integer (fractional) calculus, the “spring-pot”, (intermediate mechanical element between a solid and a fluid), non-integer order three element (Zener) solid model, finally a user-defined large strain non-integer order viscoelastic constitutive model was constructed to be used in finite element simulations. Using the constitutive equation developed, by utilizing inverse finite element method and in vivo indentation experiments, soft tissue material identification was performed. Results: The results indicate that material coefficients obtained from relaxation experiments, when optimized with creep experimental data could simulate relaxation, creep and cyclic loading and unloading experiments accurately.Conclusions: Non-integer calculus viscoelastic constitutive models, having physical interpretation and modeling experimental data accurately is a good alternative to classical phenomenological viscoelastic constitutive equations.
    Źródło:
    Acta of Bioengineering and Biomechanics; 2014, 16, 4; 13-21
    1509-409X
    2450-6303
    Pojawia się w:
    Acta of Bioengineering and Biomechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-4 z 4

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