4,775 research outputs found

    Study on the generalized formulations with the aim to reproduce the viscoelastic dynamic behavior of polymers

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    Appropriate modelling of the real behavior of viscoelastic materials is of fundamental importance for correct studies and analyses of structures and components where such materials are employed. In this paper, the potential to employ a generalized Maxwell model and the relative fraction derivative model is studied with the aim to reproduce the experimental behavior of viscoelastic materials. For both models, the advantage of using the pole-zero formulation is demonstrated and a specifically constrained identification procedure to obtain the optimum parameters set is illustrated. Particular emphasis is given on the ability of the models to adequately fit the experimental data with a minimum number of parameters, addressing the possible computational issues. The question arises about the minimum number of experimental data necessary to estimate the material behavior in a wide frequency range, demonstrating that accurate results can be obtained by knowing only the data of the upper and low frequency plateaus plus the ones at the loss tangent peak

    On Rosenau-Type Approximations to Fractional Diffusion Equations

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    Owing to the Rosenau argument in Physical Review A, 46 (1992), pag. 12-15, originally proposed to obtain a regularized version of the Chapman-Enskog expansion of hydrodynamics, we introduce a non-local linear kinetic equation which approximates a fractional diffusion equation. We then show that the solution to this approximation, apart of a rapidly vanishing in time perturbation, approaches the fundamental solution of the fractional diffusion (a L\'evy stable law) at large times

    A distributed order viscoelastic model for small deformations

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    In this work we discuss the connection between classical, fractional and dis- tributed order viscoelastic Maxwell models, presenting the basic theory supporting these constitutive equations, and establishing some background on the admissibility of the dis- tributed order Maxwell model. We derive the storage and loss modulus functions for the distributed order viscoelastic model and perform a fitting to experimental data. The fitting results are compared with the Maxwell and Fractional Maxwell models.L.L. Ferr´as would also like to thank FCT for financial support through projects UIDB/ 00013/2020 and UIDP/00013/2020. M.L. Morgado aknowledges funding by FCT through project UID/Multi/04621/2019 of CEMAT/IST-ID, Center for Computational and Stochastic Mathematics, Instituto Su perior T´ecnico, University of Lisbon. This work was partially supported by the Funda¸c˜ao para a Ciˆencia e a Tecnologia (Por tuguese Foundation for Science and Technology) through the project UIDB/00297/2020 (Centro de Matem´atica e Aplica¸c˜oes). The authors also acknowledge financial support from COST Action CA15225, a network supported by COST (European Cooperation in Science and Technology)
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