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Optimisation Approach for Parameter Estimation of the Generalised PTT Viscoelastic Model

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Computational Science and Its Applications – ICCSA 2021 (ICCSA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12952))

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Abstract

The exponential form of the original Phan-Thien and Tanner (PTT) model is often used to study complex viscoelastic fluids. Recently, a generalised version of the PTT model, that uses the Mittag-Leffler function to compute a new function of the trace of the stress tensor, was proposed. This new model adds one or two additional fitting parameters that allow for greater fitting capability. In this paper, we propose two optimisation problems for estimating the model parameters when fitting experimental data in shear (storage modulus, loss modulus, shear viscosity). We also propose a numerical sequential approach for solving one of these problems. The optimal values for the parameters produced by the optimisation approach allow the model to reproduce almost exactly the experimental data.

Supported by FCT - Fundação para a Ciência e a Tecnologia, through projects UIDB/00013/2020 and UIDP/00013/2020, and CMAT - Centre of Mathematics, University of Minho.

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References

  1. Holzapfel, G.: Nonlinear Solid Mechanics. A continuum Approach for Engineering (2001)

    Google Scholar 

  2. Phan-Thien, N., Tanner, R.I.: New constitutive equation derived from network theory. J. Nonnewton. Fluid Mech. 2(4), 353–365 (1977)

    Article  Google Scholar 

  3. Phan-Thien, N.: A nonlinear network viscoelastic model. J. Rheol. 22(3), 259–283 (1978)

    Article  Google Scholar 

  4. Tanner, R.I., Huilgol, R.R.: On a classification scheme for flow fields. Rheologica Acta 14(11), 959–962 (1975). https://doi.org/10.1007/BF01516297

    Article  MATH  Google Scholar 

  5. Ferrás, L.L., Morgado, M.L., Rebelo, M., Mckinley, G.H., Afonso, A.: A generalized phan-thien - tanner model. J. Nonnewton. Fluid Mech. 269, 88–99 (2019)

    Article  Google Scholar 

  6. Podlubny, I.: Fractional Differential Equations: an Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. vol. 198, Elsevier, San Diego (1998)

    Google Scholar 

  7. Huilgol, R.R., Phan-Thien, N.: Fluid Mechanics of Viscoelasticity: General Principles, Constitutive Modelling, Analytical and Numerical Techniques. Elsevier, Amsterdam (1997)

    Google Scholar 

  8. Alves, M.A., Pinho, F.T., Oliveira, P.J.: Study of steady pipe and channel flows of a single-mode phan-thien - tanner fluid. J. Nonnewton. Fluid Mech. 101(1–3), 55–76 (2001)

    Article  Google Scholar 

  9. Ansari, M., Hatzikiriakos, S.G., Mitsoulis, E.: Slip effects in HDPE flows. J. Nonnewton. Fluid Mech. 167, 18–29 (2012)

    MATH  Google Scholar 

  10. Nocedal, J., Wächter, A., Waltz, R.A: Adaptive barrier strategies for nonlinear interior methods. SIAM J. Optim. 19(4), 1674–1693 (2009)

    Google Scholar 

  11. Wächter, A., Biegler, L.T.: Line search filter methods for nonlinear programming: local convergence. SIAM J. Optim. 16(1), 32–48 (2005)

    Article  MathSciNet  Google Scholar 

  12. Wächter, A., Biegler, L.T.: Line search filter methods for nonlinear programming: motivation and global convergence. SIAM J. Optim. 16(1), 1–31 (2005)

    Article  MathSciNet  Google Scholar 

  13. Wächter, A., Biegler, L.T.: On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming. Math. Program. 106(1), 25–57 (2006)

    Article  MathSciNet  Google Scholar 

  14. Wächter, A.: n interior point algorithm for large-scale nonlinear optimization with applications in process engineering. PhD thesis. Carnegie Mellon University, Pittsburgh, PA, USA (2002)

    Google Scholar 

  15. Coleman, T.F., Li, Y.: An interior trust region approach for nonlinear minimization subject to bounds. SIAM J. Optim. 6(2), 418–445 (1996)

    Article  MathSciNet  Google Scholar 

  16. Gill, P.E., Murray, W., Wright, M.H.: Pract. Optim. Academic Press, London (1981)

    Google Scholar 

  17. Han, S.P.: A globally convergent method for nonlinear programming. J. Optim. Theory Appl. 22(3), 297–309 (1977)

    Article  MathSciNet  Google Scholar 

  18. Powell, M.J.D.: A fast algorithm for nonlinearly constrained optimization calculations. In: Watson, G.A. (ed.) Numerical Analysis. LNM, vol. 630, pp. 144–157. Springer, Heidelberg (1978). https://doi.org/10.1007/BFb0067703

    Chapter  Google Scholar 

  19. Powell, M.J.D., The convergence of variable metric methods for nonlinearly constrained optimization calculations. In: Nonlinear Programming, vol. 3, pp. 27–63. Academic Press (1978)

    Google Scholar 

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Authors and Affiliations

  1. Centre of Mathematics University of Minho, Campus de Gualtar, 4710-057, Braga, Portugal

    M. Fernanda P. Costa, C. Coelho & L. L. Ferrás

Authors
  1. M. Fernanda P. Costa
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  2. C. Coelho
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  3. L. L. Ferrás
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Corresponding author

Correspondence to M. Fernanda P. Costa .

Editor information

Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Potenza, Italy

    Beniamino Murgante

  3. Covenant University, Ota, Nigeria

    Sanjay Misra

  4. University of Cagliari, Cagliari, Italy

    Chiara Garau

  5. University of Cagliari, Cagliari, Italy

    Ivan Blečić

  6. Monash University, Clayton, VIC, Australia

    David Taniar

  7. Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  8. University of Minho, Braga, Portugal

    Ana Maria A. C. Rocha

  9. Polytechnic University of Bari, Bari, Italy

    Eufemia Tarantino

  10. Polytechnic University of Bari, Bari, Italy

    Carmelo Maria Torre

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Costa, M.F.P., Coelho, C., Ferrás, L.L. (2021). Optimisation Approach for Parameter Estimation of the Generalised PTT Viscoelastic Model. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2021. ICCSA 2021. Lecture Notes in Computer Science(), vol 12952. Springer, Cham. https://doi.org/10.1007/978-3-030-86973-1_34

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  • DOI: https://doi.org/10.1007/978-3-030-86973-1_34

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-86972-4

  • Online ISBN: 978-3-030-86973-1

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