Skip to main navigation menu Skip to main content Skip to site footer
ASPTA Baner

Vol. 2 No. 2 (2003)

Artykuły

A scheme for identification of continuous relaxation time spectrum of biological viscoelastic materials

DOI: https://doi.org/10.24326/aspta.2003.2.10
Submitted: May 18, 2023
Published: 2003-12-31

Abstract

The purpose of the paper is to investigate an algorithm for recovery of the continuous relaxation time spectrum of viscoelastic materials from time-measurements of linear relaxation modulus. A new identification scheme based on the least-squares approximation of relaxation modulus by finite serious of modified Bessel functions is proposed. The analysis of the scheme properties, in particular the convergence and model error analysis, as well as the numerical studies conducted indicates that the scheme proposed is an accuracy and easy implementable tool for recovery of the relaxation time spectra. The identification algorithm can be successfully applied to study the mechanical properties of highly hydrated plant materials subjected to various kinds of loading as well as different water solutions used in the food industry.

References

  1. Brabec Ch. J., Rögl H., Schausberger A., 1997. Investigation of relaxation properties of polymer melts by comparison of relaxation time spectra calculated with different algorithms. Rheol. Acta 36, 667–676. DOI: https://doi.org/10.1007/BF00367363
  2. Baumgaertel M., Winter H. H., 1989. Determination of discrete relaxation and retardation time spectra from dynamic mechanical data. Rheol. Acta 28, 511–519. DOI: https://doi.org/10.1007/BF01332922
  3. Chen P., Chen S., 1986. Stress relaxation functions of apple under high loading rates. Transaction of the ASAE 29, 1754–1759. DOI: https://doi.org/10.13031/2013.30384
  4. Chen P., 1994. Creep response of generalised Maxwell model. Int. Agrophysics 8, 555–558.
  5. Christensen R. M., 1971. Theory of Viscoelasticity. An Introduction. Academic Press New York.
  6. De Baerdemeaker J. G., Segerlind L. J., 1976. Determination of the viscoelastic properties of the apple flesh. Transaction of the ASAE 19, 346–353. DOI: https://doi.org/10.13031/2013.36025
  7. Derski W., Ziemba S., 1968. Analiza modeli reologicznych. PWN Warszawa.
  8. Elster C., Honerkamp J., Weese J., 1991. Using regularization methods for the determination of relaxation and retardation spectra of polymeric liquids. Rheol. Acta 30, 161–174. DOI: https://doi.org/10.1007/BF00373238
  9. Fujihara S., Yamamoto R., Masuda Y. 1995. Maxwellian Spectra of Stress Relaxation in the Cell Wall and Growth Regulation in Higher Plants. Proc. of Int. Workshop Stress Relaxation in Solids and Biological Origin, Prague 1995, 47–51.
  10. George S., Nair M. T., 1994. Parameter choice by discrepancy principles for ill-posed problems leading to optimal convergence rates. J. Optim. Theory Appl. 183, 217–222. DOI: https://doi.org/10.1007/BF02191771
  11. Gołacki K., 1998. Charakterystyki lepkosprężyste korzeni marchwi w szerokim zakresie prędkości obciążeń mechanicznych. Rozprawy Naukowe Akademii Rolniczej w Lublinie, 216.
  12. Gołacki K., Stankiewicz A., 2002. Algorytm obliczeniowy wyznaczania współczynnika Poissona lepkosprężystego materiału roślinnego. Acta Agrophysica 78, 51–61.
  13. Groetsch C. W., 1993. Inverse Problems in the Mathematical Sciences, Vieweg Publishing Wiesbaden. DOI: https://doi.org/10.1007/978-3-322-99202-4
  14. Hasiewicz Z., Stankiewicz A., 1985. On Input-Independent System Identification by Monte-Carlo Approach. IEEE Transaction on Automatic Control 30 (5), 480–483. DOI: https://doi.org/10.1109/TAC.1985.1103975
  15. Hellebrand H. J., 1995. Comparison of Models for Evaluation of Stress Relaxation. Proc. of Int. Workshop Stress Relaxation in Solids and Biological Origin, Prague 1995, 3–10.
  16. Kaczorek T., 1998. Wektory i macierze w automatyce i elektrotechnice. WNT Warszawa.
  17. Malkin A. Ya., Masalova I., 2001. From dynamic modulus via different relaxation spectra to relaxation and creep functions. Rheol. Acta 40, 261–271. DOI: https://doi.org/10.1007/s003970000128
  18. Morozov V. A.1966. On the solution of functional equations by the method of regularization. Soviet Mathematics Dokłady 7, 414–417.
  19. Orbey N., Dealy J. M., 1991. Determination of the relaxation spectrum from oscillatory shear data. J. Rheol. 35(6), 1035–1049. DOI: https://doi.org/10.1122/1.550164
  20. Owens R. G., Phillips T. N., 2002. Computational Rheology. Imperial College Press London. DOI: https://doi.org/10.1142/p160
  21. Paulson K. S., Jouravleva S., McLeod C. N. 2000. Dielectric Relaxation Time Spectroscopy. IEEE Trans. on Biomedical Engineering 47, 1510–1517. DOI: https://doi.org/10.1109/10.880103
  22. Phan-Thien N., Safari-Ardi M., 1998. Linear viscoelastic properties of flour-water doughs at different water concentrations. J. Non-Newtonian Fluid Mech. 74, 137–150. DOI: https://doi.org/10.1016/S0377-0257(97)00071-2
  23. Stankiewicz A., 1995. A decentralized three-level scheme for global identification of complex steady-state systems. Proc. Second International Symposium on Methods and Models in Automation and Robotics. Międzyzdroje 1995, 299–304.
  24. Syed Mustapha S. M. F. D., Phillips T. N., 2000. A dynamic nonlinear regression method for the determination of the discrete relaxation spectrum. J. Phys. D: Appl. Phys. 33, 1219–1229. DOI: https://doi.org/10.1088/0022-3727/33/10/313
  25. Ter Haar D., 1950. A Phenomenological Theory of Visco-Elastic Behaviour. I. Physica XVI, 719–737. DOI: https://doi.org/10.1016/0031-8914(50)90039-5
  26. Tichonow A. N., Samarski A. A., 1963. Równania fizyki matematycznej. PWN Warszawa.
  27. Tikhonov A. N., 1963. Solution of incorrectly formulated problems and the regularization method. Soviet Mathematics Doklady 4, 1035–1038.
  28. Winter H. H., 1997. Analysis of dynamical mechanical data: inversion into a relaxation time spectrum and consistency check. J. Non-Newtonian Mech. 68, 225–239. DOI: https://doi.org/10.1016/S0377-0257(96)01512-1
  29. Węgrzyn S., 1958. Przebiegi nieustalone w elektrycznych liniach i układach łańcuchowych. PWN Warszawa.

Downloads

Download data is not yet available.