Logarithmic method for continuous relaxation spectrum and comparison with previous methods

作者: Jung-Eun Bae , Kwang Soo Cho

DOI: 10.1122/1.4922851

关键词: Chebyshev polynomialsPower seriesDynamic dataApplied mathematicsViscoelasticityLogarithmLaplace transformElastic modulusMathematicsSpectrum (functional analysis)

摘要: Various algorithms for determining relaxation time spectrum have been to the fore, because plays an important role in interconversion between various viscoelastic functions. In this study, a new algorithm is developed by means of double-logarithmic power series approximation and Levenberg–Marquardt method. Compared with most previous algorithms, applicable not only dynamic data but also Laplace transform modulus, which available optical from generalized Stokes–Einstein equation or creep ringing. It worth noticing that determines continuous without any additional parameters precedent procedures. This paper suggests such framework newly its applications kinds data.

参考文章(46)
Wolfgang Thimm, Christian Friedrich, Tobias Roths, Josef Honerkamp, Molecular weight distribution dependent kernels in generalized mixing rules Journal of Rheology. ,vol. 44, pp. 1353- 1361 ,(2000) , 10.1122/1.1315307
G. Marin, W. W. Graessley, Viscoelastic properties of high molecular weight polymers in the molten state Rheologica Acta. ,vol. 16, pp. 527- 533 ,(1977) , 10.1007/BF01525652
R.S. Anderssen, D.W. Mead, Theoretical derivation of molecular weight scaling for rheological parameters Journal of Non-newtonian Fluid Mechanics. ,vol. 76, pp. 299- 306 ,(1998) , 10.1016/S0377-0257(97)00123-7
D. R. Wiff, RQP Method of Inferring a Mechanical Relaxation Spectrum Journal of Rheology. ,vol. 22, pp. 589- 597 ,(1978) , 10.1122/1.549491
Kwang Soo Cho, Gun Woo Park, Fixed-point iteration for relaxation spectrum from dynamic mechanical data Journal of Rheology. ,vol. 57, pp. 647- 678 ,(2013) , 10.1122/1.4789786
Hiroshi Watanabe, Satoshi Ishida, Yumi Matsumiya, Tadashi Inoue, Test of Full and Partial Tube Dilation Pictures in Entangled Blends of Linear Polyisoprenes Macromolecules. ,vol. 37, pp. 6619- 6631 ,(2004) , 10.1021/MA0495689
J. Honerkamp, Ill-posed problems in rheology Rheologica Acta. ,vol. 28, pp. 363- 371 ,(1989) , 10.1007/BF01336803
M. Simhambhatla, A. I. Leonov, The extended Padé-Laplace method for efficient discretization of linear viscoelastic spectra Rheologica Acta. ,vol. 32, pp. 589- 600 ,(1993) , 10.1007/BF00369076
Ian McDougall, Nese Orbey, John M. Dealy, Inferring meaningful relaxation spectra from experimental data Journal of Rheology. ,vol. 58, pp. 779- 797 ,(2014) , 10.1122/1.4870967
D. R. Wiff, Matatiahu Gehatia, Inferring mechanical relaxation spectra as an ill-posed problem Journal of Applied Physics. ,vol. 46, pp. 4231- 4234 ,(1975) , 10.1063/1.321404