Numerical interconversion between linear viscoelastic material functions with regularization

International Journal of Solids and Structures

Volumn 44, Issue 3-4, 2007, Pages 1291-1303

  Sorvari, Joonas ^a   Malinen, Matti ^a  

^a UNIVERSITY OF EASTERN FINLAND   (Finland)

Author keywords

Interconversion; Linear viscoelasticity; Non ideal loading; Regularization; Relaxation test

Indexed keywords

COMPUTER SIMULATION; CREEP; ELASTIC MODULI; INTEGRAL EQUATIONS; RELAXATION PROCESSES;

INTERCONVERSION; LINEAR VISCOELASTICITY; NON-IDEAL LOADING; REGULARIZATION;

VISCOELASTICITY;

EID: 33751005585     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2006.06.029     Document Type: Article

References (17)

1. Dooling P.J., Buckley C.P., and Hinduja S. An intermediate model method for obtaining a discrete relaxation spectrum for creep data. Rheol. Acta. 36 (1997) 472-482
2. Flory A., and McKenna G.B. Finite step rate corrections in stress relaxation experiments: a comparison of two methods. Mech. Time Mater. 8 (2004) 17-37
3. Hansen P.C. Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion (1998), SIAM, Philadelphia
4. Honerkamp J., and Weese J. Tikhonovs regularization method for ill-posed problems-A comparison of different methods for the determination of the regularization parameter. Continuum Mech. Thermodyn. 2 (1990) 17-30
5. Hopkins I.L., and Hamming R.W. On creep and relaxation. J. Appl. Phys. 28 8 (1957) 906-909
6. Knoff W.F., and Hopkins I.L. An improved numerical interconversion for creep compliance and relaxation modulus. J. Appl. Polym. Sci. 16 (1972) 2963-2972
7. Lee S., and Knauss W.G. A note on the determination of relaxation and creep data from ramp tests. Mech. Time Mater. 4 (2000) 1-7
8. Linz P. Analytical and numerical methods for Volterra equations (1985), SIAM, Philadelphia
9. Liu Y. A direct method for obtaining discrete relaxation spectra from creep data. Rheol. Acta. 40 (2001) 256-260
10. Mead D.W. Numerical interconversion of linear viscoelastic material functions. J. Rheol. 38 6 (1994) 1769-1794
11. Meissner J. Combined constant strain rate and stress relaxation test for linear viscoelastic studies. J. Polym. Sci: Polym. P. Educ. 16 (1978) 915-919
12. Park S.W., and Schapery R.A. Methods of interconversion between linear viscoelastic material functions. Part I-a numerical method based on Prony series. Int. J. Solids Struct. 36 (1999) 1653-1675
13. Ramkumar D.H.S., Caruthers J.M., Mavridis H., and Shroff R. Computation of the linear viscoelastic relaxation spectrum from experimental data. J. Appl. Polym. Sci. 64 (1997) 2177-2189
14. Sorvari, J., Malinen M., 2006. Determination of relaxation modulus of a linearly viscoelastic material. Mechanics of time-dependent materials, doi: 10.1007/s11043-006-9011-4.
15. Tikhonov A.N. Regularization of incorrectly posed problems. Soviet Mathematics-Doklady 4 (1963) 1624-1627
16. Tschoegl N.W. The Penomenological Theory of Linear Viscoelastic Behaviour (1989), Springer-Verlag, Berlin
17. Zapas L.J., and Phillips J.C. Simple shearing flows in polyisobutylene solutions. J. Res. Nat. Bur. Stds. 75A 1 (1971) 33-40