On the direct estimation of creep and relaxation functions

Mechanics of Time-Dependent Materials

Volumn 11, Issue 2, 2007, Pages 143-157

  Sorvari, Joonas ^a   Malinen, Matti ^b  

^a VTT TECHNICAL RESEARCH CENTRE OF FINLAND   (Finland)

^b UNIVERSITY OF EASTERN FINLAND   (Finland)

Author keywords

Creep compliance; Linear viscoelasticity; Optimization; Regularization; Relaxation modulus

Indexed keywords

INTEGRAL EQUATIONS; LINEAR EQUATIONS; MATERIALS SCIENCE; RANDOM PROCESSES; RELAXATION PROCESSES;

CREEP COMPLIANCE; LINEAR VISCOELASTICITY; REGULARIZATION; RELAXATION MODULUS;

CREEP;

EID: 36049052536     PISSN: 13852000     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11043-007-9038-1     Document Type: Article

References (29)

1. Bradshaw, R.D., Brinson, L.C.: A sing control method for fitting and interconverting material functions for linearly viscoelastic solids. Mech. Time-Depend. Mater. 1, 85-108 (1997)
2. Bruhns, O.T., Anding, D.K.: On the simultaneous estimation of model parameters used in constitutive laws for inelastic material behaviour. Int. J. Plast. 15, 1311-1340 (1999)
3. Christensen, R.M.: Restrictions upon viscoelastic relaxation functions and complex moduli. J. Rheol. 16, 603-614 (1972)
4. Dooling, P.J., Buckley, C.P., Hinduja, S.: An intermediate model method for obtaining a discrete relaxation spectrum for creep data. Rheol. Acta 36, 472-482 (1997)
5. Findley, W.N., Lai, J.S., Onaran, K.: Creep and Relaxation of Nonlinear Viscoelastic Materials. Dover, New York (1989)
6. Flory, A., McKenna, G.B.: Finite step rate corrections in stress relaxation experiments: a comparison of two methods. Mech. Time-Depend. Mater. 8, 17-37 (2004)
7. Goh, S.M., Charalambides, M.N., Williams, J.G.: Determination of the constitutive constants of non-linear viscoelastic materials. Mech. Time-Depend. Mater. 8, 255-268 (2004)
8. Hansen, P.C., O'Leary, D.P.: The use of the L-curve in the regularization of discrete ill-posed problems. SIAM J. Sci. Comput. 14, 1487-1503 (1993)
9. Hansen, P.C.: Rank-Deficient and Discrete Ill-Posed Problems. SIAM, Philadelphia (1998)
10. Honerkamp, J., Weese, J.: Tikhonovs regularization method for ill-posed problems. Continuum Mech. Thermodyn. 2, 17-30 (1990)
11. Hopkins, I.L., Hamming, R.W.: On creep and relaxation. J. Appl. Phys. 28, 906-909 (1957)
12. Jao, S.Y., Arora, J.S., Wu, H.C.: An optimization approach for material-constant determination for the endochronic constitutive model. Comput. Mech. 8, 25-41 (1991)
13. Kouko, J., Kekko, P., Kurki, M.: Effect of strain rate on the strength properties of paper. In: Progress in Paper Physics Seminar (2006)
14. Lee, S., Knauss, W.G.: A note on the determination of the relaxation and creep data from ramp tests. Mech. Time-Depend. Mater. 4, 1-7 (2000)
15. Linz, P.: Analytical and Numerical Methods for Volterra Equations. SIAM, Philadelphia (1985)
16. Liu, Y.: Calculation of discrete relaxation modulus and creep compliance. Rheol. Acta 38, 357-364 (1999)
17. Liu, Y.: A direct method for obtaining discrete relaxation spectra from creep data. Rheol. Acta 40, 256-260 (2001)
18. Mahnken, R., Stein, E.: Parameter identification for viscoplastic models based on analytical derivatives of a least-squares functional and stability investigations. Int. J. Plast. 12, 451-479 (1996)
19. Meissner, J.: Combined constant strain rate and stress relaxation test for linear viscoelastic studies. J. Polym. Sci. 16, 915-919 (1978)
20. Müller, D., Hartmann, G.: Identification of materials parameters for inelastic constitutive models using principles of biologic evolution. J. Eng. Mater. Technol. 111, 299-305 (1989)
21. Nikov, A., Davies, A.R., Emri, I.: The determination of creep and relaxation functions from a single experiment. J. Rheol. 49, 1193-1211 (2005)
22. Park, S.W., 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, 1653-1675 (1999)
23. Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Springer, Berlin (1998)
24. Smith, T.L.: Evaluation of the relaxation modulus from the response to a constant rate of strain followed by a constant strain. J. Polym. Sci. 17, 2181-2188 (1979)
25. Sorvari, J., Malinen, M.: Determination of the relaxation modulus of a linearly viscoelastic material. Mech. Time-Depend. Mater. 10, 125-133 (2006)
26. Sorvari, J., Malinen, M.: Numerical interconversion between linear viscoelastic material functions with regularization. Int. J. Solids Struct. 44, 1291-1303 (2007)
27. Taylor, R.L., Pister, K.S., Goudreau, G.L.: Thermomechanical analysis of viscoelastic solids. Int. J. Numer. Methods Eng. 2, 45-59 (1970)
28. Tschoegl, N.W.: The Phenomenological Theory of Linear Viscoelastic Behavior. Springer, Berlin (1989)
29. Zapas, L.J., Phillips, J.C.: Simple shearing flows in polyisobutylene solution. J. Res. Nat. Bureau Stand. A Phys. Chem. 75, 33-40 (1971)