Continuous relaxation and retardation spectrum method for viscoelastic characterization of asphalt concrete

Alvarez, F., Alegria, A., Colmenero, J.: Relationship between the time-domain Kohlrausch–Williams–Watts and frequency domain Havriliak–Negami relaxation functions. Phys. Rev. B 44(14), 7306–7312 (1991)

Baumgaertel, M., Winter, H.H.: Determination of discrete relaxation and retardation time spectra from dynamic mechanical data. Rheol. Acta 28, 511–519 (1989)

Baumgaertel, M., Schausberger, A., Winter, H.H.: The relaxation of polymers with linear flexible chains of uniform length. Rheol. Acta 29, 400–408 (1990)

Bažant, Z.P., Xi, Y.: Continuous retardation spectrum for solidification theory of concrete creep. J. Eng. Mech. 121(2), 281–288 (1995)

Brian, D.P., Brown, E.R., Anderson, R.M., Daniel, J.S., Swamy, A.K., Quintus, H.V., Shen, S., Carpenter, S.H., Bhattacharjee, S., Maghsoodloo, S.: Validating the fatigue endurance limit for hot mix asphalt. NCHRP Project Report #646. Transportation Research Board, National Research Council, Washington, DC, USA (2010)

Chehab, G.R., Kim, Y.R., Schapery, R.A., Witczak, M.W., Bonaquist, R.: Time-temperature superposition principle for asphalt concrete mixtures with growing damage in tension state. J. Assoc. Asph. Paving Technol. 71, 559–593 (2002)

Elster, C., Honerkamp, J., Weese, J.: Using regularization methods for the determination of relaxation and retardation spectra of polymeric liquids. Rheol. Acta 30, 161–174 (1991)

Emri, I., Tschoegl, N.W.: Generating line spectra from experimental responses. Part-I: Relaxation modulus and creep compliance. Rheol. Acta 32, 311–321 (1993a)

Emri, I., Tschoegl, N.W.: Generating line spectra from experimental responses. Part-II: Storage and loss functions. Rheol. Acta 32, 322–327 (1993b)

Emri, I., Tschoegl, N.W.: Determination of mechanical spectra from experimental responses. Int. J. Solids Struct. 32, 817–826 (1995)

Ferry, J.D.: Viscoelastic Properties of Polymers, 3rd edn. Wiley, New York (1980)

Hansen, S.: Estimation of the relaxation spectrum from dynamic experiments using Bayesian analysis and a new regularization constraint. Rheol. Acta 47, 169–178 (2008)

Havriliak, S., Negami, S.: A complex plane analysis of dispersions in some polymer systems. J. Polym. Sci., Part C 14, 99–117 (1966)

Honerkamp, J., Weese, J.: Determination of the relaxation spectrum by a regularization method. Macromolecules 22, 4372–4377 (1989)

Honerkamp, J., Weese, J.: A nonlinear regularization method for the calculation of relaxation spectra. Rheol. Acta 32, 65–73 (1993)

Liu, Y.: A direct method for obtaining discrete relaxation spectra from creep data. Rheol. Acta 40, 256–260 (2001)

Mustapha, S.M.F.D., Phillips, T.N.: A dynamic nonlinear regression method for the determination of the discrete relaxation spectrum. J. Phys. D, Appl. Phys. 33, 1–11 (2000)

Mun, S., Zi, G.: Modeling the viscoelastic function of asphalt concrete using a spectrum method. Mech. Time-Depend. Mater. 14, 191–202 (2010)

National Cooperative Highway Research Program (NCHRP): Guide for mechanistic empirical design of new and rehabilitated pavement structures: final report. Project #1-37A. Transportation Research Board, National Research Council, Washington, DC, USA (2004)

Park, S.W., Kim, Y.R.: Fitting Prony-series viscoelastic models with power-law presmoothing. J. Mater. Civ. Eng. 13, 26–32 (2001)

Provencher, S.W.: CONTIN a general purpose constrained regularization program for inverting linear algebraic or integral equations. Comput. Phys. Commun. 27, 229–242 (1982)

Ramkumar, D.H.S., Caruthers, J.M., Mavridis, H., Shroff, R.: Computation of the linear viscoelastic relaxation spectrum from experimental data. J. Appl. Polym. Sci. 64, 2177–2189 (1997)

Rowe, G.M., Khoee, S.H., Blankenship, P., Mahboub, K.C.: Evaluation of aspects of E ∗ test by using hot mix asphalt specimens with varying void contents. Transp. Res. Record 2127, 164–172 (2009)

Schapery, R.A.: A simple collocation method for fitting viscoelastic models to experimental data. Report GALCIT SM 61-23A. California Institute of Technology, Pasadena, CA (1961)

Stadler, F.J., Bailly, C.: A new method for the calculation of continuous relaxation spectra from dynamic-mechanical data. Rheol. Acta 48, 33–49 (2009)

Tschoegl, N.W.: The Phenomenological Theory of Linear Viscoelastic Behavior: An Introduction. Springer, New York (1989)

Winter, H.H., Mours, M.: IRIS-Handbook. IRIS Development, Amherst (2005)

Zorn, R.: Logarithmic moments of relaxation time distributions. J. Chem. Phys. 116(8), 3204–3209 (2002)