Alternative Function to Represent Relaxation Modulus of Viscoelastic Materials
Publication: Journal of Materials in Civil Engineering
Volume 24, Issue 2
Abstract
The generalized Maxwell model has been widely adopted for the prediction of relaxation modulus of viscoelastic materials, specifically asphalt materials. For practical reasons, relaxation modulus is rarely measured; instead it is predicted from creep compliance tests. In reality, the generalized Maxwell model is an approximate approach to simplify the process of inverting the Laplace transform of the Prony series function such that the computation process of obtaining relaxation modulus from creep compliance can become less complex. An alternative function can be derived to directly invert the Laplace transform of the Prony series function and predict relaxation moduli of viscoelastic materials. This paper presents a computation procedure on the basis of an alternative function that can be used to predict relaxation moduli of viscoelastic materials. The proposed model is capable of inverting the Laplace transform of the Prony series function and predicting the relaxation moduli of viscoelastic materials with only the component of one Maxwell model and one Kelvin element known as a Burger model. The algorithm presented in the proposed model is simple such that it can reduce the complexity of the computational process of inversing Laplace transform and generating Prony series parameters.
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References
AASHTO. (2009). “Standard method of test for determining the flexural creep stiffness of asphalt binder using the bending beam rheometer (BBR).” T 313, Washington, DC.
Ceylan, H., Gopalakrishnan, K., and Kim, S. H. (2008). “Advanced approaches to hot-mix asphalt dynamic modulus prediction.” Can. J. Civ. Eng., 35(7), 699–707.
Christensen, R. M. (2003). Theory of viscoelasticity, 2nd Ed., Dover Publications, New York.
Elseifi, M. A., Al-Qadi, I. L., and Yoo, P. J. (2006). “Viscoelastic modeling and field validation of flexible pavements.” J. Eng. Mech., 132(2), 172–178.
Findley, W. N., Lai, J. S., and Onaran, K. (1989). Creep and relaxation of nonlinear viscoelastic materials, Dover Publications, New York.
Ho, C. H. (2010). “Control of thermal-induced failures in asphalt pavements.” Ph.D. dissertation, Univ. of Utah, Salt Lake City, UT.
Ho, C. H., and Romero, P. (2011). “Using asphalt mixture beams in the bending beam rheometer: Experimental and numerical approach.” J. Road Mater. Pavement Des., 12(2), 239–262.
Huang, Y. H. (2004). Pavement analysis and design, 2nd Ed., Pearson Education, Upper Saddle River, NJ.
Kim, J. S., Roque, R., and Byron, T. (2009). “Viscoelastic analysis of flexible pavements and its effects on top-down cracking.” J. Mater. Civ. Eng., 21(7), 324–332.
Kim, J. S., Scholar, G. A., and Kim, S. G. (2008). “Determination of accurate creep compliance and relaxation modulus at a single temperature for viscoelastic solids.” J. Mater. Civ. Eng., 20(2), 147–156.
Malkin, A. Y., and Masalova, I. (2001). “From dynamic modulus via different relaxation spectra to relaxation and creep functions.” Rheol. Acta, 40(3), 261–271.
Mun, S. H., Chehab, G. R., and Kim, Y. R. (2007). “Determination of time-domain viscoelastic functions using optimized interconversion techniques.” J. Road Mater. Pavement Des., 8(2), 351–365.
Nikonov, A., Davies, A. R., and Emri, I. (2005). “The determination of creep and relaxation modulus functions from a single experiment.” J. Rheol., 49(6), 1193–1211.
Park, S. W., and Kim, Y. R. (1998). “Analysis of layered viscoelastic system with transit temperatures.” J. Eng. Mech., 124(2), 223–231.
Park, S. W., and Kim, Y. R. (1999). “Interconversion between relaxation modulus and creep compliance for viscoelastic solids.” J. Mater. Civ. Eng., 11(1), 76–82.
Velasquez, R., Marasteanu, M., and Mugurel, T. (2009). “Effect of beam size on the creep stiffness of asphalt mixtures at low temperatures.” Proc., 7th Int. RILEM Symp. on Advanced Testing and Characterization of Bituminous Materials, RILEM Publications, Bagneux, France.
Velasquez, R., Zofka, A., Turos, M., and Marasteanu, M. O. (2011). “Bending beam rheometer testing of asphalt mixtures.” Int. J. Pavement Eng., 12(5), 461–474.
Zofka, A., Marasteanu, M., and Turos, M. (2008). “Determination of asphalt mixture creep compliance at low temperatures using thin beam specimens.” Transportation Research Record 2057, Transportation Research Board, Washington, DC, 134–139.
Zofka, A., Marasteanu, M. O., Li, Xinjun, Clyne, T. R., and McGraw, J. (2005). “Simple method to obtain asphalt binders low temperature properties from asphalt mixtures properties.” J. Assoc. Asphalt Paving Technol., 74, 255–282.
Information & Authors
Information
Published In
Journal of Materials in Civil Engineering
Volume 24 • Issue 2 • February 2012
Pages: 152 - 158
Copyright
© 2012 American Society of Civil Engineers.
History
Received: Aug 19, 2010
Accepted: Aug 17, 2011
Published online: Aug 19, 2011
Published in print: Feb 1, 2012
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