Weak Form Equation–Based Finite-Element Modeling of Viscoelastic Asphalt Mixtures
Publication: Journal of Materials in Civil Engineering
Volume 28, Issue 2
Abstract
The objective of this study is to demonstrate using weak form partial differential equation (PDE) method for a finite-element (FE) modeling of a new constitutive relation without the need of user subroutine programming. The viscoelastic asphalt mixtures were modeled by the weak form PDE-based FE method as the examples in the paper. A solid-like generalized Maxwell model was used to represent the deforming mechanism of a viscoelastic material, the constitutive relations of which were derived and implemented in the weak form PDE module of Comsol Multiphysics, a commercial FE program. The weak form PDE modeling of viscoelasticity was verified by comparing Comsol and Abaqus simulations, which employed the same loading configurations and material property inputs in virtual laboratory test simulations. Both produced identical results in terms of axial and radial strain responses. The weak form PDE modeling of viscoelasticity was further validated by comparing the weak form PDE predictions with real laboratory test results of six types of asphalt mixtures with two air void contents and three aging periods. The viscoelastic material properties such as the coefficients of a Prony series model for the relaxation modulus were obtained by converting from the master curves of dynamic modulus and phase angle. Strain responses of compressive creep tests at three temperatures and cyclic load tests were predicted using the weak form PDE modeling and found to be comparable with the measurements of the real laboratory tests. It was demonstrated that the weak form PDE-based FE modeling can serve as an efficient method to implement new constitutive models and can free engineers from user subroutine programming.
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References
ABAQUS. (2010). Abaqus analysis user’s manuals, Hibbit, Karlsson & Sorensen, Pawtucket, RI.
ARA. (2004). “Guide for mechanistic-empirical design of new and rehabilitated pavement structures.”, Transportation Research Board, Washington, DC.
Biligiri, K. P., Kaloush, K., and Uzan, J. (2010). “Evaluation of asphalt mixtures’ viscoelastic properties using phase angle relationships.” Int. J. Pavement Eng., 11(2), 143–152.
COMSOL. (2013a). Comsol multiphysics reference manual (Version 4.3b), 〈www.comsol.com〉 (Sep. 27, 2013).
COMSOL. (2013b). Structural mechanics module user’s guide (Version 4.3b), 〈www.comsol.com〉 (Sep. 27, 2013).
Darabi, M. K., Abu Al-Rub, R. K., Masad, E. A., Huang, C.-W., and Little, D. N. (2012). “A modified viscoplastic model to predict the permanent deformation of asphaltic materials under cyclic-compression loading at high temperatures.” Int. J. Plast., 35, 100–134.
Findley, W. N., Lai, J. S., and Onaran, K. (1989). Creep and relaxation of nonlinear viscoelastic materials with an introduction to linear viscoelasticity, Dover, Mineola, NY.
Francken, L., and Verstraeten, J. (1998). “Interlaboratory test program on complex modulus and fatigue.”, Bituminous Binders and Mixes, London, 182–215.
Gibson, N. H., Schwartz, C. W., Schapery, R. A., and Witczak, M. W. (2003). “Viscoelastic, viscoplastic, and damage modeling of asphalt concrete in unconfined compression.”, Transportation Research Board, Washington, DC, 3–15.
Hu, S., and Zhou, F. (2010). “Development of a new interconversion tool for hot mix asphalt (Hma) linear viscoelastic functions.” Can. J. Civ. Eng., 37(8), 1071–1081.
Huang, C. W., Abu Al-Rub, R. K., Masad, E. A., and Little, D. N. (2011). “Three-dimensional simulations of asphalt pavement permanent deformation using a nonlinear viscoelastic and viscoplastic model.” J. Mater. Civ. Eng., 56–68.
Katicha, S., Flintsch, G., Loulizi, A., and Wang, L. (2008). “Conversion of testing frequency to loading time applied to the mechanistic-empirical pavement design guide.”, Transportation Research Board, Washington, DC, 99–108.
Levenberg, E., and Shah, A. (2008). “Interpretation of complex modulus test results for asphalt-aggregate mixes.” J. Test. Eval., 36(4), 326–334.
Levenberg, E., and Uzan, J. (2004). “Triaxial small-strain viscoelastic-viscoplastic modeling of asphalt aggregate mixes.” Mech. Time-Depend. Mater., 8(4), 365–384.
Mun, S., Chehab, G. R., and Kim, Y. R. (2007). “Determination of time-domain viscoelastic functions using optimized interconversion techniques.” Road Mater. Pavement Des., 8(2), 351–365.
Park, S. W., and Schapery, R. A. (1999). “Methods of interconversion between linear viscoelastic material functions. I: A numerical method based on Prony series.” Int. J. Solids Struct., 36(11), 1653–1675.
Pellinen, T. K., Witczak, M. W., and Bonaquist, R. F. (2002). “Asphalt mix master curve construction using sigmoidal fitting function with non-linear least squares optimization.” Proc., Pavement Mechanics Symp. at the 15th ASCE Engineering Mechanics Division Conf., ASCE, Reston, VA.
TxDOT (Texas Department of Transportation). (2004). “Standard specifications for construction and maintenance of highways, streets, and bridges.” Austin, TX.
TxDOT (Texas Department of Transportation). (2008). “Test procedure for design of bituminous mixtures.”, Austin, TX.
Wineman, A. S., and Rajagopal, K. R. (2001). Mechanical response of polymers: An introduction, Cambridge University Press, New York.
Witczak, M. W., Kaloush, K., Pellinen, T., and El-Basyouny, M. (2002). “Simple performance test for superpave mix design.”, Transportation Research Board, National Research Council, Washington, DC.
Zhang, Y., Luo, R., and Lytton, R. L. (2012a). “Anisotropic viscoelastic properties of undamaged asphalt mixtures.” J. Transp. Eng., 75–89.
Zhang, Y., Luo, R., and Lytton, R. L. (2012b). “Characterizing permanent deformation and fracture of asphalt mixtures by using compressive dynamic modulus tests.” J. Mater. Civ. Eng., 898–906.
Zhang, Y., Luo, R., and Lytton, R. L. (2014). “Anisotropic characterization of crack growth in tertiary flow of asphalt mixtures in compression.” J. Eng. Mech., 04014032.
Zhao, Y., Liu, H., Bai, L., and Tan, Y. (2013). “Characterization of linear viscoelastic behavior of asphalt concrete using complex modulus model.” J. Mater. Civ. Eng., 1543–1548.
Zhao, Y., Tang, J., and Liu, H. (2012). “Construction of triaxial dynamic modulus master curve for asphalt mixtures.” Constr. Build. Mater., 37(12), 21–26.
Zhu, H., and Sun, L. (2013). “Mechanistic rutting prediction using a two-stage viscoelastic-viscoplastic damage constitutive model of asphalt mixtures.” J. Eng. Mech., 1577–1591.
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© 2015 American Society of Civil Engineers.
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Received: Oct 22, 2014
Accepted: Jun 16, 2015
Published online: Jul 30, 2015
Discussion open until: Dec 30, 2015
Published in print: Feb 1, 2016
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