Asphalt pavement rutting simulated using granular micromechanics-based rate-dependent damage-plasticity model

References

• Abu Al-Rub, R.K. and Darabi, M.K. , 2012. A thermodynamic framework for constitutive modeling of time- and rate-dependent materials. Part I: theory. International Journal of Plasticity , 34, 61–92.10.1016/j.ijplas.2012.01.002
   Web of Science ®Google Scholar
• Abu Al-Rub, R.K. , et al. , 2010. A micro-damage healing model that improves prediction of fatigue life in asphalt mixes. International Journal of Engineering Science , 48 (11), 966–990.10.1016/j.ijengsci.2010.09.016
   Web of Science ®Google Scholar
• Benoit, H. , et al. , 1976. Characterization of polystyrene networks by small-angle neutron scattering. Journal of Polymer Science: Polymer Physics Edition , 14 (12), 2119–2128.
   Web of Science ®Google Scholar
• Brünig, M. , et al. , 2008. A ductile damage criterion at various stress triaxialities. International Journal of Plasticity , 24 (10), 1731–1755.10.1016/j.ijplas.2007.12.001
   Web of Science ®Google Scholar
• Carcaterra, A. , 2005. Ensemble energy average and energy flow relationships for nonstationary vibrating systems. Journal of Sound and Vibration , 288 (3), 751–790.10.1016/j.jsv.2005.07.015
   Web of Science ®Google Scholar
• Carcaterra, A. and Akay, A. , 2007. Theoretical foundations of apparent-damping phenomena and nearly irreversible energy exchange in linear conservative systems. The Journal of the Acoustical Society of America , 121 (4), 1971–1982.10.1121/1.2697030
   PubMed Web of Science ®Google Scholar
• Cauchy, A.-L. , 1826–1830. Sur l’equilibre et le mouvement d’un systeme de points materiels sollicites par des forces d’attraction ou de repulsion mutuelle. Excercises de Mathematiques , 3, 188–212.
   Google Scholar
• Chaboche, J.L. , 2008. A review of some plasticity and viscoplasticity constitutive theories. International Journal of Plasticity , 24 (10), 1642–1693.10.1016/j.ijplas.2008.03.009
   Web of Science ®Google Scholar
• Chang, C.S. and Hicher, P.Y. , 2005. An elasto-plastic model for granular materials with microstructural consideration. International Journal of Solids and Structures , 42 (14), 4258–4277.10.1016/j.ijsolstr.2004.09.021
   Web of Science ®Google Scholar
• Chang, C.S. and Misra, A. , 1989. Theoretical and experimental-study of regular packings of granules. Journal of Engineering Mechanics-ASCE , 115 (4), 704–720.10.1061/(ASCE)0733-9399(1989)115:4(704)
   Web of Science ®Google Scholar
• Chang, C.S. and Misra, A. , 1990. Packing structure and mechanical-properties of granulates. Journal of Engineering Mechanics-ASCE , 116 (5), 1077–1093.10.1061/(ASCE)0733-9399(1990)116:5(1077)
   Web of Science ®Google Scholar
• Chang, C.S. , Misra, A. , and Acheampong, K. , 1992. Elastoplastic deformation for particulates with frictional contacts. Journal of Engineering Mechanics-ASCE , 118 (8), 1692–1707.10.1061/(ASCE)0733-9399(1992)118:8(1692)
   Web of Science ®Google Scholar
• Chen, L. , Shao, J.F. , and Huang, H.W. , 2010. Coupled elastoplastic damage modeling of anisotropic rocks. Computers and Geotechnics , 37 (1–2), 187–194.10.1016/j.compgeo.2009.09.001
   Web of Science ®Google Scholar
• Clausius, R. , 1870. XVI. On a mechanical theorem applicable to heat. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science , 40 (265), 122–127.
   Google Scholar
• Coleman, B.D. , 1964. Thermodynamics of materials with memory. Archive for Rational Mechanics and Analysis , 17 (1), 1–46.
   Web of Science ®Google Scholar
• Collard, C. , et al. , 2010. Role of discrete intra-granular slip bands on the strain-hardening of polycrystals. International Journal of Plasticity , 26 (2), 310–328.10.1016/j.ijplas.2009.07.004
   Web of Science ®Google Scholar
• Contrafatto, L. and Cuomo, M. , 2002. A new thermodynamically consistent continuum model for hardening plasticity coupled with damage. International Journal of Solids and Structures , 39 (25), 6241–6271.10.1016/S0020-7683(02)00470-5
   Web of Science ®Google Scholar
• Contrafatto, L. and Cuomo, M. , 2006. A framework of elastic-plastic damaging model for concrete under multiaxial stress states. International Journal of Plasticity , 22 (12), 2272–2300.10.1016/j.ijplas.2006.03.011
   Web of Science ®Google Scholar
• Cosserat, E. and Cosserat, F. , 1909. Theory of deformable bodies . Paris: Scientific Library A. Hermann and Sons.
   Google Scholar
• Culla, A. , Sestieri, A. , and Carcaterra, A. , 2003. Energy flow uncertainties in vibrating systems: definition of a statistical confidence factor. Mechanical Systems and Signal Processing , 17 (3), 635–663.10.1006/mssp.2002.1487
   Web of Science ®Google Scholar
• Darabi, M.K. , et al. , 2011. A thermo-viscoelastic-viscoplastic-viscodamage constitutive model for asphaltic materials. International Journal of Solids and Structures , 48 (1), 191–207.10.1016/j.ijsolstr.2010.09.019
   Web of Science ®Google Scholar
• Darabi, M.K. , et al. , 2012. A thermodynamic framework for constitutive modeling of time- and rate-dependent materials. Part II: numerical aspects and application to asphalt concrete. International Journal of Plasticity , 35, 67–99.10.1016/j.ijplas.2012.02.003
   Web of Science ®Google Scholar
• Darabi, M.K. , et al. , 2013. Constitutive modeling of fatigue damage response of asphalt concrete materials with consideration of micro-damage healing. International Journal of Solids and Structures , 50 (19), 2901–2913.10.1016/j.ijsolstr.2013.05.007
   Web of Science ®Google Scholar
• De Gennes, P.G. , 1979. Scaling concepts in polymer physics . Ithaca, NY: Cornell University Press.
   Google Scholar
• Deresiewicz, H. , 1958. Stress-strain relations for a simple model of a granular medium. Journal of Applied Mechanics , 25, 402–406.
   Google Scholar
• Deshpande, V. and Cebon, D. , 2004. Micromechanical modeling of steady-state deformation in asphalt. Journal of Materials in Civil Engineering , 16 (2), 100–106.10.1061/(ASCE)0899-1561(2004)16:2(100)
   Web of Science ®Google Scholar
• Digby, P.J. , 1981. The effective elastic moduli of porous granular rocks. Journal Applied Mechanics , 48, 803–808.10.1115/1.3157738
   Web of Science ®Google Scholar
• Drescher, A. , Kringos, N. , and Scarpas, T. , 2010. On the behavior of a parallel elasto-visco-plastic model for asphaltic materials. Mechanics of Materials , 42 (2), 109–117.10.1016/j.mechmat.2009.10.005
   Web of Science ®Google Scholar
• Drozdov, A.D. , 1997. A constitutive model for nonlinear viscoelastic media. International Journal of Solids and Structures , 34 (21), 2685–2707.10.1016/S0020-7683(96)00178-3
   Web of Science ®Google Scholar
• Duffy, J. and Mindlin, R.D. , 1957. Stress-strain relations of a granular medium. Journal of Applied Mechanics , 24 (4), 585–593.
   Google Scholar
• Eringen, A.C. , 1999. Microcontinuum field theories: foundations and solids . New York, NY : Springer.10.1007/978-1-4612-0555-5
   Google Scholar
• Germain, P. , 1973a. Method of virtual power in continuum mechanics. 2. Microstructure. SIAM Journal on Applied Mathematics , 25 (3), 556–575.10.1137/0125053
   Web of Science ®Google Scholar
• Germain, P. 1973b. Virtual power method in mechanics of elastic-materials.1. Second gradient theory. Journal De Mecanique , 12(2), 235–274.
   Google Scholar
• Green, A.E. and Rivlin, R.S. , 1957. The mechanics of non-linear materials with memory. Archive for Rational Mechanics and Analysis , 1 (1), 1–21.10.1007/BF00297992
   Web of Science ®Google Scholar
• Green, A.E. and Rivlin, R.S. , 1964. Multipolar continuum mechanics. Archive for Rational Mechanics and Analysis , 17 (2), 113–147.
   Web of Science ®Google Scholar
• Greene, M.S. , et al. , 2013. The archetype-genome exemplar in molecular dynamics and continuum mechanics. Computational Mechanics , 53 (4), 687–737.
   Web of Science ®Google Scholar
• Guéry, A.A.-C. , et al. , 2008. A micromechanical model of elastoplastic and damage behavior of a cohesive geomaterial. International Journal of Solids and Structures , 45 (5), 1406–1429.10.1016/j.ijsolstr.2007.09.025
   Web of Science ®Google Scholar
• Hazony, D. , et al. , 2006. Average acoustic pulse dispersion length in condensed matter channels. Philosophical Magazine , 86 (20), 3043–3060.10.1080/14786430600664130
   Web of Science ®Google Scholar
• Horstemeyer, M.F. and Bammann, D.J. , 2010. Historical review of internal state variable theory for inelasticity. International Journal of Plasticity , 26 (9), 1310–1334.10.1016/j.ijplas.2010.06.005
   Web of Science ®Google Scholar
• Houlsby, G.T. and Puzrin, A.M. , 2006. Principles of hyperplasticity: an approach to plasticity theory based on thermodynamic principles . London: Springer.
   Google Scholar
• Huang, C.W. , et al. , 2011. Three-dimensional simulations of asphalt pavement permanent deformation using a nonlinear viscoelastic and viscoplastic model. Journal of Materials in Civil Engineering , 23 (1), 56–68.10.1061/(ASCE)MT.1943-5533.0000022
   Web of Science ®Google Scholar
• Irving, J.H. and Kirkwood, J.G. , 1950. The statistical mechanical theory of transport processes. 4. The equations of hydrodynamics. Journal of Chemical Physics , 18 (6), 817–829.10.1063/1.1747782
   Web of Science ®Google Scholar
• dell’Isola, F. , Seppecher, P. , and Madeo, A. , 2012. How contact interactions may depend on the shape of Cauchy cuts in Nth gradient continua: approach “à la D’Alembert”. Zeitschrift für angewandte Mathematik und Physik , 63 (6), 1119–1141.10.1007/s00033-012-0197-9
   Web of Science ®Google Scholar
• dell’Isola, F. , et al. , 2014. The complete works of Gabrio Piola: volume I: commented English translation-English and Italian edition . New York, NY: Springer International Publishing.
   Google Scholar
• dell’Isola, F. , Andreaus, U. , and Placidi, L. 2015. At the origins and in the vanguard of peri-dynamics, non-local and higher gradient continuum mechanics. An underestimated and still topical contribution of Gabrio Piola. Mechanics and Mathematics of Solids , 20(8), 887–928.
   Web of Science ®Google Scholar
• Kamrin, K. , 2010. Nonlinear elasto-plastic model for dense granular flow. International Journal of Plasticity , 26 (2), 167–188.10.1016/j.ijplas.2009.06.007
   Web of Science ®Google Scholar
• Khan, A. and Huang, S. , 1995. Continuum theory of plasticity . New York: Wiley-Interscience.
   Google Scholar
• Kim, Y.R. , Little, D.N. and Lytton, R.L. , 2003. Fatigue and healing characterization of asphalt mixtures. Journal of Materials in Civil Engineering , 15 (1), 75–83.10.1061/(ASCE)0899-1561(2003)15:1(75)
   Web of Science ®Google Scholar
• Kutay, M.E. and Lanotte, M. , 2017. Viscoelastic continuum damage (VECD) models for cracking problems in asphalt mixtures. International Journal of Pavement Engineering , 1–12.10.1080/10298436.2017.1279492
   Web of Science ®Google Scholar
• Lai, J. and Bakker, A. , 1996. 3-D schapery representation for non-linear viscoelasticity and finite element implementation. Computational Mechanics , 18 (3), 182–191.10.1007/BF00369936
   Web of Science ®Google Scholar
• Lai, Y.M. , et al. , 2010. Strength criterion and elastoplastic constitutive model of frozen silt in generalized plastic mechanics. International Journal of Plasticity , 26 (10), 1461–1484.
   Web of Science ®Google Scholar
• Levenberg, E. and Uzan, J. , 2004. Triaxial small-strain viscoelastic-viscoplastic modeling of asphalt aggregate mixes. Mechanics of Time-Dependent Materials , 8 (4), 365–384.10.1007/s11043-004-1592-1
   Web of Science ®Google Scholar
• Magoariec, H. , Danescu, A. , and Cambou, B. , 2008. Nonlocal orientational distribution of contact forces in granular samples containing elongated particles. Acta Geotechnica , 3, 49–60.10.1007/s11440-007-0050-z
   Web of Science ®Google Scholar
• Masad, E. , et al. , 2005. Viscoplastic modeling of asphalt mixes with the effects of anisotropy, damage and aggregate characteristics. Mechanics of Materials , 37 (12), 1242–1256.10.1016/j.mechmat.2005.06.003
   Web of Science ®Google Scholar
• Maugin, G.A. , 1992. The thermomechanics of plasticity and fracture . Cambridge: Cambridge University Press.10.1017/CBO9781139172400
   Google Scholar
• Mindlin, R.D. , 1964. Micro-structure in linear elasticity. Archive for Rational Mechanics and Analysis , 16 (1), 51–78.
   Web of Science ®Google Scholar
• Misra, A. and Chang, C.S. , 1993. Effective elastic moduli of heterogeneous granular solids. International Journal of Solids and Structures , 30 (18), 2547–2566.10.1016/0020-7683(93)90165-4
   Web of Science ®Google Scholar
• Misra, A. and Poorsolhjouy, P. 2015. Granular micromechanics model for damage and plasticity of cementitious materials based upon thermomechanics. Mathematics and Mechanics of Solids , 1081286515576821.
   Google Scholar
• Misra, A. and Poorsolhjouy, P. , 2017. Grain-and macro-scale kinematics for granular micromechanics based small deformation micromorphic continuum model. Mechanics Research Communications , 81, 1–6.10.1016/j.mechrescom.2017.01.006
   Web of Science ®Google Scholar
• Misra, A. and Singh, V. , 2013. Micromechanical model for viscoelastic materials undergoing damage. Continuum Mechanics and Thermodynamics , 25 (2–4), 343–358.10.1007/s00161-012-0262-9
   Web of Science ®Google Scholar
• Misra, A. and Singh, V. , 2014a. Nonlinear granular micromechanics model for multi-axial rate-dependent behavior. International Journal of Solids and Structures , 51 (13), 2272–2282.10.1016/j.ijsolstr.2014.02.034
   Web of Science ®Google Scholar
• Misra, A. and Singh, V. , 2014b. Thermomechanics-based nonlinear rate-dependent coupled damage-plasticity granular micromechanics model. Continuum Mechanics and Thermodynamics , 27 (4–5), 787–817.
   Web of Science ®Google Scholar
• Misra, A. and Yang, Y. , 2010. Micromechanical model for cohesive materials based upon pseudo-granular structure. International Journal of Solids and Structures , 47 (21), 2970–2981.10.1016/j.ijsolstr.2010.07.002
   Web of Science ®Google Scholar
• Mohr, D. , 2005. Mechanism-based multi-surface plasticity model for ideal truss lattice materials. International Journal of Solids and Structures , 42 (11–12), 3235–3260.10.1016/j.ijsolstr.2004.10.032
   Web of Science ®Google Scholar
• Mozaffari, N. and Voyiadjis, G.Z. , 2015. Phase field based nonlocal anisotropic damage mechanics model. Physica D: Nonlinear Phenomena , 308, 11–25.10.1016/j.physd.2015.06.003
   Web of Science ®Google Scholar
• Muraleetharan, K.K. , et al. , 2009. An elastoplatic framework for coupling hydraulic and mechanical behavior of unsaturated soils. International Journal of Plasticity , 25 (3), 473–490.10.1016/j.ijplas.2008.04.001
   Web of Science ®Google Scholar
• Naderi, M. , Hoseini, S.H. and Khonsari, M.M. , 2013. Probabilistic simulation of fatigue damage and life scatter of metallic components. International Journal of Plasticity , 43, 101–115.10.1016/j.ijplas.2012.11.001
   Web of Science ®Google Scholar
• Navier, C.L. , 1827. Sur les lois de l’equilibre et du mouvement des corps solides elastiques. Memoire de l’Academie Royale de Sciences , 7, 375–393.
   Google Scholar
• Nicot, F. , Sibille, L. , and Darve, F. , 2012. Failure in rate-independent granular materials as a bifurcation toward a dynamic regime. International Journal of Plasticity , 29, 136–154.10.1016/j.ijplas.2011.08.002
   Web of Science ®Google Scholar
• Ossa, E. , Deshpande, V. , and Cebon, D. , 2010. Triaxial deformation behavior of bituminous mixes. Journal of Materials in Civil Engineering , 22 (2), 124–135.10.1061/(ASCE)0899-1561(2010)22:2(124)
   Web of Science ®Google Scholar
• Park, S.W. , Richard Kim, Y.R. , and Schapery, R.A. , 1996. A viscoelastic continuum damage model and its application to uniaxial behavior of asphalt concrete. Mechanics of Materials , 24 (4), 241–255.10.1016/S0167-6636(96)00042-7
   Web of Science ®Google Scholar
• Pipkin, A.C. and Rogers, T.G. , 1968. A non-linear integral representation for viscoelastic behaviour. Journal of the Mechanics and Physics of Solids , 16 (1), 59–72.10.1016/0022-5096(68)90016-1
   Web of Science ®Google Scholar
• Placidi, L. , 2014a. A variational approach for a nonlinear 1-dimensional second gradient continuum damage model. Continuum Mechanics and Thermodynamics , 27 (4–5), 1–16.
   Web of Science ®Google Scholar
• Placidi, L. , 2014b. A variational approach for a nonlinear one-dimensional damage-elasto-plastic second-gradient continuum model. Continuum Mechanics and Thermodynamics , 28 (1–2), 1–19.
   Web of Science ®Google Scholar
• Poorsolhjouy, P. and Misra, A. , 2017. Effect of intermediate principal stress and loading-path on failure of cementitious materials using granular micromechanics. International Journal of Solids and Structures , 108, 139–152.10.1016/j.ijsolstr.2016.12.005
   Web of Science ®Google Scholar
• Rinaldi, A. , 2013. Bottom-up modeling of damage in heterogeneous quasi-brittle solids. Continuum Mechanics and Thermodynamics , 25 (2–4), 359–373.10.1007/s00161-012-0265-6
   Web of Science ®Google Scholar
• Rinaldi, A. and Lai, Y.C. , 2007. Statistical damage theory of 2D lattices: Energetics and physical foundations of damage parameter. International Journal of Plasticity , 23 (10–11), 1796–1825.10.1016/j.ijplas.2007.03.005
   Web of Science ®Google Scholar
• Rinaldi, A. , et al. , 2008. Lattice models of polycrystalline micro structures: a quantitative approach. Mechanics of Materials , 40 (1–2), 17–36.10.1016/j.mechmat.2007.02.005
   Web of Science ®Google Scholar
• Schapery, R.A. , 1969. On the characterization of nonlinear viscoelastic materials. Polymer Engineering & Science , 9 (4), 295–310.10.1002/(ISSN)1548-2634
   Web of Science ®Google Scholar
• Schapery, R.A. , 2000. Nonlinear viscoelastic solids. International Journal of Solids and Structures , 37 (1–2), 359–366.10.1016/S0020-7683(99)00099-2
   Web of Science ®Google Scholar
• Seppecher, P. , 2002. Second-gradient theory: application to Cahn-Hilliard fluids. Continuum Thermomechanics. Springer, 379–388.10.1007/0-306-46946-4
   Google Scholar
• Shen, W.Q. , et al. , 2012. A micro-macro model for clayey rocks with a plastic compressible porous matrix. International Journal of Plasticity , 36, 64–85.10.1016/j.ijplas.2012.03.006
   Web of Science ®Google Scholar
• Shim, J. and Mohr, D. , 2011. Rate dependent finite strain constitutive model of polyurea. International Journal of Plasticity , 27 (6), 868–886.10.1016/j.ijplas.2010.10.001
   Web of Science ®Google Scholar
• Solar, M. , et al. , 2012. Mechanical behavior of linear amorphous polymers: comparison between molecular dynamics and finite-element simulations. Physical Review E , 85 (2), 1–14.
   Web of Science ®Google Scholar
• Steinhauser, M.O. , et al. , 2009. Impact failure of granular materials – non-equilibrium multiscale simulations and high-speed experiments. International Journal of Plasticity , 25 (1), 161–182.10.1016/j.ijplas.2007.11.002
   Web of Science ®Google Scholar
• Subramaniyan, A.K. and Sun, C.T. , 2008. Continuum interpretation of virial stress in molecular simulations. International Journal of Solids and Structures , 45 (14–15), 4340–4346.10.1016/j.ijsolstr.2008.03.016
   Web of Science ®Google Scholar
• Swenson, R.J. , 1983. Comments on virial theorems for bounded systems. American Journal of Physics , 51 (10), 940–942.10.1119/1.13390
   Web of Science ®Google Scholar
• Tordesillas, A. , et al. , 2012. Multiscale characterisation of diffuse granular failure. Philosophical Magazine , 92 (36), 4547–4587.10.1080/14786435.2012.715766
   Web of Science ®Google Scholar
• Toupin, R.A. , 1964. Theories of Elasticity with Couple-Stress. Archive for Rational Mechanics and Analysis , 17 (2), 85–112.
   Web of Science ®Google Scholar
• Tsai, D.H. , 1979. Virial theorem and stress calculation in molecular-dynamics. Journal of Chemical Physics , 70 (3), 1375–1382.10.1063/1.437577
   Web of Science ®Google Scholar
• Tsutsumi, S. and Kaneko, K. , 2008. Constitutive response of idealized granular media under the principal stress axes rotation. International Journal of Plasticity , 24 (11), 1967–1989.10.1016/j.ijplas.2008.05.001
   Web of Science ®Google Scholar
• Vignjevic, R. , Djordjevic, N. and Panov, V. , 2012. Modelling of dynamic behaviour of orthotropic metals including damage and failure. International Journal of Plasticity , 38, 47–85.10.1016/j.ijplas.2012.04.006
   Web of Science ®Google Scholar
• Voyiadjis, G.Z. , Abu Al-Rub, R.K. and Palazotto, A.N. , 2004. Thermodynamic framework for coupling of non-local viscoplasticity and non-local anisotropic viscodamage for dynamic localization problems using gradient theory. International Journal of Plasticity , 20 (6), 981–1038.10.1016/j.ijplas.2003.10.002
   Web of Science ®Google Scholar
• Walton, K. , 1987. The effective elastic moduli of a random packing of spheres. Journal of the Mechanics and Physics of Solids , 35, 213–226.10.1016/0022-5096(87)90036-6
   Web of Science ®Google Scholar
• Wineman, A. , 2009. Nonlinear viscoelastic solids – a review. Mathematics and Mechanics of Solids , 14 (3), 300–366.10.1177/1081286509103660
   Web of Science ®Google Scholar
• Wu, Z. and Chen, X. , 2011. Prediction of permanent deformation of pavement base and subgrade materials under accelerated loading. International Journal of Pavement Research and Technology , 4 (4), 231–237.
   Google Scholar
• Wu, B. , Xu, Z. , and Li, Z. , 2008. A note on imposing displacement boundary conditions in finite element analysis. International Journal for Numerical Methods in Biomedical Engineering , 24 (9), 777–784.
   Google Scholar
• Yin, Z.Y. , Chang, C.S. , and Hicher, P.Y. , 2010. Micromechanical modelling for effect of inherent anisotropy on cyclic behaviour of sand. International Journal of Solids and Structures , 47 (14–15), 1933–1951.10.1016/j.ijsolstr.2010.03.028
   Web of Science ®Google Scholar
• Zhou, M. , 2003. A new look at the atomic level virial stress: on continuum-molecular system equivalence. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences , 459 (2037), 2347–2392.10.1098/rspa.2003.1127
   Web of Science ®Google Scholar
• Ziegler, H. , 1983. An Introduction to thermomechanics . 2nd ed. Amsterdam: North-Holland.
   Google Scholar