Computational Mechanics

, Volume 51, Issue 2, pp 187–201 | Cite as

A two-way coupled multiscale model for predicting damage-associated performance of asphaltic roadways

  • Yong-Rak Kim
  • Flavio V. Souza
  • Jamilla Emi Sudo Lutif Teixeira
Original Paper

Abstract

This paper presents a quasi-static multiscale computational model with its verification and rational applications to mechanical behavior predictions of asphaltic roadways that are subject to viscoelastic deformation and fracture damage. The multiscale model is based on continuum thermo-mechanics and is implemented using a finite element formulation. Two length scales (global and local) are two-way coupled in the model framework by linking a homogenized global scale to a heterogeneous local scale representative volume element. With the unique multiscaling and the use of the finite element technique, it is possible to take into account the effect of material heterogeneity, viscoelasticity, and anisotropic damage accumulation in the small scale on the overall performance of larger scale structures. Along with the theoretical model formulation, two example problems are shown: one to verify the model and its computational benefits through comparisons with analytical solutions and single-scale simulation results, and the other to demonstrate the applicability of the approach to model general roadway structures where material viscoelasticity and cohesive zone fracture are involved.

Keywords

Multiscale modeling Asphalt pavement Viscoelasticity Fracture Cohesive zone Finite element method 

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References

  1. 1.
    Masad E, Niranjanan S, Bahia H, Kose S (2001) Modeling and experimental measurements of localized strain distribution in asphalt mixes. J Transp Eng 127(6): 477–485CrossRefGoogle Scholar
  2. 2.
    Papagiannakis AT, Abbas A, Masad E (2002) Micromechanical analysis of viscoelastic properties of asphalt concretes. Transp Res Rec 1789: 113–120CrossRefGoogle Scholar
  3. 3.
    Guddati MN, Feng Z, Kim YR (2002) Towards a micromechanics-based procedure to characterize fatigue performance of asphalt concrete. Transp Res Rec 1789: 121–128CrossRefGoogle Scholar
  4. 4.
    Sadd MH, Dai Q, Parameswaran V, Shukla A (2003) Simulation of asphalt materials using a finite element micromechanical model with damage mechanics. Transp Res Rec 1832: 86–95CrossRefGoogle Scholar
  5. 5.
    Soares BJ, Freitas F, Allen DH (2003) Crack modeling of asphaltic mixtures considering heterogeneity of the material. Transp Res Rec 1832: 113–120CrossRefGoogle Scholar
  6. 6.
    Dai Q, Sadd MH, Parameswaran V, Shukla A (2005) Prediction of damage behaviors in asphalt materials using a micromechanical finite-element model and image analysis. J Eng Mech 131(7): 668–677CrossRefGoogle Scholar
  7. 7.
    Buttlar W, You Z (2001) Discrete element modeling of asphalt concrete: microfabric approach. Transp Res Rec 1757: 111–118CrossRefGoogle Scholar
  8. 8.
    Kim H, Buttler WG (2005) Micromechanical fracture modeling of hot-mix asphalt concrete based on a disk-shaped compact tension test. Electron J Assoc Asph Paving Technol 74E:209–223Google Scholar
  9. 9.
    Abbas A, Masad E, Papagiannakis T, Shenoy A (2005) Modeling of asphalt mastic stiffness using discrete elements and micromechanics analysis. Int J Pavement Eng 6(2): 137–146CrossRefGoogle Scholar
  10. 10.
    Fish J, Wagiman A (1993) Multiscale finite element method for a locally non-periodic heterogeneous medium. Comput Mech 12: 164–180MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Fish J, Belsky V (1995) Multigrid method for periodic heterogeneous media, part II: multiscale modeling and quality control in multidimensional cases. Comput Methods Appl Mech Eng 126: 17–38MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Oden JT, Zohdi TI (1997) Analysis and adaptive modeling of highly heterogeneous elastic structures. Comput Methods Appl Mech Eng 172: 3–25MathSciNetCrossRefGoogle Scholar
  13. 13.
    Feyel F (1999) Multiscale FE2 elastoviscoplastic analysis of composite structures. Comput Mater Sci 16: 344–354CrossRefGoogle Scholar
  14. 14.
    Lee K, Moorthy S, Ghosh S (1999) Multiple scale computational model for damage in composite materials. Comput Methods Appl Mech Eng 172: 175–201MATHCrossRefGoogle Scholar
  15. 15.
    Oden JT, Vemaganti K, Moes N (1999) Hierarchical modeling of heterogeneous solids. Comput Methods Appl Mech Eng 148: 367–391CrossRefGoogle Scholar
  16. 16.
    Feyel F, Chaboche JL (2000) FE2 multiscale approach for modeling the elastoviscoplastic behavior of long fibre SiC/Ti composite materials. Comput Methods Appl Mech Eng 183: 309–330MATHCrossRefGoogle Scholar
  17. 17.
    Fish J, Shek K (2000) Multiscale analysis of composite materials and structures. Compos Sci Technol 60: 2547–2556CrossRefGoogle Scholar
  18. 18.
    Ghosh S, Lee K, Raghavan P (2001) A multi-level computational model for multiscale damage analysis in composite and porous materials. Int J Solids Struct 38: 2335–2385MATHCrossRefGoogle Scholar
  19. 19.
    Raghavan P, Moorthy S, Ghosh S, Pagano NJ (2001) Revisiting the composite laminate problem with an adaptive multi-level computational model. Compos Sci Technol 61: 1017–1040CrossRefGoogle Scholar
  20. 20.
    Haj-Ali RM, Muliana AH (2004) A multi-scale constitutive formulation for the nonlinear viscoelastic analysis of laminated composite materials and structures. Int J Solids Struct 41: 3461–3490MATHCrossRefGoogle Scholar
  21. 21.
    Dugdale DS (1960) Yielding of steel sheets containing slits. J Mech Phys Solids 8: 100–104CrossRefGoogle Scholar
  22. 22.
    Barenblatt GI (1962) The mathematical theory of equilibrium cracks in brittle fracture. Adv Appl Mech 7: 55–129MathSciNetCrossRefGoogle Scholar
  23. 23.
    Needleman A (1987) A continuum model for void nucleation by inclusion debonding. J Appl Mech 54: 525–531MATHCrossRefGoogle Scholar
  24. 24.
    Tvergaard V (1990) Effect of fiber debonding in a whisker-reinforced metal. Mater Sci Eng 125(2): 203–213CrossRefGoogle Scholar
  25. 25.
    Geubelle PH, Baylor J (1998) The impact-induced delamination of laminated composites: a 2D simulation. Composites B 29: 589–602CrossRefGoogle Scholar
  26. 26.
    Ortiz M, Pandolfi A (1999) Finite-deformation irreversible cohesive elements for three-dimensional crack propagation analysis. Int J Numer Methods Eng 44(9): 1267–1282MATHCrossRefGoogle Scholar
  27. 27.
    Espinosa HD, Zavattieri PD (2003) A grain level model for the study of failure initiation and evolution in polycrystalline brittle materials. part I: theory and numerical implementation. Mech Mater 35: 333–364CrossRefGoogle Scholar
  28. 28.
    Park K, Paulino GH, Roesler JR (2009) A unified potential-based cohesive model of mixed-mode fracture. J Mech Phys Solids 57: 891–908CrossRefGoogle Scholar
  29. 29.
    Yoon C, Allen DH (1999) Damage dependent constitutive behavior and energy release rate for a cohesive zone in a thermoviscoelastic solid. Int J Fract 96: 55–74CrossRefGoogle Scholar
  30. 30.
    Allen DH, Searcy CR (2000) Numerical aspects of a micromechanical model of a cohesive zone. J Reinf Plast Compos 19(3): 240–248CrossRefGoogle Scholar
  31. 31.
    Allen DH, Searcy CR (2001) A micromechanical model for a viscoelastic cohesive zone. Int J Fract 107: 159–176CrossRefGoogle Scholar
  32. 32.
    Souza FV, Allen DH (2010) Multiscale modeling of impact on heterogeneous viscoelastic solids containing evolving microcracks. Int J Numer Methods Eng 82: 464–504MathSciNetMATHGoogle Scholar
  33. 33.
    Souza FV, Allen DH (2010) Modeling failure of heterogeneous viscoelastic solids under dynamic/impact loading due to multiple evolving cracks using a two-way coupled multiscale model. Mech Time-Dependent Mater 14(2): 125–151CrossRefGoogle Scholar
  34. 34.
    Nemat-Nasser S, Hori M (1993) Micromechanics: overall properties of heterogeneous materials. North Holland, New YorkGoogle Scholar
  35. 35.
    Allen DH (2001) Homogenization principles and their application to continuum damage mechanics. Compos Sci Technol 61: 2223–2230CrossRefGoogle Scholar
  36. 36.
    Kouznetsova VG (2002) Computational homogenization for the multi-scale analysis of multi-phase materials. PhD Dissertation, Technische Universiteit EindhovenGoogle Scholar
  37. 37.
    Zocher MA, Allen DH, Groves SE (1997) A three dimensional finite element formulation for thermoviscoelastic orthotropic media. Int J Numer Methods Eng 40: 2267–2288MathSciNetMATHCrossRefGoogle Scholar
  38. 38.
    Seidel GD, Allen DH, Helms KLE, Groves SE (2005) A model for predicting the evolution of damage in viscoelastic particle-reinforced composites. Mech Mater 37: 163–178CrossRefGoogle Scholar
  39. 39.
    Hill R (1967) The essential structure of constitutive laws for metal composites and polycrystals. J Mech Phys Solids 15(2): 79–95CrossRefGoogle Scholar
  40. 40.
    Souza FV (2009) Multiscale modeling of impact on heterogeneous viscoelastic solids with evolving microcracks. PhD Dissertation, University of Nebraska-Lincoln, NebraskaGoogle Scholar
  41. 41.
    Kim Y, Lutif JS, Allen DH (2009) Determining representative volume elements of asphalt concrete mixtures without damage. Transp Res Rec 2127: 52–59CrossRefGoogle Scholar
  42. 42.
    Kim Y, Lee J, Lutif JS (2010) Geometrical evaluation and experimental verification to determine representative volume elements of heterogeneous asphalt mixtures. J Test Eval 38(6): 660–666Google Scholar
  43. 43.
    Kim Y, Aragão FTS, Allen DH, Little DN (2010) Damage modeling of bituminous mixtures through computational micromechanics and cohesive zone fracture. Can J Civ Eng 37: 1125–1136CrossRefGoogle Scholar
  44. 44.
    Aragão FTS (2011) Computational microstructure modeling of asphalt mixtures subjected to rate-dependent fracture. PhD Dissertation, University of Nebraska, Lincoln, NebraskaGoogle Scholar
  45. 45.
    Aragão FTS, Kim Y, Lee J, Allen DH (2011) Micromechanical model for heterogeneous asphalt concrete mixtures subjected to fracture failure. J Mater Civ Eng 23(1): 30–38CrossRefGoogle Scholar
  46. 46.
    Hugo F, Kennedy T (1985) Surface cracking of asphalt mixtures on southern africa. Proc Assoc Asph Paving Technol 54: 454–496Google Scholar
  47. 47.
    Jacobs M (1995) Crack growth in asphaltic mixes. PhD Dissertation, Delft Institute of Technology, NetherlandsGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Yong-Rak Kim
    • 1
  • Flavio V. Souza
    • 2
  • Jamilla Emi Sudo Lutif Teixeira
    • 3
  1. 1.Department of Civil EngineeringKyung Hee UniversityYongin-si, Gyeonggi-doSouth Korea
  2. 2.Multimech Research and Development, LLCOmahaUSA
  3. 3.Centro Tecnológico, Departamento de Engenharia Civil (CT-DEC)Universidade Federal do Espírito Santo (UFES)VitoriaBrazil

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