A continuum mechanical approach to model asphalt

References

• Bagley, R. and Torvik, P., 1983. A theoretical basis for the application of fractional calculus to viscoelasticity. Journal of Rheology, 27, 201–210.
   Web of Science ®Google Scholar
• Beecken, G., et al., 1994. Shell Bitumen für den Straßenbau und andere Anwendungsgebiete. 7th ed.Hamburg: Elbe Druck GmbH.
   Google Scholar
• Bergström, J. and Boyce, M., 2000. Large strain time-dependent behavior of filled elastomers. Mechanics of Materials, 32, 627–644.
   Web of Science ®Google Scholar
• Buttlar, W.G. and Roque, R., 1996. Evaluation of empirical and theoretical models to determine asphalt mixture stiffnesses at low temperatures (with discussion). Journal of the Association of Asphalt Paving Technologists, 65, 99–141.
   Google Scholar
• Collop, A.C., et al., 2003. Development and finite element implementation of stress-dependent elastoviscoplastic constitutive model with damage for asphalt. Transportation Research Record: Journal of the Transportation Research Board, 1832, 96–104.
   Google Scholar
• Crispinoa, M. and Nicolosi, V., 2001. Temperature analysis in prediction of the rutting of asphalt concrete bridge pavements. Road Materials and Pavement Design, 2, 403–419.
   Google Scholar
• Dal, H. and Kaliske, M., 2009. Bergström–Boyce model for nonlinear finite rubber viscoelasticity: theoretical aspects and algorithmic treatment for the FE method. Computational Mechanics, 44, 809–823.
   Web of Science ®Google Scholar
• Di Benedetto, H. and Olard, F., 2009. DBN law for the thermo-visco-elasto-plastic behavior of asphalt concrete. In: Modeling of asphalt concrete. New York: McGraw-Hill, 245–265.
   Google Scholar
• DIN 18134, 2012. Baugrund – Versuche und Versuchsgeräte – Plattendruckversuch. Berlin: Deutsches Institut für Normung, Beuth Verlag GmbH.
   Google Scholar
• Feyissa, B.A., 2009. Analysis and modeling of rutting for long life asphalt concrete pavement. Thesis (PhD). Technische Universität Darmstadt.
   Google Scholar
• González, J.M., et al., 2007. A viscoplastic constitutive model with strain rate variables for asphalt mixtures-numerical simulation. Computational Materials Science, 38, 543–560.
   Web of Science ®Google Scholar
• Grünwald, A., 1867. Über ‘begrenzte’ Derivationen und deren Anwendung. Zeitschrift für Angewandte Mathematik und Physik, 12, 441–480.
   Google Scholar
• Harvey, J.T., Weissman, S.L., and Monismith, C.L., 2009. Rutting characterization of asphalt concret using simple shear tests. In: Modeling of Asphalt Concrete. New York: McGraw-Hill, 269–315.
   Google Scholar
• Holzapfel, G.A., 2010. Nonlinear Solid Mechanics: a Continuum Approach for Engineering. Chichester: Wiley.
   Google Scholar
• Kai-Xin, H. and Ke-Qin, Z., 2009. Mechanical analogies of fractional elements. Chinese Physics Letters, 26, 108301-1–108301-3.
   Google Scholar
• Kaliske, M., 1995. Zur Theorie und Numerik von Polymerstrukturen unter statischen und dynamischen Einwirkungen. Thesis (PhD). Universität Hannover.
   Google Scholar
• Kaliske, M., 2010. Numerical modeling in tire mechanics. In: 9. LS-DYNA Forum 2010, Bamberg. Stuttgart, Germany: DYNAmore Gesellschaft für FEM Ingenieurdienstleistungen mbH, A-I-27–A-I-35.
   Google Scholar
• Kayser, S., 2011. Dimensionierung: Charakteristische Temperaturprofile und Regionalisierung ihrer Auftretenswahrscheinlichkeiten für die rechnerische Dimensionierung von Asphaltstraßenkonstruktionen. Straße und Autobahn, 9, 605–617.
   Google Scholar
• Kim, Y.R., 2009. Modeling of asphalt concrete. In: Modeling of Asphalt Concrete. New York: McGraw-Hill, 1–7.
   Google Scholar
• Lion, A. and Kardelky, C., 2004. The Payne effect in finite viscoelasticity: constitutive modelling based on fractional derivatives and intrinsic time scales. International Journal of Plasticity, 20, 1313–1345.
   Web of Science ®Google Scholar
• Miehe, C., 1994. Aspects of the formulation and finite element implementation of large strain isotropic elasticity. International Journal for Numerical Methods in Engineering, 37, 1981–2004.
   Web of Science ®Google Scholar
• Miehe, C. and Keck, J., 2000. Superimposed finite elastic-viscoelastic-plastoelastic stress response with damage in filled rubbery polymers. Experiments, modelling and algorithmic implementation. Journal of the Mechanics and Physics of Solids, 48, 323–365.
   Web of Science ®Google Scholar
• Müller, S., et al., 2011. A nonlinear fractional viscoelastic material model for polymers. Computational Materials Science, 50, 2938–2949.
   Web of Science ®Google Scholar
• Netzker, C., Dal, H., and Kaliske, M., 2010. An endochronic plasticity formulation for filled rubber. International Journal of Solids and Structures, 47, 2371–2379.
   Web of Science ®Google Scholar
• Nunn, M.E., Lawrence, D., and Brown, A., 2000. Development of a practical test to assess the deformation resistance of asphalt. In: 2nd Eurasphalt & Eurobitume Congress, Barcelona.
   Google Scholar
• Oeser, M., 2010. Nichtlineare numerische Simulationsmodelle für Verkehrswegebefestigungen: unter Berücksichtigung von mechanischen, thermischen und hydraulischen Einwirkungen. Thesis (Habilitation). Technische Universität Dresden.
   Google Scholar
• Oeser, M., et al., 2008. Studies on creep and recovery of rheological bodies based upon conventional and fractional formulations and their application on asphalt mixture. International Journal of Pavement Engineering, 9, 373–386.
   Google Scholar
• Olard, F. and Di Benedetto, H., 2003. General 2S2P1D model and relation between the linear viscoelastic behaviours of bituminous binders and mixes. Road Materials and Pavement Design, 4, 185–224.
   Google Scholar
• Oldham, K.B. and Spanier, J., 1988. The fractional calculus: theory and applications of differentiation and integration to arbitrary order. 3rd ed.San Diego, CA: Academic Press.
   Google Scholar
• RStO 01, 2001. Richtlinien für die Standardisierung des Oberbaus von Verkehrsflächen. Köln: Forschungsgesellschaft für Strassen- und Verkehrswesen, FGSV Verlag GmbH.
   Google Scholar
• RStO 12, 2012. Richtlinien für die Standardisierung des Oberbaus von Verkehrsflächen. Köln: Forschungsgesellschaft für Strassen- und Verkehrswesen, FGSV Verlag GmbH.
   Google Scholar
• Schmidt, A. and Gaul, L., 2002. Finite element formulation of viscoelastic constitutive equations using fractional time derivatives. Nonlinear Dynamics, 29, 37–55.
   Web of Science ®Google Scholar
• Schmidt, A. and Gaul, L., 2003. Implementation von Stoffgesetzen mit fraktionalen Ableitungen in die Finite Elemente Methode. Zeitschrift für Angewandte Mathematik und Mechanik, 83, 26–37.
   Web of Science ®Google Scholar
• Schwartz, C.W. and Kamil, E.K., 2009. Permanent deformation assessment for asphalt concrete pavement and mixture design. In: Modeling of Asphalt Concrete. New York: McGraw-Hill, 317–351.
   Google Scholar
• Simo, J., 1992. Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory. Computer Methods in Applied Mechanics and Engineering, 99, 61–112.
   Web of Science ®Google Scholar
• Simo, J.C. and Hughes, T.J.R., 2000. Computational Inelasticity. 7th ed.New York: Springer-Verlag.
   Google Scholar
• Tashman, L., et al., 2005. A microstructure-based viscoplastic model for asphalt concrete. International Journal of Plasticity, 21, 1659–1685.
   Web of Science ®Google Scholar
• Valanis, K., 1971. A theory of viscoplasticity without a yield surface. Archives of Mechanics, 23, 517–533.
   Web of Science ®Google Scholar
• Vinogradov, G.V., et al., 1977. Rheological properties of road bitumens. Rheologica Acta, 16, 266–281.
   Web of Science ®Google Scholar
• Weise, C., Wellner, F., and Werkmeister, S., 2007. Determination of the fatigue behaviour of asphalt mixes using the results of direct, indirect and triaxial tensile tests. In: Advanced Characterisation of pavement and Soil Engineering Materials, Volume 1: Proceedings of the International Conference on Advanced Characterisation of Pavement and Soil Engineering, 20–22 June 2007, Athens, Greece. London: Taylor & Francis, 175–184.
   Google Scholar
• Wellner, F. and Kayser, S., 2008. Grundlagen zur Erfassung der Temperaturbedingungen für eine analytische Bemessung von Asphaltbefestigungen. Forschung Straßenbau und Straßenverkehrstechnik. Bremerhaven: Wirtschaftsverlag NW Verlag für neue Wissenschaft.
   Google Scholar
• Wellner, F., et al., 2011. Dimensionierungsrelevante Eingansgrößen für Asphaltbefestigungen. Forschung Straßenbau und Straßenverkehrstechnik. Bremerhaven: Wirtschaftsverlag NW Verlag für neue Wissenschaft NW, Verlag für Neue Wissenschaft.
   Google Scholar
• Wollny, I. and Kaliske, M., 2013. Numerical simulation of pavement structures with inelastic material behaviour under rolling tyres based on an arbitrary Lagrangian Eularian (ALE) formulation. Road Materials and Pavement Design, 14, 71–89.
   Web of Science ®Google Scholar
• Yang, J. and Yin, C., 2009. Laboratory study of porus asphalt mixture made with Rubber Bitumen. In: Asphalt material characterization, accelerated testing, and highway management. Reston, VA: American Society of Civil Engineers, 22–31.
   Google Scholar
• Zeißler, A., et al., 2011. Experimental testing and investigation of the stress-dependent material behaviour of asphalt via the triaxial test. In: PIARC XXIVth World Road Congress, Conference Proceedings, Mexico City, Mexico.
   Google Scholar
• Zopf, C. and Kaliske, M., 2013. Constitutive description of green rubber material for forming simulation. Kautschuk Gummi Kunststoffe, 66, 32–35.
   Google Scholar
• Zopf, C., Hoque, E.S., and Kaliske, M., 2014. Comparison of approaches to model viscoelasticity based on fractional time derivatives. Computational Materials Science, in review.
   Google Scholar