A modified viscoplastic model to predict the permanent deformation of asphaltic materials under cyclic-compression loading at high temperatures

Masoud K. Darabi, Rashid K. Abu Al-Rub, Eyad A. Masad, Chien Wei Huang, Dallas N. Little

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82 Scopus citations


When subjected to cyclic creep (ratcheting) loading with rest periods between the loading cycles, the viscoplastic behavior of asphaltic materials changes such the rate of accumulation of the viscoplastic strain at the beginning of the subsequent loading cycle increases comparing to that at the end of the preceding loading cycle. This phenomenon is referred to as the hardening-relaxation (or viscoplastic-softening) and is a key element in predicting the permanent deformation (rutting) of asphalt pavements which is one of the most important distresses in asphalt pavements. This paper presents a phenomenological-based rate-dependent hardening-relaxation model to significantly enhance the prediction of the permanent deformation in asphaltic materials subjected to cyclic-compression loadings at high temperatures. A hardening-relaxation memory surface is defined in the viscoplastic strain space as the general condition for the initiation and evolution of the hardening-relaxation (or viscoplastic-softening). The memory surface is formulated to be a function of an internal state variable memorizing the maximum viscoplastic strain for which the softening has been occurred during the deformation history. The evolution function for the hardening-relaxation model is then defined as a function of the hardening-relaxation internal state variable. The proposed viscoplastic-softening model is coupled to the nonlinear Schapery's viscoelastic and Perzyna's viscoplastic models. The numerical algorithms for the proposed model are implemented in the well-known finite element code Abaqus via the user material subroutine UMAT. The model is then calibrated and verified by comparing the model predictions and experimental data that includes cyclic creep-recovery loadings at different stress levels, loading times, rest periods, and confinement levels. Model predictions show that the proposed approach provides a promising tool for constitutive modeling of cyclic hardening-relaxation in asphaltic materials and in general in time- and rate-dependent materials.

Original languageBritish English
Pages (from-to)100-134
Number of pages35
JournalInternational Journal of Plasticity
StatePublished - Aug 2012


  • Asphalt concrete
  • Constitutive modeling
  • Hardening-relaxation
  • Viscoelasticity
  • Viscoplastic-softening


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