Constitutive modeling of fatigue damage response of asphalt concrete materials with consideration of micro-damage healing

• Time-dependent damage model is asphalt concrete is developed and verified.
• Micro-damage healing, viscoelasticity, and viscoplasticity are considered.
• Low concentrations of long CNTs are more effective than high volume of short CNTs.
• Calibration procedures are presented for finding materials parameters.
• The model is validated against a large set of experimental data in tension.

A continuum mechanics-based viscodamage (VD) constitutive relationship is proposed to model fatigue damage of asphalt concrete. The form for the evolution of the viscodamage function is postulated based on the damage density which was determined from uniaxial constant strain rate tests that were performed at different strain rates. The proposed viscodamage model is coupled with Schapery’s nonlinear viscoelastic (VE), Perzyna’s viscoplastic (VP), and micro-damage healing (H) models to simulate the nonlinear mechanical response of asphalt concrete during fatigue. Numerical algorithms are implemented in the finite element code Abaqus via the user material subroutine UMAT. The proposed model is validated against extensive experimental data including constant strain rate, cyclic displacement controlled, and cyclic stress controlled tests over a range of temperatures, strain rates, loading frequencies, and stress/strain levels/amplitudes. The model predictions show that the VE–VP–VD–H model is capable of predicting the fatigue damage response of asphalt concrete subjected to different loading conditions. The results demonstrate that micro-damage healing occurs not only during the rest period, but also during the cyclic strain controlled tests even in the absence of the resting time.