A micro-damage healing model that improves prediction of fatigue life in asphalt mixes Rashid K. Abu Al-Rub a , Masoud K. Darabi a , Dallas N. Little a,⇑ , Eyad A. Masad a,b a Zachry Department of Civil Engineering, Texas A&M University, College Station, TX 77843, USA b Mechanical Engineering Program, Texas A&M University at Qatar, Doha, Qatar article info Article history: Available online 12 October 2010 Keywords: Micro-damage healing Viscoelasticity Viscoplasticity Viscodamage Healing natural configuration abstract The focus of the current paper is on the development and validation of a micro-damage healing model that improves the ability of an integrated nonlinear viscoelastic, viscoplas- tic, and viscodamage constitutive model based on continuum damage mechanics for pre- dicting the fatigue life of asphalt paving mixtures. The model parameters of the continuum-based healing model are related to fundamental material properties. Recur- sive–iterative and radial return algorithms are used for the numerical implementation of viscoelasticity and viscoplasticity models respectively, whereas the viscodamage and micro-damage healing models are implemented using the concept of the effective undam- aged-healed natural configuration. Numerical algorithms are implemented into the well- known finite element code Abaqus via the user material subroutine UMAT. Finally, the model is validated by comparing its predictions with experimental data on an asphalt mix that include repeated creep-recovery tests for different loading times and rest periods in both tension and compression. The significant enhancement of the ability of the consti- tutive model to predict fatigue life due to inclusion of the micro-damage healing is clearly demonstrated. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction Experimental observations in the last few decades have clearly shown that various classes of engineering materials (e.g. polymers, bitumen, bio-inspired materials, rocks) have the potential to heal with time and recover part of their strength and stiffness under specific circumstances (e.g. [42,26,8,54,15,25,7]). Constitutive models that do not account for healing of these materials significantly underestimate their fatigue life that will lead to very conservative design of structural systems made of such materials. Therefore, it is imperative to model healing for more accurate fatigue life predictions, which is the focus of the current work. Changes in the material’s microstructure during deformation usually cause significant micro-damage (micro-cracks and micro-voids) under service loading conditions. The creation and growth of micro-damages lead to degradation in the mate- rial’s mechanical properties including strength and stiffness. This process of degradation can progressively continue up to complete failure. Theories based on continuum damage mechanics have been successfully used to explain these degradation mechanisms in different materials (e.g. [22,43,48,23,65,37,31]). However, a common assumption in the theories based on continuum damage mechanics is that the damage process is irreversible (e.g. [22,23,38,37,66,24,31,67,64,36,4,3,62]). In other words, the damage variable is usually assumed to be a monotonically increasing function. However, during the unloading 0020-7225/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijengsci.2010.09.016 ⇑ Corresponding author. Tel.: +1 979 845 9847. E-mail address: D-Little@tamu.edu (D.N. Little). International Journal of Engineering Science 48 (2010) 966–990 Contents lists available at ScienceDirect International Journal of Engineering Science journal homepage: www.elsevier.com/locate/ijengsci