This thesis demonstrates the effect of micro-damage healing on stress and displacement fields in the vicinity of a crack tip in the material that tend to self-heal. The micro-damage healing model is modeled by incorporating time-dependent traction within the crack faces. This time-dependent traction occurs in a small zone referred to as healing process zone. The effect of the micro-damage healing on crack propagation in elastic media is investigated by deriving analytical relations for Stress Intensity Factor (SIF) when micro-damage healing mechanism is in effect. It is shown that the larger values of both healing process zone and bonding strength decrease the value of SIF near the crack tip. In order to clearly capture this phenomenon, a novel technique based on complex variables is used to derive the equations to calculate the stress and displacement fields in elastic media. Using the third correspondence principle, which is suitable in analyzing the crack shortening (healing phenomenon), the corresponding results of stress and displacement fields in elastic media are converted into viscoelastic media. Since asphalt has time-dependent material properties, the viscoelastic result is more accurate than the elastic. It is shown that an increase in the value of both healing process zone and bonding strength results in a decrease in the stress and displacement fields near the crack tip. Finally, the effect of using different coefficients in defining the bonding strength and relaxation time is evaluated. Asphalt concrete pavements are concurrently subjected to mechanical and environmental loading conditions during their service life. Applied mechanical and environmental loadings gradually degrade properties of asphalt concrete pavements. However, under specific conditions, asphalt concrete has the potential to heal and regain part of its strength. Identifying a model for the healing process is crucial. This proposed model is not dependent on the test methods that empower its usage in computational modeling. Moreover, this research considers both effects of instantaneous healing (a result of wetting) and time-dependent bond strength (a result of molecular diffusion between the crack faces), using the complex-variable method. Schapery (1989) considered only instantaneous healing and regarded it as the total bond strength. Therefore, considering both effects of instantaneous and time-dependent bond-strength makes this model superior with respect to the analogous model. It is hoped that this research provides insight on the healing mechanism at micro-scale.

Time- and rate-dependent materials such as polymers, bituminous materials, and soft materials clearly display all four fundamental responses (i.e. viscoelasticity, viscoplasticity, viscodamage, and healing) where contribution of each response strongly depends on the temperature and loading conditions. This study proposes a new general thermodynamic-based framework to specifically derive thermo-viscoelastic, thermo-viscoplastic, thermo-viscodamage, and micro-damage healing constitutive models for bituminous materials and asphalt mixes. The developed thermodynamic-based framework is general and can be applied for constitutive modeling of different materials such as bituminous materials, soft materials, polymers, and biomaterials. This framework is build on the basis of assuming a form for the Helmohelotz free energy function (i.e. knowing how the material stores energy) and a form for the rate of entropy production (i.e. knowing how the material dissipates energy). However, the focus in this work is placed on constitutive modeling of bituminous materials and asphalt mixes. A viscoplastic softening model is proposed to model the distinct viscoplastic softening response of asphalt mixes subjected to cyclic loading conditions. A systematic procedure for identification of the constitutive model parameters based on optimized experimental effort is proposed. It is shown that this procedure is simple and straightforward and yields unique values for the model material parameters. Subsequently, the proposed model is validated against an extensive experimental data including creep, creep-recovery, repeated creep-recovery, dynamic modulus, constant strain rate, cyclic stress controlled, and cyclic strain controlled tests in both tension and compression and over a wide range of temperatures, stress levels, strain rates, loading/unloading periods, loading frequencies, and confinement levels. It is shown that the model is capable of predicting time-, rate-, and temperature-dependent of asphalt mixes subjected to different loading conditions.