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This paper presents a computational micromechanics modeling approach to predict damage-induced mechanical response of asphalt mixtures. Heterogeneous geometric characteristics and inelastic mechanical behavior were taken into account by introducing finite element modeling techniques and a viscoelastic material model. The modeling also includes interface fracture to represent crack growth and damage evolution. The interface fracture is modeled by using a micromechanical nonlinear viscoelastic cohesive-zone constitutive relation. Fundamental material properties and fracture characteristics were measured from simple laboratory tests and then incorporated into the model to predict rate-dependent viscoelastic damage behavior of the asphalt mixture. Simulation results demonstrate that each model parameter significantly influences the mechanical behavior of the overall asphalt mixture. Within a theoretical framework of micromechanics, this study is expected to be suitable for evaluating damage-induced performance of asphalt mixtures by measuring only material properties and fracture properties of each mix component and not by recursively performing expensive laboratory tests that are typically required for continuum damage mechanics modeling.