Based on continuum damage mechanics (CDM), an isotropic and anisotropic damage model coupled with a novel plasticity model for plain concrete is proposed in this research. Two different damage evolution laws for both tension and compression are formulated for a more accurate prediction of the plain concrete behavior. In order to derive the constitutive equations, the strain equivalence hypothesis is adopted. The proposed constitutive model has been shown to satisfy the thermodynamics requirements, and detailed numerical algorithms are developed for the Finite Element implementation of the proposed model. Moreover, the numerical algorithm is coded using the user subroutine UMAT and then implemented in the commercial finite element analysis program Abaqus, and the overall performance of the proposed model is verified by comparing the model predictions to various experimental data on macroscopic level. Using the proposed coupled plasticity-damage constitutive model, the effect of the micromechanical properties of concrete, such as aggregate shape, distribution, and volume fraction, the ITZ thickness, and the strength of the ITZ and mortar matrix on the tensile behavior of concrete is investigated on 2-D and 3-D meso-scale. As a result of simulation, the tensile strength and thickness of the ITZ is the most important factor that control the global strength and behavior of concrete, and the aggregate shape and volume fraction has somewhat effect on the tensile behavior of concrete while the effect of the aggregate distribution is negligible. Furthermore, using the proposed constitutive model, the pull-out analysis of the single straight and curved CNT embedded in cement matrix is carried out. In consequence of the analysis, the interfacial fracture energy is the key parameter governing the CNT pull-out strength and ductility at bonding stage, and the Young's modulus of the CNT has also great effect on the pull-out behavior of the straight CNT. In case of the single curved CNT, while the ultimate pull-out force of the curved CNT at sliding stage is governed by the initial sliding force when preexisting normal force is relatively high, the ultimate pull-out force, when the preexisting normal force is not significant, is increased linearly proportional to the curvature and the Young's modulus of the CNT due to the additionally induced normal force by the bending stiffness of the curved CNT.