Abstract: Inspired by peridynamics and the unified phase-field model, a new nonlocal macro-meso-scale consistent damage model has been proposed recently, which provides a new method for the numerical simulation of crack propagation. In the present paper, the criterion for meso-scale damage in this model is modified, and a \bar\lambda-\ell damage language is proposed to depict the displacement discontinuity in a cracked solid. In the modified model, the meso-scale damage characterizing the performance degradation of bond between two material points (namely a material point pair), is firstly determined according to the maximum exceedance of deformation of the point pair in terms of the critical elongation quantity during loading history. Then, by the weighted averaging over the meso-scale damage of material point pairs in the influence domain, the macro-scale topologic damage is obtained. Further, by advocating the energetic degradation function, the energy-based damage can be connected to the topologic damage, and in turn can be inserted into the framework of continuum damage mechanics such that governing equations are readily established. The proposed method is a nonlocal model, and it can be numerically implemented by the finite element discretization, where the problem of mesh size sensitivity that occurs in the classical continuum damage mechanics model is circumvented. The modified model is applied to crack modeling problems involving strong nonlinear snap-back property. Examples are studied, showing that the proposed method can not only characterize the crack patterns, but also capture quantitatively the load-deformation curves. The problems to be studied in the future are also discussed.