The present chapter is part of an approach that attempts to represent the mechanical behaviors of brittle/quasi-brittle materials. At the mesoscopic scale, the studied material is considered as heterogeneous materials. The used model in this study is referred to as the enriched finite element method (EFEM) (Ortiz et al., Comput Methods Appl Mech Eng 61:189, 1987; Simo et al., Comput Mech 12:277, 1993). As a finite element-based model, this model performs two kinds of enhancements: (i) strong discontinuities, which allow an illustration of cracks and fractures, and (ii) weak discontinuities, which manage to represent heterogeneities explicitly without any need of mesh adaptation. Many existing EFEM models have shown their ability to simulate a lot of main features of brittle/quasi-brittle materials at the macroscopic scale, such as the asymmetric responses in traction/compression. With a large number of finite elements and explicit heterogeneous structures, the mechanical behaviors that applied at the local scale could be very simple. In this chapter, we are looking forward to describing more of the main characters of such material by adding a closure mechanism to the model.