We present a Finite Element model, which is devoted to describing the failure mechanics of quasi-brittle materials (e.g. concrete), such as the stiffness recovery effect at the transition from tension to compression, and the cyclic behavior with a low number of cycles. The material is studied at the meso-scale, and thus considered as a heterogeneous medium. The model is formulated within the framework of the strong discontinuity analysis and implemented using the Enhanced Finite Element Method (E-FEM). The key point is to locally embed the discontinuities inside the finite elements. Here, we take advantage of this strategy for two kinds of discontinuities. On the one hand, strong discontinuities aim to model cracks, at fine scale, that can open along mode-I. On the other hand, weak discontinuities are used to describe the elastic heterogeneity. In addition to the initiation and propagation of cracks, our main contribution is to add a closure mechanism. We show the ability of the model to simulate some of the well-known characteristics of such materials at macroscale, such as the unsymmetrical tension/compression behavior, the stiffness recovery effect, and hysterical load/displacement curve.