In this paper, a new constitutive law aiming at describing the quasi-brittle behavior when subjected to cyclic loading is presented.The proposed model is formulated with in the frame work of isotròpic contínuum damage mechanics.The cauchy stress tensor is split in to two contributions: one related to the matrix (without cracks) behavior the other related to the crack behavior.This strategy allows accounting for both the crack closure effect and the hysteretic effect in an eficient way making possible large-scale computations.In addition,a specific attention is paid to the way of identifying the material parameters, often requiring complex experimental tests not always easy to carry out. A virtual testing approach based on the use of a discrete element model is used for this purpose.