The authors acknowledge the support of CNPq and CAPES (Brazil) and the Agencia Nacional de Promoción Científica y Tecnológica (Argentina).

The lattice discrete element method has been successfully used to simulate the evolution of damage in structural mechanics. The approach has led to new perspectives in the solution of fracture problems in nonhomogeneous materials. For such purpose, it is necessary to introduce correctly the parameters that characterize the random nature of the material. In this article, the fracture toughness of the material is considered a three-dimensional random field, characterized by a probability density and the spatial distribution of the simulated random field which is governed by the correlation length. The methodology used to separate the random field simulated from the discretization level used is depicted in detail. Examples are shown that verify the objectivity of the results obtained respecting the discretization levels. Finally, the article concludes by emphasizing the relevance of this implementation in the damage simulation process in the so-called heterogeneous materials.