This article presents a new approach to grain fragmentation, its implementation in a discrete element method code, and an experimental validation. This approach is an improvement, compared with those models currently available in the literature. This new approach includes the use of polygonal particles, an estimation of stresses within the particles, a failure criterion, and a mode of rupture. The estimation of stresses is performed as a function of the forces exerted at the contacts, and the size and shape of the grains. The failure criterion is a function of the tensile strength of the material, and the mode of rupture depends on the orientation of the major principal stress. A comparison between experiments and its simulations showed a good match.