Since their first use by Hoover et al (1974) in models for crystalline materials and Cundall & Strack (1979) in geotechnical problems, Discrete Elements Methods (DEM) have found a large field of applications in granular materials, soil and rock mechanics by allowing to compute materials' strain and cracking in a unified framework. This talk will present a possible formalization of DEM leading to a general discretization method for PDEs and allowing to write convergence proofs. Also several strategies for computing cracking under dynamical loading with DEM will be presented and their methodology compared to phase-field methods.