This thesis introduces a model for simulating fracture in brittle continuum materials using the Discrete Element Method (DEM). The model employs either spheres or Voronoı̈ cells approximated by multi-spheres to represent the material and uses beam forces that closely resemble Finite Element Method (FEM) matrix elastic frame elements to capture the interactions among them. The introduced beam forces allow us to integrate realistic failure criteria (like Mohr-Coulomb) and energy dissipation models (like Rayleigh damping), making it easy to employ real material parameters. The developed model successfully reproduces the elastic response of a metamaterial composed of glass beads connected by hardened glue bridges and the elastic and failure behavior of adobe bricks, a sustainable and affordable building material, and the simulation results are validated against experimental data. The brick model with Voronoı̈ cells so developed can be used in the study of walls and other adobe structures and their potential applications as sustainable and affordable housing solutions, as well as the simulation of other brittle materials. In addition to the model itself, this work introduces a novel integration algorithm for rotational motion that surpasses in accuracy, stability, and efficiency all existing algorithms used in state-of-the-art DEM codes and excels when integrating the motion of non-spherical particles, an algorithm with the potential to become a new standard in the field. The work goes beyond material modeling and is a highly valuable contribution to the field of fracture modeling and the discrete element method in general.