Along with motion and deformation, fracture is a fundamental behaviour for solid materials, playing a critical role in physically-based animation. Many simulation methods including both continuum and discrete approaches have been used by the graphics community to animate fractures for various materials. However, compared with motion and deformation, fracture remains a challenging task for simulation, because the material's geometry, topology and mechanical states all undergo continuous (and sometimes chaotic) changes as fragmentation develops. Recognizing the discontinuous nature of fragmentation, we propose a discrete approach, namely the Bonded Discrete Element Method (BDEM), for fracture simulation. The research of BDEM in engineering has been growing rapidly in recent years, while its potential in graphics has not been explored. We also introduce several novel changes to BDEM to make it more suitable for animation design. Compared with other fracture simulation methods, the BDEM has some attractive benefits, e.g., efficient handling of multiple fractures, simple formulation and implementation, and good scaling consistency. But it also has some critical weaknesses, e.g., high computational cost, which demand further research. A number of examples are presented to demonstrate the pros and cons, which are then highlighted in the conclusion and discussion.