Particle methods in the study of fracture

This article reviews particle methods in the study of fracture. It focuses on the exact solution of dynamic cracks in an ideal brittle solid. Topics that arise include Cherenkov radiation of phonons, how calculations in a strip let one connect continuum fracture mechanics to atomic solutions, and the use of Wiener-Hopf techniques for analytical results. Then the article discusses molecular dynamics solutions, focusing on how to set them up making use of insights from the exactly solvable models. The particular case of silicon is discussed in detail. Finally there is a brief discussion of mesoscopic particle models.