An atomistic-to-continuum analysis of crystal cleavage in a two-dimensional model problem

摘要

A two-dimensional atomic mass spring system is investigated for criticalfracture loads and its crack path geometry. We rigorously prove that, in thediscrete-to-continuum limit, the minimal energy of a crystal under uniaxialtension leads to a universal cleavage law and energy minimizers are eitherhomogeneous elastic deformations or configurations that are completely crackedand do not store elastic energy. Beyond critical loading, the specimengenerically cleaves along a unique optimal crystallographic hyperplane. Forspecific symmetric crystal orientations, however, cleavage might fail. In thiscase a complete characterization of possible limiting crack geometries isobtained.