From atomistic to continuum theory for brittle materials: A two-dimensional model problem

Details From atomistic to continuum theory for brittle materials: A two-dimensional model problem From atomistic to continuum theory for brittle materials: A two-dimensional model problem

2011-08-18

arxiv.org/abs/1108.3696v1

Mathematics

Analysis of PDEs

Scientific paper

A two-dimensional atomic mass spring system is investigated for critical fracture loads and its crack path geometry. We rigorously prove that in the discrete-to-continuum limit, the minimal energy leads to a universal cleavage law and energy minimizers are either homogeneous elastic deformations or configurations that are cracked along specific crystallographic hyperplanes. Furthermore, we identify an effective continuum model through Gamma-convergence.

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