Continuum Limit of a One-Dimensional Atomistic Energy Based on Local Minimization
Christoph Ortner · Oxford University Research Archive (ORA) (University of Oxford) · 2005
For atomistic energies, global minimization gives the wrong qualitative behaviour and therefore continuum limits should be formulated in terms of local minimization. In this paper, a possible process is suggested, to describe local minimization for a simple one-dimensional problem with body and surface energy. It is shown that an atomistic gradient flow evolution converges to a continuum gradient flow as the spacing between the atomis tends to zero. In addition, the convergence of local minimizers is investigated, in the case of both elastic deformation and fracture.