  The accurate approximation of critical strains for lattice instability is a
key criterion for predictive computational modeling of materials. In this
paper, we present a comparison of the lattice stability for atomistic chains
modeled by the embedded atom method (EAM) with their approximation by local
Cauchy-Born models. We find that both the volume-based local model and the
reconstruction-based local model can give O(1) errors for the critical strain
since the embedding energy density is generally strictly convex. The critical
strain predicted by the volume-based model is always larger than that predicted
by the atomistic model, but the critical strain for reconstruction-based models
can be either larger or smaller than that predicted by the atomistic model.
