  A controversy exists among literature reports of constraints on elastic
constants. In particular, it has been reported that embedded atom method (EAM)
potentials generally impose three constraints on elastic constants of crystals
that are inconsistent with experiments. However, it can be shown that some EAM
potentials do not impose such constraints at all. This paper first resolves
this controversy by identifying the necessary condition when the constraints
exist and demonstrating the condition is physically necessary. Furthermore,
this paper reports that these three constraints are eliminated under all
conditions, by using response EAM (R-EAM) potentials.
