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An elastic stability criterion is generally formulated based on local elasticity, where the second-order elastic constants of a crystalline system in an arbitrary deformed state are required. While simple in formalism, such a formulation demands extensive computational effort in either an ab initio calculation or an atomistic simulation and often lacks clear physical interpretation. Here, we present a nonlinear theoretical formulation employing higher-order elastic constants beyond the second-order ones; the elastic constants needed in the theory are those at a zero stress state or in any arbitrary deformed state, many of which are now available. We use the published second- and higher-order elastic constants of several cubic crystals, including Au, Al, and Cu, as well as diamond-structure Si, with transcription under different coordinate frames, to test the stability conditions of these crystals under uniaxial and hydrostatic loading. The stability region, ideal strength, and potential bifurcation mode of those cubic crystals under loading are obtained using this theory. The results obtained are in good agreement with the results from the ab initio calculation or embedded atom method. The overall good quality of the results confirms the desired utility of this new approach to predict elastic stability and related properties of crystalline materials without involving intense computation.

Nonlinear theoretical formulation of elastic stability criterion of crystal solids