Relationship between two-body interatomic potentials in a lattice model and elastic constants. II

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Abstract
General equations are derived for the second-, third-, and fourth-order elastic constants given by a lattice model for a monatomic material, based on two-body central interactions and volume-dependent energy contributions. Explicit equations for a cubic lattice are given. The Brugger definition of the elastic constants is used with the required expansions in terms of the Lagrangian strain parameter. The relationship between the two-body and volume-dependent terms arising from the condition of equilibrium at zero initial stress is discussed in detail.