Studying equilibrium values of moduli of elasticity, using models of the mechanics of finite deformations of a continuous medium

Abstract

The physical content of an equation of state in the form of σ = σ(υ) is discussed as it applies to the theory of the elastic properties of crystals. Here, σ is pressure and υ is a change in the volume of the crystal under the effect of pressure. We assume that the energy of a deformed state is determined using an elastic modulus no higher than the third order. The forms of the analytical dependences of σ = σ(υ) for the eight most popular equations of state in the mechanics of finite deformations of a continuous medium then coin cide, and with the same equation of the state predicted by the Mott model. As an example, differences between the values of the elastic moduli of Cu and Al, calculated using different equations of state for the mechanics of finite deformations of continuous media in the Mott model, are discussed.