Abstract:
The investigation of non-linear elasticity of solids is performed. The Gibbs free energy of a polycrystalline solid at given pressure $P$ and temperature $T$ is decomposed over the invariants of the Lagrange finite deformations tensor, including fourth-order contributions of deformation components. Based on this, we define the fourth-order elastic moduli for polycrystal (fourth-order Lame coefficients) under arbitrary pressure (the corresponding coefficients of the second and third order are well known). The linear invariants of the fourth-order elastic constants tensor are used to obtain the relations that define the fourth-order Lame coefficients through the fourth-order elastic constants of single crystal grains with hexagonal symmetry, which form a polycrystal. The data for the second, third, and fourth-order Lame coefficients for magnesium and erbium are obtained using the available data for the corresponding order elastic constants of single crystals.
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