Physics of the Solid State
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Fourth-Order Elastic Moduli for Polycrystal: Isotropic Aggregate of Hexagonal Single Crystals
Krasilnikov O.M.
1, Vekilov Yu. Kh.
1
1National University of Science and Technology MISiS, Moscow, Russia
Email: omkras@mail.ru, yuri.vekilov@gmail.com
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. Keywords: polycrystalline materials, non-linear elasticity, fourth-order Lame coefficients.
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