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Journal of Applied Mechanics and Technical Physics

2016 year, number 4

Extremality Conditions of Elastic Constants and Main Anisotropy Axes

N. I. Ostrosablin
Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: линейно-упругие материалы, анизотропия, постоянные упругости, условия экстремальности, главные оси анизотропии, триклинная сингония, кубическая сингония, linear-elastic materials, anisotropy, elastic constants, extremality conditions, main anisotropy axes, triclinic crystal system, cubic crystal system


This paper describes the derivation of extremality conditions of each elasticity coefficient (Young's modulus, shear modulus, et al.,) for the general case of linear-elastic anisotropic materials. The stationarity conditions are obtained, and they determine the orthogonal coordinate systems being the main anisotropy axes, where the number of independent elasticity constants decreases from 21 to 18 and, in some cases of anisotropy, to 15 or lower. An example of a material with cubic symmetry is given.