On symmetries of higher-order elastic constants

In elastic crystals, a hyperelastic description is conventionally assumed, and the strain energy potential is idealized as a Taylor-series expansion in strain about an unstrained reference state. Coefficients of quadratic terms are second-order or linear elastic constants. Coefficients of higher-order terms are elastic constants of third order, fourth order, and so on. Recently published work by Telyatnik [Acta Cryst. (2024), A80, 394-404] extends prior knowledge of symmetry properties for anisotropic elastic constants of single crystals, as well as transversely isotropic and isotropic solids, to terms up to sixth order. Effective elastic constants for polycrystalline aggregates, with possible anisotropy, were reported by Telyatnik, in the same article, to the same order. A terse summary of nonlinear crystal elasticity and independent elastic constants of orders two and three are given in this commentary for context. Methods and results of Telyatnik, anticipated to be of great utility to crystal elasticity research, are then highlighted.