On symmetries of higher-order elastic constants.

IF 1.9 4区材料科学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Acta Crystallographica Section A: Foundations and Advances Pub Date : 2025-01-01 DOI:10.1107/S2053273324011021

J D Clayton

引用次数: 0

Abstract

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.

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关于高阶弹性常数的对称性。

在弹性晶体中，通常假定采用超弹性描述，应变能势被理想化为围绕未应变参考状态的泰勒序列应变扩展。二次项系数为二阶或线性弹性常数。高阶项系数是三阶、四阶等弹性常数。Telyatnik 最近发表的论文[Acta Cryst. (2024), A80, 394-404]将单晶体、横向各向同性和各向同性固体各向异性弹性常数的对称性知识扩展到六阶项。Telyatnik 在同一篇文章中还报告了具有各向异性的多晶聚集体的有效弹性常数。本评注简要概述了非线性晶体弹性以及二阶和三阶的独立弹性常数，以供参考。然后重点介绍了 Telyatnik 的方法和结果，预计这些方法和结果将对晶体弹性研究大有裨益。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Acta Crystallographica Section A: Foundations and Advances CHEMISTRY, MULTIDISCIPLINARYCRYSTALLOGRAPH-CRYSTALLOGRAPHY

CiteScore

2.60

自引率

11.10%

发文量

419

期刊介绍： Acta Crystallographica Section A: Foundations and Advances publishes articles reporting advances in the theory and practice of all areas of crystallography in the broadest sense. As well as traditional crystallography, this includes nanocrystals, metacrystals, amorphous materials, quasicrystals, synchrotron and XFEL studies, coherent scattering, diffraction imaging, time-resolved studies and the structure of strain and defects in materials. The journal has two parts, a rapid-publication Advances section and the traditional Foundations section. Articles for the Advances section are of particularly high value and impact. They receive expedited treatment and may be highlighted by an accompanying scientific commentary article and a press release. Further details are given in the November 2013 Editorial. The central themes of the journal are, on the one hand, experimental and theoretical studies of the properties and arrangements of atoms, ions and molecules in condensed matter, periodic, quasiperiodic or amorphous, ideal or real, and, on the other, the theoretical and experimental aspects of the various methods to determine these properties and arrangements.