This review examines the elastic response of solids under load. The definition of isothermal and adiabatic elastic constants of nth order (n ⩾ 2) for the loaded crystal is given. For the case of hydrostatic pressure, two techniques are proposed for calculating the second-, third- and fourth-order elastic constants from the energy—strain and stress—strain relations. As an example, using the proposed approach within the framework of the density functional theory, the second- to fourth-order elastic constants of bcc tungsten are calculated for the pressure range of 0—600 GPa.

Keywords: high pressures, metals, second- and higher-order elastic constants, equation of state, elastic phase transitions PACS: 61.50.Ks, 62.20.de, 62.50.−p, 64.30.Ef (all) DOI: 10.3367/UFNe.0185.201511f.1215 URL: https://ufn.ru/en/articles/2015/11/e/ 000369654900005 2015PhyU...58.1106V Citation: Vekilov Yu Kh, Krasil’nikov O M, Lugovskoy A V "Elastic properties of solids at high pressure" Phys. Usp. 58 1106–1114 (2015) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks @article{Vekilov:2015, author = {Yu. Kh. Vekilov and O. M. Krasil’nikov and A. V. Lugovskoy}, title = {Elastic properties of solids at high pressure}, publisher = {Physics-Uspekhi}, year = {2015}, journal = {Phys. Usp.}, volume = {58}, number = {11}, pages = {1106-1114}, url = {https://ufn.ru/en/articles/2015/11/e/}, doi = {10.3367/UFNe.0185.201511f.1215} } Received: 9th, April 2015, revised: 11th, August 2015, accepted: 12th, August 2015 Оригинал: Векилов Ю Х, Красильников О М, Луговской А В «Упругие свойства твёрдых тел при высоких давлениях» УФН 185 1215–1224 (2015); DOI: 10.3367/UFNr.0185.201511f.1215