Abstract:
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.
Citation:
N. I. Ostrosablin, “Extreme conditions of elastic constants and principal axes of anisotropy”, Prikl. Mekh. Tekh. Fiz., 57:4 (2016), 192–210; J. Appl. Mech. Tech. Phys., 57:4 (2016), 740–756
\Bibitem{Ost16}
\by N.~I.~Ostrosablin
\paper Extreme conditions of elastic constants and principal axes of anisotropy
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2016
\vol 57
\issue 4
\pages 192--210
\mathnet{http://mi.mathnet.ru/pmtf827}
\crossref{https://doi.org/10.15372/PMTF20160419}
\elib{https://elibrary.ru/item.asp?id=26493353}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2016
\vol 57
\issue 4
\pages 740--756
\crossref{https://doi.org/10.1134/S0021894416040192}
Linking options:
https://www.mathnet.ru/eng/pmtf827
https://www.mathnet.ru/eng/pmtf/v57/i4/p192
This publication is cited in the following 3 articles:
B. D. Annin, N. I. Ostrosablin, R. I. Ugryumov, “Using eigenmoduli and eigenstates to evaluate the possibility of martensitic phase transformations”, J. Appl. Mech. Tech. Phys., 62:5 (2021), 707–716
L Bodnárová, M Zelený, P Sedlák, L Straka, O Heczko, A Sozinov, H Seiner, “Switching the soft shearing mode orientation in Ni–Mn–Ga non-modulated martensite by Co and Cu doping”, Smart Mater. Struct., 29:4 (2020), 045022
B. D. Annin, N. I. Ostrosablin, “Structure of Elasticity Tensors in Transversely Isotropic Material with Paradox Behavior under Hydrostatic Pressure”, J Min Sci, 55:6 (2019), 865
Citation in format AMSBIB
Contact us: