Average elastic constants and tensor invariants

A general formalism is presented that can be used to calculate the average elastic constants of a polycrystal in terms of the elastic constant of the single crystal. The formalism is based on the invariants of the second‐rank tensors and scalars obtained by a contraction of indices of the fourthrank...

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Autores principales: Povolo, F., Bolmaro, R.E.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00318965_v99_n2_p423_Povolo
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_00318965_v99_n2_p423_Povolo2023-10-03T14:41:55Z Average elastic constants and tensor invariants Povolo, F. Bolmaro, R.E. A general formalism is presented that can be used to calculate the average elastic constants of a polycrystal in terms of the elastic constant of the single crystal. The formalism is based on the invariants of the second‐rank tensors and scalars obtained by a contraction of indices of the fourthrank tensor of the elastic constants. It is shown that both, Voigt and Reuss averages are particular cases of the proposed method. The results are compared with actual experimental data obtained in crystals with different symmetries and the physical significance of some of the invariants is discussed. Finally, a general relationship expressing Hooke's law in terms of 3 × 3 matrices of the elastic constants is given. Copyright © 1987 WILEY‐VCH Verlag GmbH & Co. KGaA Fil:Povolo, F. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00318965_v99_n2_p423_Povolo
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description A general formalism is presented that can be used to calculate the average elastic constants of a polycrystal in terms of the elastic constant of the single crystal. The formalism is based on the invariants of the second‐rank tensors and scalars obtained by a contraction of indices of the fourthrank tensor of the elastic constants. It is shown that both, Voigt and Reuss averages are particular cases of the proposed method. The results are compared with actual experimental data obtained in crystals with different symmetries and the physical significance of some of the invariants is discussed. Finally, a general relationship expressing Hooke's law in terms of 3 × 3 matrices of the elastic constants is given. Copyright © 1987 WILEY‐VCH Verlag GmbH & Co. KGaA
format JOUR
author Povolo, F.
Bolmaro, R.E.
spellingShingle Povolo, F.
Bolmaro, R.E.
Average elastic constants and tensor invariants
author_facet Povolo, F.
Bolmaro, R.E.
author_sort Povolo, F.
title Average elastic constants and tensor invariants
title_short Average elastic constants and tensor invariants
title_full Average elastic constants and tensor invariants
title_fullStr Average elastic constants and tensor invariants
title_full_unstemmed Average elastic constants and tensor invariants
title_sort average elastic constants and tensor invariants
url http://hdl.handle.net/20.500.12110/paper_00318965_v99_n2_p423_Povolo
work_keys_str_mv AT povolof averageelasticconstantsandtensorinvariants
AT bolmarore averageelasticconstantsandtensorinvariants
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