Vol. 9, No. 1, 2021

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Symmetry classes in piezoelectricity from second-order symmetries

Marc Olive and Nicolas Auffray

Vol. 9 (2021), No. 1, 77–105
DOI: 10.2140/memocs.2021.9.77
Abstract

The piezoelectricity law is a constitutive model that describes how mechanical and electric fields are coupled within a material. In its linear formulation this law comprises three constitutive tensors of increasing order: the second-order permittivity tensor S, the third-order piezoelectricity tensor P, and the fourth-order elasticity tensor C. In the first part of the paper, the symmetry classes of the piezoelectricity tensor alone are investigated. Using a new approach based on the use of the so-called clips operations, we establish the 16 symmetry classes of this tensor and provide their associated normal forms. Second-order orthogonal transformations (plane symmetries and π-angle rotations) are then used to characterize and classify directly 11 out of the 16 symmetry classes of the piezoelectricity tensor. An additional step to distinguish the remaining classes is proposed.

Keywords
piezoelectricity tensor, symmetry classes, normal forms
Mathematical Subject Classification
Primary: 74E10
Secondary: 74F99, 20C35
Milestones
Received: 22 November 2020
Revised: 19 December 2020
Accepted: 21 January 2021
Published: 17 March 2021

Communicated by Martin Ostoja-Starzewski
Authors
Marc Olive
Laboratoire de Mécanique et Technologie
Université Paris-Saclay
ENS Paris-Saclay
CNRS UMR 8535
Gif-sur-Yvette
France
Nicolas Auffray
Laboratoire Modélisation et Simulation Multi Echelle
Université Gustave-Eiffel
Université Paris-Est
CNRS UMR 8208
Marne-la-Vallée
France