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Abstract
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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
, the third-order piezoelectricity
tensor
, and the fourth-order
elasticity tensor
.
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
-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.
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Keywords
piezoelectricity tensor, symmetry classes, normal forms
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Mathematical Subject Classification
Primary: 74E10
Secondary: 74F99, 20C35
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Milestones
Received: 22 November 2020
Revised: 19 December 2020
Accepted: 21 January 2021
Published: 17 March 2021
Communicated by Martin Ostoja-Starzewski
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