Symmetry classes in piezoelectricity from second-order symmetries

TL;DR

This paper classifies the symmetry groups of the piezoelectricity tensor using a novel approach, identifying 16 classes and providing normal forms, which advances understanding of symmetry in piezoelectric materials.

Contribution

It introduces a new method based on clips operations to determine the 16 symmetry classes of the piezoelectricity tensor and classifies 11 of these classes using second order orthogonal transformations.

Findings

Identified 16 symmetry classes of the piezoelectricity tensor.

Provided normal forms for these symmetry classes.

Classified 11 classes using second order orthogonal transformations.

Abstract

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