Symmetry classes in piezoelectricity from second-order symmetries
The authors propose a general approach using the so-called clips operations, to directly obtain the 16 symmetry classes of the third-order piezoelectricity tensor. It is shown that this approach adapts better to more complicated situations. In addition to this classification, the authors provide two explicit harmonic decompositions of the piezoelectricity tensor and the normal forms of this tensor for each of the 16 symmetry classes. The work is organized in four sections and three appendices. In Section 1, the authors recall the mathematical formulation of the physical coupling between electricity and elasticity. The definitions of tensor symmetry groups and classes are introduced. In Section 2, the harmonic decomposition of the piezoelectricity tensor is introduced. Two particular explicit harmonic decompositions of the space of piezoelectricity tensors are proposed. In Section 3, the existence of the 16 symmetry classes for the piezoelectric tensor is established using clips operations. In Section 4, two-order symmetries are used to obtain a direct characterization of 11 out of 16 piezoelectricity symmetry classes. A method to distinguish between the remaining classes is proposed. The article has three appendices that present the main definitions of the closed O(3)-subgroups and the explicit matrix expression of normal form in each symmetry class, in addition to some useful formulas about the dimension of spaces associated with the normal forms.
scientific article; zbMATH DE number 7632498
scientific article