The polar analysis of a third order piezoelectricity-like plane tensor

The derivation of the invariants for a tensor of the third order in a two dimensional space is presented in the paper. The mathematical technique to obtain the expression of the invariants is based upon the so-called polar method, proposed as early as 1979 by G. Verchery as an alternative method to represent a plane tensor by its invariants. The polar components of a third order planar tensor are also introduced. When considered in the framework of piezoelectricity, an energetic interpretation of these components is given.