A unified approach to invariants of plane elasticity tensors

The action of the orthogonal group \(O(2)\) on the space of plane elasticity tensors has been the subject of some recent investigations. It is shown here that the approach based on the “harmonic decomposition” technique, which is also used in a three-dimensional setting, gives a unified perspective on this issue. We construct explicit relationships between invariants and quantities derived from such an approach and what was found earlier by Tsai and Pagano and, more recently, through the “polar method” and the use of complex variables.