An integrity basis for plane elasticity tensors

Abstract

An isotropic functional basis of 5 polynomials is shown to be also an integrity basis for the space of plane elasticity tensors. A decomposition of each element in this space into a direct sum of "harmonic" tensors is used to compute or estimate the distance between an arbitrary elasticity tensor and the three non-trivial symmetry classes, to allow for the determination of the material symmetry when the elastic coefficients are known only to within a given approximation.