Identifiability of Planar Cauchy Elasticity from Phase-Speed Data without Major Symmetry

Abstract Acoustic identification of planar elastic moduli is well established under major symmetry. Once this symmetry is relaxed, the acoustic tensor becomes nonsymmetric and the information contained in phase speeds and polarizations changes. We determine what these two ob-servables identify for a nine-parameter planar Cauchy-elastic law with symmetric stress. The complete phase-speed field contains only eight independent phase-speed invariants, and the associated map has generic rank eight, leaving a local one-parameter constitutive ambiguity. The six-parameter major-symmetric class occupies a lower-dimensional subset of the same eight-dimensional invariant space. Phase speeds can therefore detect departure from major symmetry for a generic anisotropic material even though they do not uniquely recover the three odd coefficients. For weak odd coupling, the phase-speed signature is quadratic whereas the polarization response is linear; special D 2 , C 4 , and SO(2)-invariant families have exactly the same phase-speed branches as certain major-symmetric materials. Polarization data, through the right eigenvectors of the acoustic tensor, supply the missing constitutive information. Two propagation directions leave one null direction in the major-symmetric part and one in the odd part, whereas three distinct directions give unique recovery. With the fourth-order stiffness Frobenius norm on constitutive space and the stacked acoustic-tensor Frobenius norm on data space, equal 60° spacing attains the sharp minimum worst-case amplification of the three-direction consti-tutive inverse. For experiments, phase speeds can reveal loss of major symmetry in generic anisotropy, while stable recovery of the full constitutive tensor requires polarization-resolved measurements and three suitably chosen propagation directions.