Optimal determination of the material symmetry axes and associated elasticity tensor from ultrasonic velocity data

A simultaneous identification of the angular parallax locating the higher symmetry coordinate system and the associated optimal stiffness tensor from wave speed measurements of obliquely ultrasonic bulk waves in an arbitrarily oriented coordinate system is presented. The property used in classifying a material with regard to its elastic symmetry is the existence and the number of planes of reflective or mirror symmetry. That leads to considering the problem of determining the symmetry class and the directions of the elements of symmetry. To consider the uncertainties of the experimental data, the wave speed measurements are only used to determine the symmetry frames and the optimal stiffness tensor. The proposed inverse propagation algorithm consists of minimizing a functional where the unknowns are the elasticity constants and the Euler angles between the geometric coordinate system and the frame of higher symmetry. Stability of the used least-square algorithm to the initial guesses and to the noise in the wave speed measurements is shown by using simulated data for materials with the most general anisotropy. The applicability of the method is demonstrated using experimental data for arbitrarily oriented but known composite materials.