Optimal recovery of the elasticity tensor of general anisotropic materials from ultrasonic velocity data

An ultrasonic wave approach is presented for the optimal identification of the 21 independent elasticity constants of the most general linear homogeneous anisotropic elastic solid from wave speed measurements of obliquely incident ultrasonic bulk waves. Since the symmetry of acquisition planes is not taken into account, this inversion process is generalized to materials that do not possess three mutually orthogonal planes of symmetry. Minimization of an overdetermined system of nonlinear algebraic equations is solved by a constrained optimization method. Various classes of symmetry are considered. Several critical factors (initial guesses, scatter in experimental data) which can influence the accuracy of the elastic property reconstruction algorithm have been investigated by means of numerical examples that simulate in the best way a typical experiment. The sensitivity of the reconstruction algorithm to each identified elasticity constant is detected a posteriori by means of the estimation of a confidence interval associated with each identified constant. The generalized reconstruction method is applied to the experimental data for materials with various symmetry classes.