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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.

A method is described to optimally determine the elastic constants of anisotropic solids from wave-speeds measurements in arbitrary nonprincipal planes. For such a problem, the characteristic equation is a degree-three polynomial which generally does not factorize. By developing and rearranging this polynomial, a nonlinear system of equations is obtained. The elastic constants are then recovered by minimizing a functional derived from this overdetermined system of equations. Calculations of the functional are given for two specific cases, i.e., the orthorhombic and the hexagonal symmetries. Some numerical results showing the efficiency of the algorithm are presented. A numerical method is also described for the recovery of the orientation of the principal acoustical axes. This problem is solved through a double-iterative numerical scheme. Numerical as well as experimental results are presented for a unidirectional composite material.

After describing the crucial role of microcracking in the behavior of ceramic matrix composites, we introduce a phenomenological model in the framework of continuum damage mechanics, where damage is defined as the change of the tensor of elasticity. For damage identification, we have developed a specific ultrasonic device. This immersion set-up was connected to a suitable data processing system for an optimum recovery of the stiffness matrix coefficients from convenient sets of velocity measurements. Linked to a tensile machine, it enabled us to measure the stiffness changes and the anisotropic damage induced by a uniaxial tensile test.

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