Ultrasonic characterization of generally anisotropic elasticity implementing optimal zeroth-order elastic bounds and a wave-fitting approach

Abstract: The elastic behavior of materials is of critical importance for the design, fabrication, and testing of industrial and structural components. The ease with which the wave angle of incidence can be varied makes ultrasonic techniques well suited for the characterization of anisotropic materials, whose properties are direction-dependent. This work aims to develop an ultrasonic goniometry method in which a wave is transmitted through a sample while scanning over spherical coordinates. A plane-wave model is formulated that accounts for fluid-solid interfaces and is applicable to a wide range of sample thicknesses. The model assumes general anisotropy, enabling the characterization of materials with symmetries up to triclinic, and does not require precise sample alignment. Specially designed transducers support the plane-wave approximation, thereby avoiding the need for more computationally expensive finite-beam models. Furthermore, implementation of the forward model on GPU architectures significantly reduces the computational cost associated with the numerous evaluations required during the waveform fitting inversion. The introduction of optimal zeroth-order bounds is used to tightly delimit the search space, and an isotropic self-consistent solution is shown to provide an effective initial guess. Finally, measurements on plate-like samples are compared with the literature and diffraction-based methods.