Resonant ultrasound spectroscopy applications: Elastic moduli computation with x-ray computed tomography input for irregularly shaped objects

Resonant ultrasound spectroscopy is a technique that uses a combination of experimentally measured resonant frequencies and physics-based computation of these frequencies to determine the entire set of single crystal elastic moduli of the material. Computation of the resonances is most often accomplished using the Rayleigh–Ritz energy minimization technique, and a basis function that requires sample with canonical geometry, such as a cylinder or a rectangular parallelepiped. Any deviation from canonical geometry can have a significant impact on the calculated resonance frequencies and the inverted elastic moduli. To overcome this limitation, this paper describes an approach that uses x-ray computed tomography data to generate accurate solid part model of components with complex geometry. The part model is then imported into an off-the-shelf finite element method (FEM) software to perform the forward problem. The FEM was combined with surrogate modeling for computation of resonance frequencies of both canonical and non-canonical samples, and ultimately, the inversion of elastic moduli.