Application of differential evolution on elasticity measurement of low quality factor materials using FEM-based resonant ultrasound spectroscopy

Finite element method based resonant ultrasound spectroscopy (FEM-based RUS) allows elasticity measurement for a material with high quality factor (Q) and arbitrary geometry by minimizing the differences between its theoretically calculated resonant frequencies and the corresponding experimentally measured ones. As Q decreases, some experimental frequencies remain undetermined, which makes it difficult to pair the calculated and experimental frequencies and to correctly identify the elastic constants. Additional difficulty need be tackled for irregularly-shaped low-Q materials due to the adoption of time-consuming FEM, thus efficiency of the identification method needs to be focused on. To apply FEM-based RUS to low-Q materials, a new elastic constant identification method is proposed based on a differential evolution algorithm in this paper. This method can perform a global search combining with local optimizations in the elastic constant space, and improve the overall efficiency by limiting the number of the frequency calculations. By using numerical experiments, the effectiveness of the proposed method under different frequency missing situations was verified and its efficiency was measured from the required frequency calculation numbers, showing an approximate two third reduction compared with an existing method. Finally, the elastic constants of an actual irregular cortical bone-mimicking material (Q ≈ 25) were measured using the two methods, yielding consistent Young's moduli (calculated from the identified constants) with the data provided by the manufacturer and a similar improvement in computational efficiency of the proposed method.