A Two-Stage Guided-Wave Acoustoelastic Inversion Method for Second- and Third-Order Elastic Constants of Metallic Rods Using CMA-ES Optimization

Second- and third-order elastic constants (SOEs and TOEs) are essential parameters for characterizing the nonlinear elastic behavior of metallic materials. However, their determination in small-diameter slender rods remains challenging due to the stringent requirements of existing bulk-wave acoustoelastic and resonant ultrasound methods on the specimen dimensions and measurement conditions. This study proposes a two-stage guided-wave acoustoelastic inversion method for identifying the second- and third-order elastic constants of isotropic metallic rods. A high-accuracy forward model based on the wave finite element (WFE) method is developed to calculate the L(0,1) guided-wave dispersion and acoustoelastic responses under different combinations of elastic constants and uniaxial prestress. The sensitivity characteristics of group velocity dispersion and acoustoelastic coefficients are systematically investigated to provide a basis for objective function construction and test frequency selection. A surrogate-assisted Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is employed to solve the resulting ill-conditioned and non-separable inversion problem. Numerical validations demonstrate that the proposed method can accurately recover both SOEs and TOEs while substantially reducing the computational cost of iterative inversion.