Enriched Numerical Method for Wave Propagation and Assessing Material Damage Using Nonlinear Acoustics

When ultrasonic waves propagate through media, the material nonlinearity triggers the generation of higher-order harmonics (HOH), the frequency of which are integer multiples of the excitation frequency. In nonlinear ultrasonic techniques, the HOH can be measured and related to material damage. In order to enhance the measurement of HOH, wavelet-based signal processing algorithms are introduced to obtain the second harmonic-based and third harmonic-based acoustic nonlinearity parameters. The HOH generation, however, can be triggered by many sources. Finite element numerical modeling with mesoscale heterogeneities explicitly modeled for the nonlinear wave propagation is presented to understand HOH generation due to heterogeneity and non-uniform deformations. Numerical studies indicate that non-uniform variations in different length scales affect the generation of both the second and the third-harmonics and that both second- and third-harmonics acoustic nonlinearity parameters grow with the increase of plastic strain level. However, the third-harmonics acoustic nonlinearity parameter is more sensitive when micro-, meso- and macrostructural variations are considered. The numerical results and predictions are validated with nonlinear ultrasonic experiments and microscale imaging, including X-ray Diffraction (XRD) scanning. Since the frequency of ultrasonic signals are generally high, excessively fine mesh is required to obtain desired solution accuracy for HOH. Therefore, second part of this thesis is devoted to the development of enhanced numerical methods to effectively solve for linear and nonlinear wave propagation problems. Two specific enriched methods are developed: enriched Finite Element (FE) and Harmonic-Enriched Reproducing Kernel Particle Method (RKPM). In enriched FE, standard FE shape functions are enriched with the characteristic solution of the wave propagation problems under the framework of partition of unity. Additional degrees of freedom are introduced in the discrete system for the enrichment functions. To further reduce the computational cost and benefit from the advantages of element free methods, a harmonic-enriched RKPM (H-RKPM) is newly developed. The desired harmonic functions are introduced as the basis function for construction of reproducing kernel and the reproducing condition is enforced. This approach allows the characteristic function to be embedded in the approximation without adding more degrees of freedom. As a result, the high frequency wave problem can be solved using less nodes, enhancing both computational efficiency and accuracy. The methods are verified with benchmark problems and their performance is compared with other conventional methods.