Spectral finite element method for efficient simulation of nonlinear interactions between Lamb waves and breathing cracks within the bi-potential framework

• Published in: International journal of mechanical sciences Vol. 215; p. 106954
• Main Authors: Chen, Huijian, Feng, Zhiqiang, Du, Yuehao, Chen, Qianwei, Miao, Hongchen
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.02.2022
• Subjects: Bi-potential contact theory; Contact acoustic nonlinearity; Guided wave; Spectral finite element method; Guided wave; Bi-potential contact theory; Contact acoustic nonlinearity; Spectral finite element method
• ISSN: 0020-7403; 1879-2162
• DOI: 10.1016/j.ijmecsci.2021.106954

•Spectral FEM within the bi-potential framework is developed for modeling CAN.•A semi-explicit algorithm is proposed to facilitate high computational efficiency.•Contact force can be calculated by bi-potential method without defined parameters.•Computational efficiency of the proposed method is much higher than that of FEM.•The proposed method can capture classical contact acoustic nonlinearity features. Nonlinear ultrasonic guided waves are of great importance in structural health monitoring, since they have both the large-area inspection capability of guided waves and the desirable sensitivity to incipient defects from nonlinear ultrasonic features. Efficient numerical methods play a key role in investigating the nonlinear features of guided waves. In this work, a time domain spectral finite element method (TDSFEM) combined with the bi-potential contact theory is developed to capture the nonlinear interactions between guided waves and breathing cracks. The bi-potential approach has better accuracy than the conventional penalty method, since there is no any user-defined parameter for computation in the former method while the latter one requires a user-experience-based penalty factor. In addition, a semi-explicit algorithm is proposed to integrate the wave equation, which can take full advantage of the diagonal mass matrix of TDSFEM while not sacrificing numerical stability. Numerical verifications against ANSYS show that the computational efficiency of the bi-potential method-based TDSFEM is much higher than that of the FEM via the penalty method. Numerical case studies are then performed to investigate the nonlinear interactions between Lamb waves and breathing cracks. Results show that the proposed method can successfully capture the classical nonlinear features, such as higher harmonic generation and zero frequency (DC) response. Moreover, the influence of the length and gap of a breathing crack on the contact acoustic nonlinearity (CAN) is investigated. As an efficient numerical approach, the bi-potential method-based TDSFEM may be a good tool for investigating the CAN. [Display omitted]