Constitutive model for third harmonic generation in elastic solids |
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| Institution: | 1. Acoustics and Sensors group, MPA 11, Los Alamos National Laboratory, NM 87545, United States;2. Department of Engineering Science and Mechanics, The Pennsylvania State University, 16802 PA, United States;1. School of Traffic and Transportation Engineering, Central South University, Changsha, Hunan 410075, China;2. Department of Mechanical Engineering, Wonkwang University, Iksan, Jeonbuk 54538, Republic of Korea;3. College of Automotive and Mechanical Engineering, Changsha University of Science and Technology, Changsha, Hunan 410114, China;1. School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA;2. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA;3. School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA;4. Department of Civil and Environmental Engineering, Northwestern University, Evanston, IL 60208, USA;1. Department of Aeronautics, Xiamen University, 422, South Siming Road, 361005 Xiamen, China;2. School of Mechanical Engineering, Pusan National University, 10511, San 30, Jangjeon-dong, Geumjeong-gu, 609-735 Busan, South Korea;1. Department of Engineering Science and Mechanics, The Pennsylvania State University, University Park, PA, 16802, USA;2. Department of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong |
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| Abstract: | In this article, we present a new constitutive model for studying ultrasonic third harmonic generation in elastic solids. The model is hyperelastic in nature with two parameters characterizing the linear elastic material response and two other parameters characterizing the nonlinear response. The limiting response of the model as the nonlinearity parameters tend to zero is shown to be the well-known St Venant–Kirchhoff model. Also, the symmetric response of the model in tension and compression and its role in third harmonic generation is shown. Numerical simulations are carried out to study third harmonic generation in materials characterized by the proposed constitutive model. Predicted third harmonic guided wave generation reveals an increasing third harmonic content with increasing nonlinearity. On the other hand, the second harmonics are independent of the nonlinearity parameters and are generated due to the geometric nonlinearity. The feasibility of determining the nonlinearity parameters from third harmonic measurements is qualitatively discussed. |
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| Keywords: | Nonlinear elasticity Nonlinear ultrasonics Higher harmonic Generation Constitutive model |
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