Numerical simulation of elastic wave propagation in isotropic media considering material and geometrical nonlinearities
Numerical simulation of elastic wave propagation in isotropic media considering material and geometrical nonlinearities
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DOI：
10.1088/0964-1726/24/4/045027
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发表时间：
2015-04
影响因子：
4.1
通讯作者：
N. Rauter;R. Lammering
中科院分区：
文献类型：
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作者：
N. Rauter;R. Lammering
为了准确地检测微观结构损伤，目前正在开发新的方法。一种有前途的工具是由板状结构中的非线性兰姆波传播引起的高次谐波模式的生成。由于振幅非常小，因此使用累积效应。为了更好地了解这种检查方法，数值模拟至关重要。先前的研究已经基于五常数非线性弹性理论对这种现象进行了分析描述。该解析解已得到数值模拟的认可。在这项工作中，首先对考虑线弹性各向同性薄板中的微观结构裂纹的非线性累积波传播进行了模拟和分析。结果表明，考虑到 S1-S2 模式对，存在累积效应。此外，还验证了与这些损坏有关的相对声学非线性参数的敏感性。此外，还观察到裂纹尺寸和方向对非线性波传播行为的影响。第二步，用非线性材料模型代替微观结构裂纹。使用常用有限元软件中实现的超弹性材料模型代替五常数非线性弹性理论来模拟高次谐波兰姆波生成的累积效应。通过使用这些超弹性材料模型，可以发现 S1-S2 和 S2-S4 模式对的累积效应以及不同的非线性行为。结果表明，一方面考虑微观结构裂纹，另一方面考虑非线性材料的数值模拟得出的结果具有可比性。此外，与五常数非线性弹性理论相比，使用 Neo-Hooke 和 Mooney-Rivlin 等成熟的超弹性材料模型是模拟累积高次谐波产生的合适替代方案。
In order to detect micro-structural damages accurately new methods are currently developed. A promising tool is the generation of higher harmonic wave modes caused by the nonlinear Lamb wave propagation in plate like structures. Due to the very small amplitudes a cumulative effect is used. To get a better overview of this inspection method numerical simulations are essential. Previous studies have developed the analytical description of this phenomenon which is based on the five-constant nonlinear elastic theory. The analytical solution has been approved by numerical simulations. In this work first the nonlinear cumulative wave propagation is simulated and analyzed considering micro-structural cracks in thin linear elastic isotropic plates. It is shown that there is a cumulative effect considering the S1–S2 mode pair. Furthermore the sensitivity of the relative acoustical nonlinearity parameter regarding those damages is validated. Furthermore, an influence of the crack size and orientation on the nonlinear wave propagation behavior is observed. In a second step the micro-structural cracks are replaced by a nonlinear material model. Instead of the five-constant nonlinear elastic theory hyperelastic material models that are implemented in commonly used FEM software are used to simulate the cumulative effect of the higher harmonic Lamb wave generation. The cumulative effect as well as the different nonlinear behavior of the S1–S2 and S2–S4 mode pairs are found by using these hyperelastic material models. It is shown that, both numerical simulations, which take into account micro-structural cracks on the one hand and nonlinear material on the other hand, lead to comparable results. Furthermore, in comparison to the five-constant nonlinear elastic theory the use of the well established hyperelastic material models like Neo–Hooke and Mooney–Rivlin are a suitable alternative to simulate the cumulative higher harmonic generation.