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Extended spectral element formulation for modeling the propagation of nonlinear ultrasonic waves produced by multiple cracks in solid media
Computers & Structures ( IF 4.4 ) Pub Date : 2024-12-27 , DOI: 10.1016/j.compstruc.2024.107639
Feilong Li, Yue Su, Xiaoqiang Sun

This study presents a novel time-domain extended spectral element method (TD-XSEM) that can efficiently and accurately simulate interactions between ultrasonic waves and multiple randomly distributed and oriented cracks in solid materials. Compared to the conventional TD-SEM, which excels at large-scale structures but struggles with small discontinuities and contact issues, our TD-XSEM integrates linear finite elements to model these challenges effectively. Moreover, it preserves the efficiency of spectral elements in intact regions. Our unique frictional contact formulation employs the Heaviside function in discontinuous elements with enriched corner nodes. Rigorous validation against interactions of longitudinal waves with randomly distributed and oriented cracks shows superior convergence and accuracy of TD-XSEM. The proposed approach is further applied to capture second harmonic Lamb wave propagation and mixing bulk wave phenomena, demonstrating its feasibility and robustness in modeling complex interactions between ultrasonic waves and multiple random cracks. Implemented in C, TD-XSEM offers unprecedented accuracy and geometric flexibility in analyzing contact acoustic nonlinearity owing to multiple frictional cracks, contributing to the field of non-destructive testing. This study establishes a new framework for efficient and accurate wave-crack interaction simulations in complex solid structures.

中文翻译:


扩展光谱元公式,用于模拟固体介质中多个裂纹产生的非线性超声波的传播



本研究提出了一种新的时域扩展光谱元方法 (TD-XSEM),它可以高效准确地模拟超声波与固体材料中多个随机分布和定向裂纹之间的相互作用。与传统的 TD-SEM 相比,传统的 TD-SEM 擅长大型结构,但难以解决小的不连续性和接触问题,而我们的 TD-XSEM 集成了线性有限元来有效地模拟这些挑战。此外,它还保留了完整区域中光谱元素的效率。我们独特的摩擦接触公式在具有丰富角节点的不连续元件中采用 Heaviside 函数。对纵波与随机分布和定向裂纹相互作用的严格验证表明 TD-XSEM 具有出色的收敛性和准确性。该方法进一步应用于捕获二次谐波兰姆波传播和混合体波现象,证明了其在模拟超声波与多个随机裂纹之间的复杂相互作用方面的可行性和鲁棒性。TD-XSEM 采用 C 语言,在分析由于多个摩擦裂纹引起的接触声学非线性方面提供了前所未有的精度和几何灵活性,为无损检测领域做出了贡献。本研究为复杂固体结构中高效、准确的波-裂纹相互作用仿真建立了一个新的框架。
更新日期:2024-12-27
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