随机复合材料中相干波传播规律的快速边界元法研究

Random composite material is a kind of composites in which the inclusions are uniform randomly distributed. The coherent wave is an ensemble averaged wave over different configurations of inclusions. Wave number of this coherent wave is a complex value, both the real and imaginary parts are functions of the macro properties of random composite materials. Investigation on these two parameters constitutes the theoretical basis for various applications of elastic waves such as in non-destructive evaluation; earth physical exploration; noise reduction and vibration isolation. However, until now, an effective approach for the evaluation of these two parameters in terms of theories; experiments or numerical simulations is still lacking, especially for cases with inclusions of complex geometries. In this project, the pre-corrected Fast Fourier Transform Accelerated Boundary Element Method for 2D elastodynamic problems is implemented due to its advantages for such kinds of problems, then the macro models for the two parameters are proposed based on a physical mechanism analysis, large scale numerical simulations are conducted subsequently to determine the detailed expressions of the proposed macro models. Since the acceleration algorithm has been adopted, the fast boundary element method to be implemented in this project can be used to simulate large scale complicated problems. In addition, because the macro models are proposed based on the physical mechanism of these two parameters, they are applicable to cases with inclusions of more general shapes.

随机复合材料是一种基体中夹杂呈随机不规则排列的复合材料。对同一种随机复合材料不同夹杂分布情况下的波场进行系综平均所得到的波场即为相干波。此相干波波数为一复数，实部和虚部均为随机复合材料宏观参数的函数。对这两个参数开展研究是弹性波在复合材料无损检测、地球物理勘探和降噪隔震等工程领域中应用的理论基础。然而，截至目前，无论是理论、实验还是数值模拟都缺乏对这两个参数的有效预测，特别是针对夹杂形状复杂情况。本项目拟充分发挥快速边界元方法在此类问题中的优势，实施多域问题的预修正快速傅里叶变换边界元方法；然后基于理论分析，提出上述两参数的宏观模型；开展大规模数值模拟并最终确定所提宏观模型。由于采用了加速算法，本项目所实施的快速边界元方法可模拟大规模复杂问题；此外，本项目所提宏观模型基于这两参数产生的物理机理，因此拟得宏观模型适用于夹杂形状更加复杂的随机复合材料。

夹杂随机分布复合材料广泛存在，如混凝土、岩石和土壤等。研究弹性波在这类材料中的传播规律是复合材料无损检测、地球物理勘探和降噪隔震等的理论基础。弹性波超材料和超表面是应用物理和固体力学等领域近些年兴起的一个热点研究方向，兴起的主要原因是此类人工材料可在亚波长尺度操控各种弹性波，在减振降噪，振动能量收集，微电子器件等很多领域有着重要的潜在应用价值。本项目首先基于边界元方法在模拟波动问题方面的优势，实施了预修正快速傅里叶变换加速边界元方法，然后对纤维随机分布复合材料中相干SH波、P波和SV波衰减系数开展了大规模数值模拟。结合单散射问题理论分析和大规模数值模拟结果，确定了预测此类随机复合材料中相干波衰减系数的独立散射宏观模型，并明确了此宏观模型的使用范围。引入界面弹簧模型，提出一配点法，考虑了复合材料中夹杂和基体界面局部损伤对弹性波散射和相干波衰减系数的影响，所得结论可用于基于超声波技术的复合材料无损检测。最后，基于工程中的薄板和梁结果单元，提出了一种调控固体中弹性SV波和薄板中弯曲波的超表面设计思想，在板中弯曲波的调控和利用以及基于薄板结构的微电子器件设计中有潜在应用。