Ultrasonic imaging in highly heterogeneous backgrounds
Ultrasonic imaging in highly heterogeneous backgrounds
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DOI：
10.1098/rspa.2022.0721
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发表时间：
2022-10
期刊：
影响因子：
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通讯作者：
Fatemeh Pourahmadian;H. Haddar
中科院分区：
文献类型：
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作者：
Fatemeh Pourahmadian;H. Haddar
这项工作正式研究了作为超声跟踪随机非均质固体中弹性相变和破裂的工具的微分演化指示器。在周期传感的框架内，假设时间t∘的背景包含(I)粘弹性、各向异性和分段均匀包裹体的多连通集合，以及(Ii)可能不相交的裂缝和孔隙的联合体。(I)和(II)中散射体的支撑体、材料性质和界面条件是未知的，但提供了基质的弹性常数。该结构域经历了任意化学-机械起源的渐进变化，从而使其在未来时间的几何构型和弹性性质是不同的。在每个感测步骤t∘、t1、…多模式事件是由一组边界激励产生的，由此产生的散射场被捕获到观测表面上。然后使用测试数据通过求解光谱散射方程来构造波前密度序列。对于一系列几何和弹性演化场景，分析了与不同的波前对相关的入射场在静止和不断变化的散射体上的变化，其中包括界面和体积变换。主要定理建立了在给定的一对时间步长之间静态裂缝和包裹体的轨迹上的相关入射场的不变性，同时证明了相同的场在修改的区域上的变化。这些结果为在复杂复合材料中成像的差异进化指示剂的理论证明提供了基础，这反过来又使得在具有许多未知特征的背景中进行唯一的进化层析成像成为可能。
This work formally investigates the differential evolution indicators as a tool for ultrasonic tracking of elastic transformation and fracturing in randomly heterogeneous solids. Within the framework of periodic sensing, it is assumed that the background at time t∘ contains (i) a multiply connected set of viscoelastic, anisotropic and piecewise homogeneous inclusions, and (ii) a union of possibly disjoint fractures and pores. The support, material properties and interfacial condition of scatterers in (i) and (ii) are unknown, while elastic constants of the matrix are provided. The domain undergoes progressive variations of arbitrary chemo-mechanical origins such that its geometric configuration and elastic properties at future times are distinct. At every sensing step t∘,t1,…, multi-modal incidents are generated by a set of boundary excitations, and the resulting scattered fields are captured over the observation surface. The test data are then used to construct a sequence of wavefront densities by solving the spectral scattering equation. The incident fields affiliated with distinct pairs of obtained wavefronts are analysed over the stationary and evolving scatterers for a suit of geometric and elastic evolution scenarios entailing both interfacial and volumetric transformations. The main theorem establishes the invariance of pertinent incident fields at the loci of static fractures and inclusions between a given pair of time steps, while certifying variation of the same fields over the modified regions. These results furnish a basisfor theoretical justification of differential evolution indicators for imaging in complex composites which, in turn, enable the exclusive tomography of evolution in a background endowed with many unknown features.