SIAM Journal on Imaging Sciences, Volume 13, Issue 3, Page 1302-1330, January 2020.
Differential evolution indicators are introduced for 3D spatiotemporal imaging of micromechanical processes in elastic solids where progressive variations due to manufacturing and/or aging are housed in a highly scattering background of a priori unknown or uncertain structure. In this vein, a three-tier imaging platform is established where (1) the domain is periodically (or continuously) subject to illumination and sensing in an arbitrary configuration; (2) sequential sets of measured data are deployed to distill far-field signatures of the domain's internal structure through carefully constructed, noniterative solutions to the scattering equation; and (3) the resulting solution sequence is then used to rigorously construct an imaging functional carrying appropriate invariance with respect to the unknown stationary components of the background, e.g., pre-existing interstitial boundaries. This gives birth to differential indicators that specifically recover the 3D support of evolution within a network of unknown scatterers. The direct scattering problem is formulated in the frequency domain where the background consists of a random distribution of monolithic fragments. The constituents are connected through highly heterogeneous interfaces of unknown elasticity and dissipation spanning from perfectly bonded to traction-free contacts which are subject to evolution in time and space. The support of interfacial boundaries is periodically illuminated by a set of incident waves and thus-induced scattered fields are captured over a generic observation surface. The performance of the proposed imaging indicator is illustrated through a set of numerical experiments for sequential reconstruction of evolving damage zones featuring randomly distributed cracks and bubbles.

中文翻译：

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未知微观/宏观结构的弹性材料中微机械演化的差分层析成像

SIAM影像科学杂志，第13卷，第3期，第1302-1330页，2020年1月。
引入了差异演化指标，用于弹性固体中微机械过程的3D时空成像，其中，由于制造和/或老化而导致的渐进变化位于先验未知或不确定结构的高度散射背景下。按照这种方式，建立了一个三层成像平台，其中（1）对该域定期（或连续）进行任意配置的照明和感测；（2）部署顺序测量数据集，以通过精心构建的散射方程的非迭代解来提取域内部结构的远场签名；（3）然后使用所得的溶液序列严格构建相对于背景的未知静止成分例如先前存在的间隙边界具有适当不变性的成像功能。这催生了差分指标，这些指标专门恢复了未知散射体网络中进化的3D支持。直接散射问题是在频域中提出的，其中背景由整体碎片的随机分布组成。这些成分通过弹性和耗散性未知的高度异构界面连接，从完全粘合到无牵引接触，这些接触会随时间和空间而变化。界面边界的支撑被一组入射波周期性地照亮，因此在一般的观察表面上捕获由此引起的散射场。通过一组数值实验对提出的成像指示器的性能进行了说明，该数值实验用于顺序重建以随机分布的裂纹和气泡为特征的演化损伤区域。