We deal with the detection and shape reconstruction of inclusions in elastic bodies based on a monotonicity method and aim to reconstruct them with experimental measurements. Thus, we base our studies on the rigorously proven theory of the linearized monotonicity tests for noisy measurement data, where the so-called Neumann-to-Dirichlet operator, its Fréchet derivative and the corresponding monotonicity properties play an essential role. Further on, we give an insight into the lab experiment itself. More specifically, we take a look at Makrolon plates with one or two circular aluminium inclusions. Concerning the realization of the measurements, we have to deal with missing data which cannot be measured due to the set-up of the experiment. Hence, we take a look at a modified spline interpolation in order to determine this data. In doing so, we state the required steps for the implementation of the linearized monotonicity tests. Finally, we present our reconstructions based on experimental data and compare them with the simulations obtained from artificial data, where we want to highlight that all inclusions can be detected from the noisy experimental data, thus, we obtain accurate results. This paper combines the rigorously proven theory of the monotonicity methods developed for linear elasticity with the explicit application of the methods, i.e. the implementation and simulation of the reconstruction of inclusions in elastic bodies for both artificial and experimental data.

我们基于单调性方法处理弹性体中夹杂物的检测和形状重建，旨在通过实验测量重建它们。因此，我们的研究基于经过严格证明的噪声测量数据线性化单调性测试理论，其中所谓的 Neumann-to-Dirichlet 算子、其 Fréchet 导数和相应的单调性属性起着至关重要的作用。进一步，我们深入了解实验室实验本身。更具体地说，我们来看看带有一两个圆形铝夹杂物的模克隆板材。关于测量的实现，我们必须处理由于实验的设置而无法测量的缺失数据。因此，我们看一下修改后的样条插值以确定这些数据。在这样做，我们陈述了实现线性化单调性测试所需的步骤。最后，我们展示了基于实验数据的重建，并将它们与从人工数据中获得的模拟进行比较，我们想强调可以从嘈杂的实验数据中检测到所有夹杂物，从而获得准确的结果。本文将针对线性弹性开发的单调性方法的经过严格证明的理论与这些方法的显式应用相结合，即针对人工和实验数据对弹性体中的夹杂物进行重构的实施和模拟。我们展示了基于实验数据的重建，并将它们与从人工数据获得的模拟进行比较，我们想强调所有夹杂物都可以从嘈杂的实验数据中检测到，从而获得准确的结果。本文将针对线性弹性开发的单调性方法的经过严格证明的理论与这些方法的显式应用相结合，即针对人工和实验数据对弹性体中的夹杂物进行重构的实施和模拟。我们展示了基于实验数据的重建，并将它们与从人工数据获得的模拟进行比较，我们想强调所有夹杂物都可以从嘈杂的实验数据中检测到，从而获得准确的结果。本文将针对线性弹性开发的单调性方法的经过严格证明的理论与这些方法的显式应用相结合，即针对人工和实验数据对弹性体中的夹杂物进行重构的实施和模拟。