Experimental detection and shape reconstruction of inclusions in elastic bodies via a monotonicity method

Abstract

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.