Recent results about the detection of unknown boundaries and inclusions in elastic plates

TL;DR

This paper reviews recent advances in inverse problems for elastic plates, focusing on boundary detection, inclusion size estimation, and stability, with applications to cavities and rigid inclusions in anisotropic materials.

Contribution

It provides new size estimates for inclusions and extends previous results to cavities and rigid inclusions in elastic plates.

Findings

Uniqueness and stability results for boundary detection.

Size estimates for elastic inclusions and cavities.

Extension of size bounds to rigid inclusions.

Abstract

In this paper we review some recent results concerning inverse problems for thin elastic plates. The plate is assumed to be made by non-homogeneous linearly elastic material belonging to a general class of anisotropy. A first group of results concerns uniqueness and stability for the determination of unknown boundaries, including the cases of cavities and rigid inclusions. In the second group of results, we consider upper and lower estimates of the area of unknown inclusions given in terms of the work exerted by a couple field applied at the boundary of the plate. In particular, we extend previous size estimates for elastic inclusions to the case of cavities and rigid inclusions. Key words: inverse problems, elastic plates, uniqueness, stability estimates, size estimates, three sphere inequality, unique continuation.