Size estimates for fat inclusions in an isotropic Reissner-Mindlin plate

In this paper we consider the inverse problem of determining, within an elastic isotropic thick plate modelled by the Reissner–Mindlin theory, the possible presence of an inclusion made of a different elastic material. Under some a priori assumptions on the inclusion, we deduce constructive upper and lower estimates of the area of the inclusion in terms of a scalar quantity related to the work developed in deforming the plate by applying simultaneously a couple field and a transverse force field at the boundary of the plate. The approach allows us to consider plates with a boundary of Lipschitz class.