Identification of cavities and inclusions in linear elasticity with a phase-field approach
Friday 14th January 2022
Aspri, A; Beretta, E.; Cavaterra, C.; Rocca, E.; Verani, M.
In this paper we deal with the inverse problem of the shape reconstruction of cavities and inclusions embedded in a linear elastic isotropic medium from boundary displacement's measurements. For this goal, we consider a constrained minimization problem involving a boundary quadratic misfit functional with a regularization term that penalizes the perimeter of the cavity or inclusion to be identified. Then using a phase field approach we derive a robust algorithm for the reconstruction of elastic inclusions and of cavities modelled as inclusions with a very small elasticity tensor.