Identification of cavities and inclusions in linear elasticity with a phase-field approach

Abstract

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, 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 modeled as inclusions with a very small elasticity tensor.

References in corpus (4)

• Shape Reconstruction in Linear Elasticity: Standard and Linearized Monotonicity Method
• Stability in the linearized problem of quantitative elastography
• Displacement field estimation from OCT images utilizing speckle information with applications in quantitative elastography
• Stable determination of an inclusion in an inhomogeneous elastic body by boundary measurements

Cited by in corpus (1)

• A phase-field approach for detecting cavities via a Kohn-Vogelius type functional