Shape Reconstruction in Linear Elasticity: Standard and Linearized Monotonicity Method

Abstract

In this paper, we deal with the inverse problem of the shape reconstruction of inclusions in elastic bodies. The main idea of this reconstruction is based on the monotonicity property of the Neumann-to-Dirichlet operator presented in a former article of the authors. Thus, we introduce the so-called standard as well as linearized monotonicity tests in order to detect and reconstruct inclusions. In addition, we compare these methods with each other and present several numerical test examples.

28 pages, 10 figures

References in corpus (2)

• Lipschitz continuous dependence of piecewise constant Lamé coefficients from boundary data: the case of non flat interfaces
• Boundary determination of the Lamé moduli for the isotropic elasticity system

Cited by in corpus (5)

• Simultaneous recovery of piecewise analytic coefficients in a semilinear elliptic equation
• Monotonicity-Based Regularization for Shape Reconstruction in Linear Elasticity
• Identification of cavities and inclusions in linear elasticity with a phase-field approach
• The inverse obstacle problem for nonlinear inclusions
• A phase-field approach for detecting cavities via a Kohn-Vogelius type functional