Identification of cavities and inclusions in linear elasticity with a phase-field approach
arXiv:2201.06554 · doi:10.1007/s00245-022-09897-6
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 (13)
- Mosco convergence for H(curl) spaces, higher integrability for Maxwell's equations, and stability in direct and inverse EM scattering problems
- The linear constraints in Poincaré and Korn type inequalities
- Sharp interface limit for a phase field model in structural optimization
- Lamé Parameter Estimation from Static Displacement Field Measurements in the Framework of Nonlinear Inverse Problems
- Shape Reconstruction in Linear Elasticity: Standard and Linearized Monotonicity Method
- Stability in the linearized problem of quantitative elastography
- Stability for the acoustic scattering problem for sound-hard scatterers
- Double obstacle phase field approach to an inverse problem for a discontinuous diffusion coefficient
- Displacement field estimation from OCT images utilizing speckle information with applications in quantitative elastography
- On an elastic model arising from volcanology: an analysis of the direct and inverse problem
- Reconstruction of material losses by perimeter penalization and phase-field methods
- Reconstruction of cracks and material losses by perimeter-like penalizations and phase-field methods: numerical results
- Stable determination of an inclusion in an inhomogeneous elastic body by boundary measurements