In this paper we deal with the inverse problem of determining 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 modelled as inclusions with a very small elasticity tensor.

Identification of Cavities and Inclusions in Linear Elasticity with a Phase-Field Approach / A. Aspri, E. Beretta, C. Cavaterra, E. Rocca, M. Verani. - In: APPLIED MATHEMATICS AND OPTIMIZATION. - ISSN 0095-4616. - 86:3(2022), pp. 32.1-32.41. [10.1007/s00245-022-09897-6]

Identification of Cavities and Inclusions in Linear Elasticity with a Phase-Field Approach

A. Aspri
Primo
;
C. Cavaterra;
2022

Abstract

In this paper we deal with the inverse problem of determining 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 modelled as inclusions with a very small elasticity tensor.
Inverse problems; Cavity; Phase-field; Linear elasticity; Primal dual active set method
Settore MAT/05 - Analisi Matematica
PRIN201719CLOVA_01 - Virtual Element Methods: Analysis and Applications - LOVADINA, CARLO - PRIN2017 - PRIN bando 2017 - 2019
PRIN202022CLOVA_01 - Advanced polyhedral discretisations of heterogeneous PDEs for multiphysics problems - LOVADINA, CARLO - PRIN2020 - PRIN bando 2020 - 2022
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/939633
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