@article{987fc459a9fb4117b8b12b031c5f9cf0,
title = "Identification of Cavities and Inclusions in Linear Elasticity with a Phase-Field Approach",
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{\textquoteright}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.",
keywords = "Cavity, Inverse problems, Linear elasticity, Phase-field, Primal dual active set method",
author = "Andrea Aspri and Elena Beretta and Cecilia Cavaterra and Elisabetta Rocca and Marco Verani",
note = "Funding Information: The authors deeply thank Dorin Bucur and Alessandro Giacomini for suggesting relevant literature and for useful discussions that led us to improve some of the results in this work. This research has been partially performed in the framework of the MIUR-PRIN Grant 2020F3NCPX “Mathematics for industry 4.0 (Math4I4)”. Andrea Aspri, Cecilia Cavaterra and Elisabetta Rocca are members of GNAMPA (Gruppo Nazionale per l{\textquoteright}Analisi Matematica, la Probabilit{\'a} e le loro Applicazioni) of INdAM (Istituto Nazionale di Alta Matematica). Marco Verani has been partially funded by MIUR PRIN research grants n. 201744KLJL and n. 20204LN5N5. Marco Verani is a member of GNCS (Gruppo Nazionale per il Calcolo Scientifico) of INdAM. Funding Information: The authors deeply thank Dorin Bucur and Alessandro Giacomini for suggesting relevant literature and for useful discussions that led us to improve some of the results in this work. This research has been partially performed in the framework of the MIUR-PRIN Grant 2020F3NCPX “Mathematics for industry 4.0 (Math4I4)”. Andrea Aspri, Cecilia Cavaterra and Elisabetta Rocca are members of GNAMPA (Gruppo Nazionale per l{\textquoteright}Analisi Matematica, la Probabilit{\'a} e le loro Applicazioni) of INdAM (Istituto Nazionale di Alta Matematica). Marco Verani has been partially funded by MIUR PRIN research grants n. 201744KLJL and n. 20204LN5N5. Marco Verani is a member of GNCS (Gruppo Nazionale per il Calcolo Scientifico) of INdAM. Funding Information: Open access funding provided by Universit{\'a} degli Studi di Milano within the CRUI-CARE Agreement. Publisher Copyright: {\textcopyright} 2022, The Author(s).",
year = "2022",
month = dec,
doi = "10.1007/s00245-022-09897-6",
language = "English (US)",
volume = "86",
journal = "Applied Mathematics and Optimization",
issn = "0095-4616",
publisher = "Springer New York",
number = "3",
}