Recovering elastic subdomains with strain-gradient elastic interfaces from force measurements: the antiplane shear setting

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Auteurs principaux: Granados, Govanni, Marzuola, Jeremy L., Rodriguez, Casey
Format: Preprint
Publié: 2025
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author Granados, Govanni
Marzuola, Jeremy L.
Rodriguez, Casey
author_facet Granados, Govanni
Marzuola, Jeremy L.
Rodriguez, Casey
contents We introduce and study a new inverse problem for antiplane shear in elastic bodies with strain-gradient interfaces. The setting is a homogeneous isotropic elastic body containing an inclusion separated by a thin interface endowed with higher-order surface energy. Using displacement-stress measurements on the exterior boundary, expressed through a certain Dirichlet-to-Neumann map, we show uniqueness in recovering both the shear and interface parameters, as well as the shape of the inclusion. To address the inverse shape problem, we adapt the factorization method to account for the complications introduced by the higher-order boundary operator and its nontrivial null space. Numerical experiments illustrate the feasibility of the approach, indicating that the framework potentially provides a practical tool for nondestructive detection of interior inhomogeneities, including damaged subvolumes.
format Preprint
id arxiv_https___arxiv_org_abs_2509_15171
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Recovering elastic subdomains with strain-gradient elastic interfaces from force measurements: the antiplane shear setting
Granados, Govanni
Marzuola, Jeremy L.
Rodriguez, Casey
Analysis of PDEs
Materials Science
Mathematical Physics
74G75, 74B05, 35R30
We introduce and study a new inverse problem for antiplane shear in elastic bodies with strain-gradient interfaces. The setting is a homogeneous isotropic elastic body containing an inclusion separated by a thin interface endowed with higher-order surface energy. Using displacement-stress measurements on the exterior boundary, expressed through a certain Dirichlet-to-Neumann map, we show uniqueness in recovering both the shear and interface parameters, as well as the shape of the inclusion. To address the inverse shape problem, we adapt the factorization method to account for the complications introduced by the higher-order boundary operator and its nontrivial null space. Numerical experiments illustrate the feasibility of the approach, indicating that the framework potentially provides a practical tool for nondestructive detection of interior inhomogeneities, including damaged subvolumes.
title Recovering elastic subdomains with strain-gradient elastic interfaces from force measurements: the antiplane shear setting
topic Analysis of PDEs
Materials Science
Mathematical Physics
74G75, 74B05, 35R30
url https://arxiv.org/abs/2509.15171