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

Abstract: 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.