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

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.

The resulting characterization relies on pairs of sampling points rather than a single-point test used in classical factorization methods.

After fixing an interior reference point, the reconstruction procedure reduces to a single-point sampling algorithm.

Focusing on the latter stage, numerical experiments illustrate the feasibility of the proposed reconstruction method and suggest that the framework has potential for the nondestructive detection of interior inhomogeneities, including damaged subvolumes.