Work

Reconstruction of shear modulus inclusions in elastostatics via divergence-free localization

Year: 2026

Type: preprint

Abstract: We formulate an improved version of the monotonicity method for shape reconstruction in the inverse problem of linear elastostatics. We show that this method can reconstruct inclusions in the second Lamé parameter, i.e., the shear modulus, independently of inhomogeneities in the first Lamé parameter. This improves on earlier methods that only recover inclusions in the bulk modulus under certain assumptions on the local interplay between the Lamé parameters. Our proofs are based on linearization and divergence-free localization of energy using harmonic vector fields.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.12141

Authors: Garde, Henrik, Hyvönen, Nuutti, Pohjola, Valter

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Emil Aaltosen Säätiö

OpenAlex ID: W7202373483

Cites: 1

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Related to: 10