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arXiv · 2608.12141

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

Henrik Garde·Nuutti Hyvönen·Valter Pohjola
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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.

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Henrik Garde, Nuutti Hyvönen, Valter Pohjola. 2026-08-23. Reconstruction of shear modulus inclusions in elastostatics via divergence-free localization. https://arxiv.org/abs/2608.12141

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