Direct reconstruction of general elastic inclusions

Sarah Eberle-Blick; Henrik Garde; Nuutti Hyvönen

doi:10.48550/arXiv.2507.04831

Direct reconstruction of general elastic inclusions

Sarah Eberle-Blick
, Henrik Garde^*
, Nuutti Hyvönen

^*Corresponding author af dette arbejde

Institut for Matematik

Publikation: Working paper/Preprint › Preprint

Abstract

The inverse problem of linear elasticity is to determine the Lamé parameters, which characterize the mechanical properties of a domain, from pairs of pressure activations and the resulting displacements on its boundary. This work considers the specific problem of reconstructing inclusions that manifest themselves as deviations from the background Lamé parameters.

The monotonicity method is a direct reconstruction method that has previously been considered for domains only containing positive (or negative) inclusions with finite contrast. That is, all inclusions have previously been assumed to correspond to a finite increase (or decrease) in both Lamé parameters compared to their background values. We prove the general outer approach of the monotonicity method that simultaneously allows positive and negative inclusions, of both finite and extreme contrast; the latter refers to either infinitely stiff or perfectly elastic materials.

Originalsprog	Engelsk
Udgiver	arxiv.org
Antal sider	26
DOI	https://doi.org/10.48550/arXiv.2507.04831
Status	Udgivet - 2025

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10.48550/arXiv.2507.04831Licens: CC BY

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Complex Calderón Problem
Garde, H. (PI), Zacharopoulos, T. (Deltager) & Johansson, D. (Deltager)
01/09/2024 → 31/08/2028
Projekter: Projekt › Forskning

Citationsformater

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title = "Direct reconstruction of general elastic inclusions",

abstract = "The inverse problem of linear elasticity is to determine the Lam{\'e} parameters, which characterize the mechanical properties of a domain, from pairs of pressure activations and the resulting displacements on its boundary. This work considers the specific problem of reconstructing inclusions that manifest themselves as deviations from the background Lam{\'e} parameters. The monotonicity method is a direct reconstruction method that has previously been considered for domains only containing positive (or negative) inclusions with finite contrast. That is, all inclusions have previously been assumed to correspond to a finite increase (or decrease) in both Lam{\'e} parameters compared to their background values. We prove the general outer approach of the monotonicity method that simultaneously allows positive and negative inclusions, of both finite and extreme contrast; the latter refers to either infinitely stiff or perfectly elastic materials.",

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author = "Sarah Eberle-Blick and Henrik Garde and Nuutti Hyv{\"o}nen",

year = "2025",

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AU - Eberle-Blick, Sarah

AU - Garde, Henrik

AU - Hyvönen, Nuutti

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N2 - The inverse problem of linear elasticity is to determine the Lamé parameters, which characterize the mechanical properties of a domain, from pairs of pressure activations and the resulting displacements on its boundary. This work considers the specific problem of reconstructing inclusions that manifest themselves as deviations from the background Lamé parameters. The monotonicity method is a direct reconstruction method that has previously been considered for domains only containing positive (or negative) inclusions with finite contrast. That is, all inclusions have previously been assumed to correspond to a finite increase (or decrease) in both Lamé parameters compared to their background values. We prove the general outer approach of the monotonicity method that simultaneously allows positive and negative inclusions, of both finite and extreme contrast; the latter refers to either infinitely stiff or perfectly elastic materials.

AB - The inverse problem of linear elasticity is to determine the Lamé parameters, which characterize the mechanical properties of a domain, from pairs of pressure activations and the resulting displacements on its boundary. This work considers the specific problem of reconstructing inclusions that manifest themselves as deviations from the background Lamé parameters. The monotonicity method is a direct reconstruction method that has previously been considered for domains only containing positive (or negative) inclusions with finite contrast. That is, all inclusions have previously been assumed to correspond to a finite increase (or decrease) in both Lamé parameters compared to their background values. We prove the general outer approach of the monotonicity method that simultaneously allows positive and negative inclusions, of both finite and extreme contrast; the latter refers to either infinitely stiff or perfectly elastic materials.

KW - linear elasticity

KW - monotonicity method

KW - perfectly elastic

KW - infinitely stiff

U2 - 10.48550/arXiv.2507.04831

DO - 10.48550/arXiv.2507.04831

M3 - Preprint

BT - Direct reconstruction of general elastic inclusions

PB - arxiv.org

ER -

Direct reconstruction of general elastic inclusions

Abstract

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Complex Calderón Problem

Citationsformater