Reconstruction of the residual stresses in a hyperelastic body using ultrasound techniques

Sunnie Joshi, Jay R. Walton

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


This paper focuses on a novel approach for characterizing the residual stress field in soft tissue using ultrasound interrogation. A nonlinear inverse spectral technique is developed that makes fundamental use of the finite strain nonlinear response of the material to a quasi-static loading. The soft tissue is modeled as a nonlinear, prestressed and residually stressed, isotropic, slightly compressible elastic body with a rectangular geometry. A boundary value problem is formulated for the residually stressed and prestressed soft tissue, the boundary of which is subjected to a quasi-static pressure, and then an idealized model for the ultrasound interrogation is constructed by superimposing small amplitude time harmonic infinitesimal vibrations on static finite deformation via an asymptotic construction. The model is studied, through a semi-inverse approach, for a specific class of deformations that leads to a system of second order differential equations with homogeneous boundary conditions of Sturm-Liouville type. By making use of the classical theory of inverse Sturm-Liouville problems, and root finding and optimization techniques, several inverse spectral algorithms are developed to approximate the residual stress distribution in the body, given the first few eigenfrequencies of several induced static pressures. © 2013 Elsevier Ltd. All rights reserved.
Original languageEnglish (US)
Pages (from-to)46-72
Number of pages27
JournalInternational Journal of Engineering Science
StatePublished - Sep 2013
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: This work is based in part on support provided by Award No. KUS-C1-016-04 from King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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