Journal
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 380, Issue 2234, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rsta.2021.0321
Keywords
nonlinear elasticity; strain-energy density functions; weakly nonlinear theory; shear modulus; elastography
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Funding
- GNFM of Italian INDAM
- PRIN 2017 research project [2017KL4EF3]
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Elastographic investigations can detect benign and malignant lesions in tissues or organs by identifying pathological regions through alterations in stiffness. This paper demonstrates that the estimation of shear modulus can be significantly improved using the fourth-order weakly nonlinear theory of elasticity, providing more precise assessment of stiffness. The article also discusses why this theory is more reliable than the fully nonlinear theory of elasticity.
Benign and malignant lesions in tissues or organs can be detected by elastographic investigations in which pathological regions are spotted from local alterations of the stiffness. As is known, the shear modulus provides a measure of the stiffness of an elastic material. Based on the classical theory of linear elasticity, an elastogram yields estimations of the linear shear modulus from measurements of the speed of small-amplitude transverse waves propagating in the medium tested. In this paper, we show that the estimation of the shear modulus can be improved significantly by employing the fourth-order weakly nonlinear theory of elasticity (FOE), and indicate how the stiffness can be assessed more precisely with the use of FOE. We discuss also why FOE provides more reliable results than the fully nonlinear theory of elasticity.This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.
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