Third- and fourth-order elasticities of biological soft tissues

Destrade, M., Gilchrist, M.D. and Ogden, R.W. (2010) Third- and fourth-order elasticities of biological soft tissues. Journal of the Acoustical Society of America, 127(4), pp. 2103-2106. (doi: 10.1121/1.3337232)

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In the theory of weakly nonlinear elasticity, Hamilton [J. Acoust. Soc. Am. 116, 41-44 (2004)] identified W=mu I-2+(A/3)I-3+DI22 as the fourth-order expansion of the strain-energy density for incompressible isotropic solids. Subsequently, much effort focused on theoretical and experimental developments linked to this expression in order to inform the modeling of gels and soft biological tissues. However, while many soft tissues can be treated as incompressible, they are not in general isotropic, and their anisotropy is associated with the presence of oriented collagen fiber bundles. Here the expansion of W is carried up to fourth order in the case where there exists one family of parallel fibers in the tissue. The results are then applied to acoustoelasticity, with a view to determining the second- and third-order nonlinear constants by employing small-amplitude transverse waves propagating in a deformed soft tissue.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Ogden, Professor Raymond
Authors: Destrade, M., Gilchrist, M.D., and Ogden, R.W.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of the Acoustical Society of America

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