Third and fourth-order elasticity of biological soft tissues
Destrade, Michel ; Gilchrist, Michael D.
Destrade, Michel
Gilchrist, Michael D.
Loading...
Repository DOI
Publication Date
2010-01-24
Type
Article
Downloads
Citation
Destrade, M., Gilchrist, M. D., & Ogden, R. W. (2013). Third and fourth-order elasticity of biological soft tissues. Journal of the Acoustical Society of America, 127.
Abstract
In the theory of weakly nonlinear elasticity, Hamilton et al. [J. Acoust. Soc. Am. 116, 41-44 (2004)] identified W = -I2+(A/3)I3+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.
Funder
Publisher
Acoustical Society of America
Publisher DOI
Rights
Attribution-NonCommercial-NoDerivs 3.0 Ireland