Invariant Formulation for Dispersed Transverse Isotropy in Tissues of the Aortic Outflow Tract
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We have proposed an efficient, invariant-based alternative to structural constitutive equations that accounts for statistical dispersion of fibers. In contrast to existing models, our new invariant theory easily handles a 3D fiber population with a single mean preferred direction. The invariant theory is based on a novel closed-form 'splay invariant' that requires a single parameter in the 2D case, and two parameters in the 3D case. The proposed model is polyconvex, and fits biaxial data for aortic valve tissue better than existing aortic-valve models Billiar and Sacks (2000). A modification in the fiber stress-strain law requires no re-formulation of the constitutive tangent matrix, making the model flexible for different types of soft tissues. Most importantly, the model is computationally expedient in a finite element analysis. © 2006 Springer-Verlag Berlin Heidelberg.
author list (cited authors)
Einstein, D. R., Freed, A. D., & Vesely, I.
Mechanics of Biological Tissue