Invariant Theory for Dispersed Transverse Isotropy: An Efficient Means for Modeling Fiber Splay

Microstructual studies suggest that in some tissues, collagen fibers are approximately normally distributed about a mean preferred fiber direction. Structural constitutive equations that account for this dispersion of fibers have been shown to capture the mechanical complexity of these tissues quite well. However, such descriptions are computationally cumbersome for two-dimensional fiber distributions, let alone for fully three dimensional fiber populations. We have developed a new constitutive law for such tissues, based on a novel invariant theory for dispersed transverse isotropy. The model is polyconvex and fits biaxial data for aortic valve tissue as accurately as the standard structural model. Modification of 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.