Elastica-based strain energy functions for soft biological tissue

Continuum strain energy density functions are developed for soft biological tissues that possess slender, fibrillar components. The treatment is based on the model of an elastica, which is our fine scale model, and is homogenized in a simple fashion to obtain a continuum strain energy density function. Notably, we avoid solving the exact, fourth-order, non-linear, partial differential equation for deformation of the elastica by resorting to other assumptions, kinematic and energetic, on the response of individual, elastica-like fibrils. The formulation, discussion of responses of different models and comparison with experiment are presented.