A structural theory for the homogeneous biaxial stress-strain relationships in flat collagenous tissues.

Abstract The stress-strain relations of flat collagenous tissues under homogeneous biaxial deformations are analyzed in terms of the tissues' constituents structure and their mechanical properties. It is assumed that the overall tissue response is the sum of contributions of the collagen and elastin fibers. The collagen fibers are undulated and slack, the elastin is prestretched. Upon deformation the fibers rotate and stretch. The stress components are determined by summing up the contributions of all the fibers passing through the unit area associated with each stress component. The resulting behavior of the tissue is governed by material constants and material distribution functions which are associated with the angular and geometrical nonuniformities in the fibers. It is shown that the nonuniformity in the angular distribution of the fibers accounts for the observed anisotropic behavior of the tissue, and that the nonuniformity in the geometrical structure of the fibers accounts for the nonlinear stress-strain relations. It is further shown that the material constants and functions of a given tissue can be determined by analyzing the data of specific experimental procedure.