The effect of fiber plasticity on domain formation in soft biological composites -- Part II: An imperfection analysis

The main objective of this work is to numerically investigate the effect of geometric imperfections on the macroscopic response and domain formation in soft biological composites that exhibit plasticity in the stiff (fiber) phase.This work builds on the corresponding bifurcation analysis in Part I of this study for simple laminates with perfectly flat layers under plane strain, nonmonotonic loading conditions, aligned with the layer direction. The post-bifurcation solution obtained in Part I for these materials corresponds physically to the formation of twin lamellar domains perpendicular to the loading axis, which is consistent with the chevron like deformation patterns that develop in tendons under cyclic loading. As biological materials are highly imperfect, and specifically tendons exhibit a high degree of so called crimp in the collagen fibers, in this study the effect of imperfections to the response is explored. For all composites with small initial imperfections that have been considered, the results of this work have been found to be in complete agreement with the corresponding analytical results of Part I, and, domains have been found to emerge at a macroscopically compressive state. However, as the imperfection amplitude is increased and becomes of the order to the layer width, or greater, domains begin to develop at macroscopically tensile stresses, which is in agreement with the fact that the loading of soft biological materials such as tendons and ligaments is tensile in nature. Thus, the findings of this work suggest strongly that plasticity and geometric imperfections of collagen fibers may play a key role on the onset and evolution of domains in actual soft biological composites.