Mechanics of composites with two families of finitely extensible fibers undergoing large deformations

Motivated by experimental measurements of the uniaxial response of collagen fibers, a new strain energy-density function for a solid which is finitely extensible along a preferred direction is proposed. Next, by application of a homogenization technique, the macroscopic strain energy-density function of composites with one and two families of fibers of this material embedded in a neo-Hookean matrix are determined. The resulting explicit expressions for the macroscopic strain energy-density functions are given in terms of the behaviors of the individual phases and their volume fractions. The responses of a few specific composites are investigated, revealing the lock-up surfaces of these composites. Finally, we examine the ability of the macroscopic model to capture experimentally measured stress-strain curves for the medial layer of a human abdominal aorta.