A micromechanical model of tendon and ligament with crimped fibers

The mechanical properties of soft tissues are strongly dependent on their microstructures which evolve with aging and diseases. In this paper, a micromechanical model is presented to investigate the mechanical properties of tendons and ligaments, which are treated as planar crimped fiber-reinforced composites. The interaction among the constituents in such a composite is accounted for by utilizing the Mori-Tanaka method. Explicit analytical solutions are derived for describing the effects of microstructures on its macroscopic elastic properties, which are in good agreement with both finite element analysis and relevant experimental results. It is found that fiber waviness has a significant influence on the elastic properties of tendon and ligament. Our findings also demonstrate that planar crimp is significant to achieve the large Poisson's ratio of ligament and tendon, thereby revealing a novel structure-function mechanism. Parametric analysis further elucidates that their Poisson's ratios are also dependent on the volume fractions of crimped fibers and the elastic properties of the matrix. This work not only provides a theoretical method to predict the constitutive relation of biocomposites containing wavy fibers, but also expands our knowledge on the microstructural origin of large Poisson's ratios of soft tissues.