A constitutive relation of hierarchical composite fibrous materials

Biomaterials are organized in a hierarchical structure with heterogeneity as to optimize their mechanical properties. For example, collagen fibrous biomaterials (e.g. tendon and ligament) are structured in hierarchical bundle and consist of various types of fibers. In this paper, through establishing a constitutive relation, the influence of hierarchy on the mechanical properties of composite fibrous materials is studied. In view of the hierarchical structure, a composite fibrous bundle based on equal load sharing model is firstly formed with various types of fiber strengths satisfying different Weibull distribution, and then a constitutive relation of hierarchical composite fibrous materials is obtained. Following, this constitutive relation is applied to evaluate the mechanical properties of composite fibrous materials, and the influences of hierarchical levels and modes are examined. The results show that, for composite fibrous bundle, the mechanical properties such as strength, toughness and rigidity can be improved by one mode simultaneously, which depends on hierarchical case; namely, the natural biomaterials are often composite while hierarchy.