Modulus of elasticity of randomly and aligned polymeric scaffolds with fiber size dependency

The stiffness of a nano-fibrous scaffold is generally enhanced due to the size-dependency of the thin nanofibers contained in the scaffold. We proposed a model that incorporates size-dependency of single nanofibers to predict the scaffold effective modulus, in which the fibers' random or orientation distribution are considered. In the model the fiber segments between rigid fiber-fiber bonds can be stretching, shearing and bending. Using deformation energy equilibrium between sum of individual fibers and the plate of nano-fibrous scaffold, the scaffold effective modulus was derived explicitly. The model was verified via finite element analysis (FEA) and published experimental results. The parametric studies revealed that the fiber diameter is the dominant parameter to stiffen the scaffold beyond the fiber density and fiber aspect ratio when the fiber diameter is reduced below the onset value of size-dependencies. As a result, the scaffold stiffness can maintain its higher value and lower decrease rate because of the size-dependency with a decreasing diameter of the nanofiber as a result of biodegradation. This inspires the idea of selecting nanofibers near the onset value of size-dependency to obtain a controlled tuning of the scaffold stiffness in the design of novel nano-fibrous scaffolds.