Finite strain response of crimped fibers under uniaxial traction: An analytical approach applied to collagen

Composite materials reinforced by crimped fibers intervene in a number of advanced structural applications. Accordingly, constitutive equations describing their anisotropic behavior and explicitly accounting for fiber properties are needed for modeling and design purposes. To this aim, the finite strain response of crimped beams under uniaxial traction is herein addressed by obtaining analytical relationships based on the Principle of Virtual Works. The model is applied to collagen fibers in soft biological tissues, coupling geometric nonlinearities related to fiber crimp with material nonlinearities due to nanoscale mechanisms.Several numerical applications are presented, addressing the influence of geometric and material features. Available experimental data for tendons are reproduced, integrating the proposed approach within an optimization procedure for data fitting. The obtained results highlight the effectiveness of the proposed approach in correlating fibers structure with composite material mechanics.