A constitutive relation for the tissue composed of type-I collagen fibers under uniaxial tension

Mechanical tests for various collagen tissues showed that the stress-strain curves are composed of two regimes with different deformation mechanisms. In this paper, the constitutive relations are first studied separately for the two regimes and then merged together. For the unfurling regime, a phenomenological power-law relation is utilized to characterize the stress-strain curve, and, for the stretching regime which is modeled as a fiber bundle material, a nonlinear constitutive relation is proposed based on the Weibull distribution and Daniels' fiber bundle theory. A technique is suggested to continuously merge the two relations for the two regimes of collagen tissues. A strategy is finally devised to quantitatively determine the critical strain for dividing the two regimes and to identify the constitutive parameters for experimental curves. The constitutive relation is first validated by comparing the identified parameters with the references, and then applied to predict the experimental stress-strain curves of collagen tissues. The present work shows that the critical strain plays an essential role in establishing the constitutive relation if experimental data are adopted.