Mechanical behavior of crimped collagen fibers under uniaxial tension

Knowledge of the highly nonlinear behavior of crimped collagen fibers has a great importance for medical diagnosis. This behavior can be associated with the gradual straightening of fibers and the amount of fibers that bears load. To model this phenomenon, we propose an explicit scalar potential, based on the Weibull distribu-tion, in terms of the fiber bundle strength. The total strain is given in terms of the stress and is defined by sum of the strain of crimped fibers, arising from the proposed potential, and the strain of completely straightened fibers by using the Hookean model. Besides three physically meaningful parameters, further two new parameters that have intuitive interpretations were considered. The proposed model was compared with the Freed-Rajagopal model and the Holzapfel-Gasser-Ogden model for verifying its ability to fit the measured data from bovine tendon samples under uniaxial tension. Our model better described the highly nonlinear behavior of the tendon. Experimental data from literature were also used for validation of the parameters of the proposed model. The estimated parameters were consistent with those found in the literature. The effectiveness of the proposed model and Freed-Rajagopal model in describing the stress-strain curve with different initial range of strain with the zero-stress state was also investigated. Unlike the Freed-Rajagopal model, the proposed model fits well in all cases, including those with wide range of strain.

Automated summary

Understanding the highly nonlinear behavior of crimped collagen fibers is crucial for medical diagnosis. A proposed model, based on a explicit scalar potential and Weibull distribution, proved to better describe tendon behavior compared to existing models. Experimental data validation and investigation of stress-strain curves further supported the effectiveness of the proposed model.