An engineering, multiscale constitutive model for fiber-forming collagen in tension

This work proposes a nonlinear constitutive model for a single collagen fiber. Fiber-forming collagen can exhibit different hierarchies of basic units, called fascicles, bundles, fibrils, microfibrils, and so forth, down to the molecular (tropocollagen) level. Exploiting the fact that at each hierarchy level the microstructure can be seen, at least approximately, as that of a wavy, or crimped, extensible cable, the proposed stress-strain model considers a given number of levels, each of which contributes to the overall mechanical behavior according to its own geometrical features (crimp, or waviness), as well as to the basic mechanical properties of the tropocollagen. The crimp features at all levels are assumed to be random variables, whose statistical integration furnishes a stress-strain curve for a collagen fiber. The soundness of this model-the first, to the Authors' knowledge, to treat a single collagen fiber as a microstructured nonlinear structural element-is checked by its application to collagen fibers for which experimental results are available: rat tail tendon, periodontal ligament, and engineered ones. Here, no attempt is made to obtain a stress-strain law for generic collagenous tissues, which exhibit specific features, often much more complex than those of a single fiber. However, it is trivial to observe that the availability of a sound, microstructurally based constitutive law for a single collagen fiber (but applicable at any sub-level, or to any other material with a similar microstructure) is essential for assembling complex constitutive models for any collagenous fibrous tissue.