Pseudo-hyperelastic model of tendon hysteresis from adaptive recruitment of collagen type I fibrils

Understanding the functional relationship between the viscoelasticity and the morphology of soft collagenous tissues is fundamental for many applications in bioengineering science. This work presents a pseudo-hyperelastic constitutive theory aiming at describing the time-dependant hysteretic response of tendons subjected to uniaxial tensile loads. A macroscopic tendon is modeled as a composite homogeneous tissue with the anisotropic reinforcement of collagen type I fibrils. The tissue microstructure is considered as an adaptive network of fibrillar units connected in temporary junctions. The processes of breakage and reformation of active fibrils are thermally activated, and are occurring at random times. An internal softening variable and a dissipation energy function account for the adaptive arrangement of the fibrillar network in the pseudo-hyperelastic model. Cyclic uniaxial tensile tests have been performed in vitro on porcine flexor digital tendons. The theoretical predictions fit accurately the experimental stress–strain data both for the loading and the unloading processes. The hysteresis behavior reflects the improvement in the efficiency and performance of the motion of the muscle-tendon unit at high strain rates. The results of the model demonstrate the microstructural importance of proteoglycans in determining the functional viscoelastic adaptability of the macroscopic tendon.