Development of a hypoelastic model for individual collagen fibrils informed by experiments

Abstract

Collagens are the primary constituents within biological tissues providing structural integrity. In this context it is an open quest to describe the biomechanical properties of collagen fibrils by a constitutive model. Here, hypoelastic models offer advantages compared to hyperelastic models, as they permit non-affine transformation and inherent rate-dependence. In this study, a hypoelastic model is built within the framework of continuum theory based on a previous experimental study of atomic microscopic force (AFM) tensile tests on individual colla-gen fibrils in low strain regimes. The resulting hypoelasticity tensor is defined by the Cauchy stress-rate and strain-rate field, which can be directly derived from the experimental data. Cur-rently this research focuses on the analysis of the measured displacement rate and calculation of the one-dimensional extensional stiffness. Results show that measured displacement rates of the collagen fibrils deviate from the displace-ment rates set in the experiment, being up to 1.72-fold higher. Despite the low strain, nonlinear extensional stiffness of collagen fibrils is still observed. The next steps are the estimation of the three-dimensional hypoelasticity tensor further with the inclusion of viscoelasticity and micro-structure.