CHARACTERIZATION OF MULTI-SCALE CONSTITUTIVE MODEL OF COLLAGEN: A MOLECULAR DYNAMICS MODELING APPROACH

Abstract

Collagen is the most abundant protein in mammals and has special mechanical behavior that enables it to play an important role in the structural integrity of many tissues, e.g., skin, tendon, bone, cartilage and blood vessels. The mechanical properties of collagen are governed by hierarchical mechanisms in different length-scales from molecule to tissue level. Currently, there is no multi-scale model that can predict the mechanical properties of collagen at macroscopic length scales from the behavior of microstructural elements at smaller length scales. This dissertation aimed at developing a multi-scale model using a bottom-up approach to predict the elastic and viscoelastic behaviors of collagen at length scales spanning from nano to microscale. Creep simulations were performed using steered molecular dynamics (SMD) method on collagen molecules, cross-link, and micro-fibrils with various lengths. A micro-fibril is considered as a combination of two collagen molecules connected by a cross-link. The strain time histories for force levels in the range of 10 to 4000 pN were characterized using quasilinear viscoelastic models. These models were utilized to make a reduced model of a micro-fibril and the reduced models, in turn, were combined to make a model of a fibril up to 300 micrometers in length. The micro-fibril and fibril models were validated with available experimental measurements. Hydrogen bonds rupture and formation of collagen molecule played a central role in its viscoelastic behavior and were used to estimate the creep growth rate. The propagation of force wave in the molecule was shown to be an important factor in providing the time-dependent properties of the fibrils. This propagation was modeled with delay elements and this allowed reducing the micro-fibril model to only three degrees of freedom. In conclusion, the results confirmed that the combination of molecular dynamics simulations and viscoelastic theory could be successfully utilized to investigate the viscoelastic behavior of collagen at small scales. The model reported in this dissertation, lays the groundwork for future studies on collagen, particularly in elucidating how each particular level of hierarchy affects the overall tissue behavior.