Toward a kinetic theory of connective tissue micromechanics

Abstract

The aim of this study is to develop unifying concepts at the microstructural level to account for macroscopic connective tissue dynamics. We establish the hypothesis that rate-dependent and rate-independent dissipative stresses arise in the interaction among fibers in the connective tissue matrix. A quantitative theoretical analysis is specified in terms of geometry and material properties of connective tissue fibers and surrounding constituents. The analysis leads to the notion of slip and diffusion boundary layers, which become unifying concepts in understanding mechanisms that underlie connective tissue elasticity and energy dissipation during various types of loading. The complex three-dimensional fiber network is simplified to the interaction of two ideally elastic fibers that dissipate energy on slipping interface surfaces. The effects of such interactions are assumed to be expressed in the aggregate matrix. Special solutions of the field equations are obtained analytically, whereas the general solution of the model field equations is obtained numerically. The solutions lead to predictions of tissue behavior that are qualitatively, if not quantitatively, consistent with reports of a variety of dynamic moduli, their dependencies on the rate and amplitude of load application, and some features associated with preconditioning.