Time-evolving collagen-like structural fibers in soft tissues: biaxial loading and spherical inflation

Abstract

This work considers a previously developed constitutive theory for the time dependent mechanical response of fibrous soft tissue resulting from the time dependent remodeling of a collagen fiber network that is embedded in a ground substance matrix. The matrix is taken to be an incompressible nonlinear elastic solid. The remodeling process consists of the continual dissolution of existing fibers and the creation of new fibers. Motivated by experimental reports on the enzyme degradation of collagen fibers, the remodeling is governed by first order chemical kinetics such that the dissolution rate is dependent upon the fiber stretch. The resulting time dependent mechanical response is sensitive to the natural configuration of the fibers when they are created, and different assumptions on the nature of the fiber's stress free state are considered here. The response under biaxial loading, a type of loading that has particular significance for the characterization of biological materials, is studied. The inflation of a spherical membrane is then analyzed in terms of the equal biaxial stretch that occurs in the membrane approximation. Different assumptions on the natural configuration of the fibers, combined with their time dependent dissolution and reforming, are shown to emulate alternative forms of creep and relaxation response. This formal similarity to viscoelastic phenomena occurs even though the underlying mechanisms are fundamentally different from the mechanism of macromolecular reconfiguration that one typically associates with viscoelastic response.