Uniaxial load analysis under stretch-dependent fiber remodeling applicable to collagenous tissue

This article investigates the relation between stress and deformation of a fibrous material that is subjected to a constant fiber creation rate and deformation-dependent fiber dissolution rate. Experimental studies show such behavior in certain highly collagenous tissue. The investigation focuses on two different constitutive hypotheses: (a) fibers that reassemble in an undeformed state and (b) fibers that reassemble in a pre-strained state that is equal to the strain state of the surrounding matrix. The matrix component of the material is treated as isotropic and hyperelastic, and its mechanical properties remain constant in time. Separate processes of step displacement and step load are considered. In each case, an initial state of homeostasis is disrupted by the step input. The system then evolves to a new state of homeostasis that can be predicted in advance. The approach to this new homeostasis requires the consideration of a Volterra-type integral equation.