Modeling the Anisotropic Finite-Deformation Viscoelastic Behavior of Soft Fiber-Reinforced Tissues

This paper presents a constitutive model for the anisotropic, finite-deformation viscoelastic behavior of soft fiber-reinforced tissues. Soft fiber-reinforced tissues, such as the cornea, tendons, and blood vessels, have a unique combination of mechanical properties that enables them to perform important structural, protective, and energy-absorbing functions. Because of their fiber-reinforced microstructure, these tissues are extraordinarily stiff and strong for their weight. Many are also flexible and tough. The toughness of these tissues arises from the ability of both the soft fiber and matrix phases to dissipate energy through large viscoelastic deformations. The viscoelastic behavior of the matrix of soft tissues can arise from fluid flow through a swollen polymer network and/or the diffusive motion of polymer segments within the network. The time-dependent behavior of the fiber reinforcements, which themselves can be composite structures, stems from the viscoelastic nature of the fiber material and/or the dissipative mechanisms of the fiber/matrix interface. To model the distinct time-dependent behavior of both fiber and matrix constituents, the tissue is represented as a continuum mixture consisting of a variety of fiber families embedded in an isotropic matrix. Both phases are required to deform with the continuum deformation gradient. However, the model attributes a different viscous stretch measure and free energy density to the matrix and fiber phases. Separate viscous flow rules are specified for the matrix phase and the individual fiber families. The flow rules for the fiber families are combined to give an anisotropic effective viscous flow rule for the fiber phase. An attractive feature of model is that key parameters can be related to the material properties (i.e., moduli, viscosities, volume fraction) of the fiber and matrix phases. Also, the anisotropy exhibited by both the elastic and viscous response of the composite arises directly from the fiber arrangement.