On mechanically induced degradation of fiber-reinforced hyperelastic materials

A finite strain model for the mechanical degradation of composite materials with multiple families of fine reinforcing fibers is developed and studied. At any instant of time the matrix material may or may not be degrading with all, some, or none of the interpenetrating fibers also undergoing degradation. This multi-component description of damage is governed by coupled differential equations when more than one damage mechanism is active. These differential equations, and the threshold values of the strain invariants that activate the damage process, emerge naturally from a general framework that describes the response of dissipative systems under a maximum rate of dissipation postulate. In this context we then study uniaxial loadings when either a constant stretch or a constant force is suddenly applied to the composite. It is found that the initial type of degradation (e.g. degrading fibers in a non-degrading matrix) may transition to an alternative type of degradation (e.g. the degradation of all constituents) at some finite time into the process. A rich variety of material and load-dependent transition possibilities are systematically uncovered using a combination of asymptotic and numerical techniques. The resulting macroscopic behavior as the material weakens involves relaxation and creep phenomena that are formally similar to viscoelastic material behavior in solids even though the underlying processes are significantly different. Describing implants and tissue constructs containing biodegradable polymers is one possible area of application.