Chemomechanics and homeostasis in active strain stabilized hyperelastic fibrous microstructures

• Time dependence of continuously oriented fiber distribution.
• A theory for chemically and mechanically induced orientation changes.
• Homeostatic orientation—creation and dissolution under constant strain.
• Relating transient orientation change to homeostatic orientation.

A constitutive theory is presented for composite materials with a time dependent fiber morphology that is due to mechanical–chemical interaction. The central modeling concept is that the density of fibers at the current time t associated with a particular direction is the result of a process of creation and dissolution of fibers at all previous times. The theory is applied to the specific example of strain dependent enzyme degradation of collagen fiber reinforced materials that has been reported in a recent experimental study. A specific set of modeling assumptions is introduced and an expression is developed for the time dependent distribution density. A special result is developed that relates it to a homeostatic fiber density that occurs when the creation and dissolution processes are in balance for a finite strain that does not vary with time.