Stress-modulated remodeling of a non-homogeneous body

Many soft tissues, and arteries in primis, exhibit residual stress after unloading, a characteristic related to the ability to self-organize their own constituents (cells and extracellular matrix proteins). This behavior can be theoretically predicted in a continuum mechanics framework assuming that the body self-remodels toward a homeostatic stress state. Open questions concern the characteristics of a stationary grown state, as dictated by the mechanical properties of the material and by the specific external load. In this paper, we illustrate a mathematical framework and we perform numerical simulations for the remodeling of a two-dimensional (axisymmetric) nonlinear elastic cylinder. In particular, we address the stress-modulated remodeling of the cylinder wall when local variations in the mechanical properties of the material occur. Our main result is that, as in one spatial dimension, the tendency of the system to homeostasis generates, thanks to the remodeling process, a residual stress that homogenizes the tension in the body under load. Possible physiological implications of this result are discussed in the final section.