Stress-modulated growth

The growth and remodeling of soft tissues depend on a number of biological, chemical and mechanical factors, including the state of tension. In many cases the stress field plays such a relevant role that "stress-modulated growth" has become a very topical subject. Recent theoretical achievements suggest that, irrespective of the specific biological material at hand, a component of the stress-growth coupling is tissue-independent and reads as an Eshelby-like tensor. In this paper we investigate the mathematical properties and the qualitative behavior predicted by equations that specialize that model under few simple assumptions. Constitutive equations that satisfy a suitable dissipation principle are compared with heuristic ones that fit well the experimental data. Numerical simulations of the growth of a symmetric annulus are discussed and compared with the predicted qualitative behavior.