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Mathematics and Mechanics of Solids
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Stress-Modulated Growth

D. Ambrosi

Dipartimento di Matematica, Politecnico di Torino, corso Duca degli Abruzzi 24, 10129 Torino, Italy

F. Guana

Dipartimento di Matematica, Università di Torino, via Carlo Alberto 10, 10123 Torino, Italy

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.

Key Words: growth • soft biological tissues • elasticity • Eshelby tensor

This version was published on June 1, 2007

Mathematics and Mechanics of Solids, Vol. 12, No. 3, 319-342 (2007)
DOI: 10.1177/1081286505059739
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