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Mathematics and Mechanics of Solids
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Article

Stress-Modulated Growth

D. Ambrosi1* Francesca Guana2

1 Dipartimento di Matematica, Politecnico di Torino, corso Duca degli Abruzzi 24, 10129 Torino, Italy
2 Dipartimento di Matematica, Università di Torino, via Carlo Alberto 10, 10123 Torino, Italy

* To whom correspondence should be addressed.


  Abstract
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

First published on November 23, 2005, doi:10.1177/1081286505059739

Mathematics and Mechanics of Solids 2007;12:319.

A more recent version of this article appeared on June 1, 2007

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