Summary: Stress­modulated remodelling
of a non­homogeneous body
D. Ambrosi, A. Guillou,
Dipartimento di Matematica, Politecnico di Torino,
corso Duca degli Abruzzi 24, 10129 Torino, Italy.
E.S. Di Martino,
Institute for Complex Engineered Systems, Cardiovascular Biomechanics Lab,
Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA 15213, USA.
December 19, 2006
Abstract
Many soft tissues, and arteries in primis, exhibit residual stress after unloading, a
characteristic related to the ability to self­organize their own constituents (cells and ex-
tracellular matrix proteins). This behavior can be theoretically predicted in a continuum
mechanics framework assuming that the body self­remodels 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 pa-
per we illustrate a mathematical framework and we perform numerical simulations for the
remodelling of a two dimensional (axisymmetric) nonlinear elastic cylinder. In particular,
we address the stress­modulated remodelling of the cylinder wall when local variations
in the mechanical properties of the material occur. Our main result is that, as in one

Source: Ambrosi, Davide - Dipartimento di Matematica, Politecnico di Torino

Collections: Mathematics