Linearization of a coupled system of nonlinear elasticity and fluid

Lorena Bociu (1) , Jean-Paul Zolesio (2)

1 INLN - Institut Non Linéaire de Nice Sophia-Antipolis
2 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE

We model the coupled system formed by an incompressible, irrotational fluid and a nonlinear elastic body. We work with large displacement, small deformation elasticity (or St Venant elasticity), which makes the problem very interesting from the physical point of view. The elastic body is three-dimensional $\Omega \in \mathbb{R}^3$, and thus it can not be reduced to its boundary $\Gamma$ (like in the case of a membrane or a shell). In this paper, we study the static problem, which contrary to common belief, it is more subtle than the dynamical one (since in real life, evolution is more plausible than equilibrium).

Mots clés: nonlinear elasticity; Navier-Stokes; linearization; coupled system

Domaines: Modélisation et simulation

Lorena Bociu, Jean-Paul Zolesio. Linearization of a coupled system of nonlinear elasticity and fluid. [Research Report] Inria. 2009. ⟨inria-00442954⟩