Fluid–Structure Interactions and Porous Media

Isaac Newton and Robert Hooke, by initiating understanding of the behavior of fluids and solids, introduced the laws that bear their names. In classical mechanics, boundary conditions are added to the law of motion in the form of partial derivatives in each of the three-dimensional space directions. The formulation of the velocity chosen to represent the behavior of solids subjected to mechanical stresses or fluid–structure coupling makes it possible to represent stresses and displacements as large deformations. The first models in the field of fluid–structure interaction were carried out from the Navier–Stokes equations modified in order to integrate the notion of shear stress and accumulation of these stresses. The presentation of the extension of Poiseuille's law to a channel of variable cross-section is based on the direction alone and an integration of viscous stresses thereon.