  This paper deals with the numerical modelling of the interaction between a
fluid and an incompressible solid (Neo Hookean) in small perturbations with the
lattice Boltzmann method (LBM). In order to use a monolithic formulation and to
solve the whole problem with the lattice Boltzmann method, an Eulerian approach
is employed for the solid medium. The initial problem is thus transformed into
a diphasic problem and a unique LBM solver is used for both phases (fluid and
solid). With this approach, the force at the fluid-solid interface does not
need to be explicitly computed. It is intrinsic to the method. This new method
approach is validated with three academic cases: the deformation of a solid at
the bottom of a lid driven cavity, with steady and unsteady boundary conditions
at the top wall of the cavity and the deformation and motion of a disk in a lid
driven cavity.
