  This paper introduces a sharp-interface approach to simulating
fluid-structure interaction involving flexible bodies described by general
nonlinear material models and across a broad range of mass density ratios. This
new flexible-body immersed Lagrangian-Eulerian (ILE) approach incorporates the
geometrical and domain solution flexibility of the immersed boundary (IB)
method with an accuracy comparable to body-fitted approaches that sharply
resolve flows and stresses up to the fluid-structure interface. Unlike many IB
methods, our ILE formulation uses distinct momentum equations for the fluid and
solid subregions with a Dirichlet-Neumann coupling strategy that connects fluid
and solid subproblems through simple interface conditions. We use a penalty
method involving two representations of the fluid-structure interface. These
two representations are connected by approximate Lagrange multiplier forces
that impose kinematic interface conditions. This approach also enables the use
of multi-rate time stepping, which allows us to take different time step sizes
for the fluid and structure subproblems. Our fluid solver relies on an immersed
interface method for discrete surfaces to impose stress jump conditions along
complex interfaces. The dynamics of the volumetric structural mesh are
determined using a standard finite element approach to large-deformation
nonlinear elasticity via a nearly incompressible solid mechanics formulation.
This formulation also readily accommodates compressible structures for cases in
which part of the solid boundary does not contact the incompressible fluid.
Comparisons are made with computational and experimental benchmarks. We also
demonstrate the capabilities of this methodology by applying it to model the
transport and capture of a cylindrical blood clot in an inferior vena cava
filter.
