  We present a loosely-coupled partitioned scheme for a benchmark problem in
fluid-composite structure interaction. The benchmark problem proposed here
consists of an incompressible, viscous fluid interacting with a composite
structure that consists of two layers: a thin elastic layer which is in contact
with the fluid, and a thick elastic layer which sits on top of the thin layer.
The motivation comes from fluid-structure interaction (FSI) in hemodyam- ics.
The equations of linear elasticity are used to model the thick structural
layer, while the Koiter member/shell equations are used to model the thin
structural layer which serves as fluid-structure interface with mass. An effi-
cient, modular, operator-splitting scheme is proposed to simulate solutions to
the coupled, nonlinear FSI problem. The operator splitting scheme sepa- rates
the elastodynamics structure problem, from a fluid problem in which the thin
structure inertia is included as a Robin-type boundary condition to achieve
unconditional stability, without requiring any sub-iterations within
time-steps. An energy estimate associated with unconditional stability is
derived for the fully nonlinear FSI problem defined on moving domains. Two
instructive numerical examples are presented to test the performance of the
scheme, where it is shown numerically, that the scheme is at least first-order
accurate in time. The second example reveals a new phenomenon in FSI problems:
the presence of a thin fluid-structure interface with mass regularizes
solutions to the full FSI problem.
