  We present a consistent approach that allows to solve challenging general
nonlinear fluid-structure-contact interaction (FSCI) problems. The underlying
continuous formulation includes both "no-slip" fluid-structure interaction as
well as frictionless contact between multiple elastic bodies. The respective
interface conditions in normal and tangential orientation and especially the
role of the fluid stress within the region of closed contact are discussed for
the general problem of FSCI. To ensure continuity of the tangential constraints
from no-slip to frictionless contact, a transition is enabled by using the
general Navier condition with varying slip length. Moreover, the fluid stress
in the contact zone is obtained by an extension approach as it plays a crucial
role for the lift-off behavior of contacting bodies. With the given continuity
of the spatially continuous formulation, continuity of the discrete problem
(which is essential for the convergence of Newton's method) is reached
naturally. As topological changes of the fluid domain are an inherent challenge
in FSCI configurations, a non-interface fitted Cut Finite Element Method
(CutFEM) is applied to discretize the fluid domain. All interface conditions,
that is the `no-slip' FSI, the general Navier condition, and frictionless
contact are incorporated using Nitsche based methods, thus retaining the
continuity and consistency of the model. To account for the strong interaction
between the fluid and solid discretization, the overall coupled discrete system
is solved monolithically. Numerical examples of varying complexity are
presented to corroborate the developments.
