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The model treats the fluid\u2013solid interaction problem in a monolithic way, where the governing equations for both sub-domains are solved on a single moving grid taking advantage of an arbitrary Lagrangian\/Eulerian framework (ALE). The unified implementation of the governing equations for both sub-domains is developed, where these are distinguished only in terms of the mesh-moving strategy and the constitutive equation coefficients. The unified formulation is derived considering a Newtonian incompressible fluid and a hypoelastic solid. Hypoelastic constitutive law is based on the strain rate and thus naturally facilitates employing velocity as a kinematic variable in the solid. Unifying the form of the governing equations and defining a semi-Lagrangian interface mesh-motion algorithm, one obtains the coupled problem formulated in terms of a unique kinematic variable. 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