Like other gravitational effects, locally, spatial expansion would manifest as a pseudo-force, but be too weak to overcome the nuclear and electromagnetic forces that keep matter bound.
However, Friedmann cosmology is only a large-scale approximation. A more realistic model is swiss-cheese cosmology, which comes with a different metric within the 'holes', and spatial expansion might indeed not act on galactic scales (though I would image it to have an indirect effect as boundary conditions at the edge of the hole have to be matched; I'm no expert on this part of the story, though).
Like other gravitational effects, locally, spatial expansion would manifest as a pseudo-force, but be too weak to overcome the nuclear and electromagnetic forces that keep matter bound.
However, Friedmann cosmology is only a large-scale approximation. A more realistic model is swiss-cheese cosmology, which comes with a different metric within the 'holes', and spatial expansion might indeed not act on galactic scales (though I would image it to have an indirect effect as boundary conditions at the edge of the hole have to be matched; I'm no expert on this part of the story, though).