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We present a variational formulation of the immersed finite element method,which allows incompressible Newtonian fluids to interact with a general hyperelastic solid: we allow(i)the mass density to be different in the solid and the fluid,(Ⅱ)the solid to be either viscoelastic of differential type or purely elastic,and(Ⅲ)the solid to be either compressible or incompressible.