  We prove that that for nonlinear elastic energies with strong enough
energetic control of the outer distortion of admissible deformations, almost
everywhere global invertibility as constraint can be obtained in the
$\Gamma$-limit of the elastic energy with an added nonlocal self-repulsion term
with asymptocially vanishing coefficient. The self-repulsion term considered
here formally coincides with a Sobolev-Slobodecki\u{i} seminorm of the inverse
deformation. Variants near the boundary or on the surface of the domain are
also studied.
