  We analyze a term penalizing surface self-penetration, as a soft constraint
for models of hyperelastic materials to approximate the Ciarlet-Ne\v{c}as
condition (almost everywhere global invertibility of deformations). For a
linear elastic energy subject to an additional local invertibility constraint,
we prove that the penalized elastic functionals converge to the original
functional subject to the Ciarlet-Ne\v{c}as condition. The approach also works
for nonlinear models of non-simple materials including a suitable higher order
term in the elastic energy, without artificial local constraints. Numerical
experiments illustrate our results for a self-contact problem in 3d.
