  We present a new penalty term approximating the Ciarlet-Ne\v{c}as condition
(global invertibility of deformations) as a soft constraint for hyperelastic
materials. For non-simple materials including a suitable higher order term in
the elastic energy, we prove that the penalized functionals converge to the
original functional subject to the Ciarlet-Ne\v{c}as condition. Moreover, the
penalization can be chosen in such a way that all low energy deformations,
self-interpenetration is completely avoided even for sufficiently small finite
values of the penalization parameter. We also present numerical experiments in
2d illustrating our theoretical results.
