Bibliography

(eng): We present a new penalty term approximating the Ciarlet-Nečas 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-Nečas condition. Moreover, the penalization can be chosen in such a way that for all low energy deformations, self-interpenetration is completely avoided already at all sufficiently small finite values of the penalization parameter. We also present numerical experiments in 2d illustrating our theoretical results.