Global injectivity in second-gradient Nonlinear Elasticity and its approximation with penalty terms
Provides a theoretically justified soft constraint for global injectivity in hyperelasticity, relevant for computational mechanics and material modeling.
The authors propose a penalty term to enforce global invertibility (Ciarlet-Nečas condition) in second-gradient nonlinear elasticity, proving convergence of penalized functionals to the constrained original and showing that self-interpenetration is avoided for small penalty parameters. Numerical 2D experiments confirm the theory.
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 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.