Surface penalization of self-interpenetration in linear and nonlinear elasticity
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We analyze a term penalizing surface self-penetration, as a soft constraint for models of hyperelastic materials to approximate the Ciarlet-Nečas 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-Nečas 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.
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