线性和非线性弹性中自相交的表面惩罚
Surface penalization of self-interpenetration in linear and nonlinear elasticity
AI总结：
本文分析了表面自相交惩罚项作为软约束以近似Ciarlet-Nečas条件，证明了线性弹性下受惩罚泛函的收敛性，并扩展至非线性非简单材料模型，数值实验验证了3d自接触问题的结果。
摘要：
我们分析了惩罚表面自相交的项，作为超弹性材料模型的软约束，以近似Ciarlet-Nečas条件（形变几乎处处全局可逆）。对于受附加局部可逆约束的线性弹性能量，我们证明了受惩罚的弹性泛函收敛于受Ciarlet-Nečas条件约束的原泛函。该方法也适用于非简单材料的非线性模型，包括弹性能量中适当的高阶项，无需人工局部约束。数值实验说明了我们在3d自接触问题中的结果。
英文摘要：
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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