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Mathematics > Analysis of PDEs

arXiv:1811.12049 (math)
[Submitted on 29 Nov 2018 (v1), last revised 9 Jan 2019 (this version, v2)]

Title:Global injectivity in second-gradient Nonlinear Elasticity and its approximation with penalty terms

Authors:Stefan Krömer, Jan Valdman
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Abstract: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.
Comments: 37 pages, 9 figures
Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph); Numerical Analysis (math.NA)
MSC classes: 35Q74, 49M99, 65Z05
Cite as: arXiv:1811.12049 [math.AP]
  (or arXiv:1811.12049v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1811.12049

Submission history

From: Stefan Krömer [view email]
[v1] Thu, 29 Nov 2018 10:22:44 UTC (1,158 KB)
[v2] Wed, 9 Jan 2019 12:32:48 UTC (1,159 KB)
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