$\Gamma$-convergence of a discrete Kirchhoff rod energy
| Autor: | Dondl, Patrick, Hounkpe, Coffi Aristide, Jesenko, Martin |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | This work is motivated by the classical discrete elastic rod model by Audoly et al. We derive a discrete version of the Kirchhoff elastic energy for rods undergoing bending and torsion and prove $\Gamma$-convergence to the continuous model. This discrete energy is given by the bending and torsion energy of an interpolating conforming polynomial curve and provides a simple formula for the bending energy depending in each discrete segment only on angle and adjacent edge lengths. For the $\liminf$-inequality, we need to introduce penalty terms to ensure arc-length parametrization in the limit. For the recovery sequence a discretization with equal Euclidean distance between consecutive points is constructed. Particular care is taken to treat the interaction between bending and torsion by employing a discrete version of the Bishop frame. Comment: 27 pages, 5 figures |
| Databáze: | arXiv |
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