Open Access
| Issue |
ESAIM: COCV
Volume 30, 2024
|
|
|---|---|---|
| Article Number | 53 | |
| Number of page(s) | 31 | |
| DOI | https://doi.org/10.1051/cocv/2024043 | |
| Published online | 12 July 2024 | |
- M. Giovanna Mora and S. Müller, Derivation of the nonlinear bending-torsion theory for inextensible rods by Γ-convergence. Calc. Var. Part. Differ. Equ. 18 (2003) 287–305. [CrossRef] [Google Scholar]
- S. Bartels, A simple scheme for the approximation of the elastic flow of inextensible curves. IMA J. Numer. Anal. 33 (2013) 1115–1125. [CrossRef] [MathSciNet] [Google Scholar]
- S. Bartels and P. Reiter, Numerical solution of a bending-torsion model for elastic rods. Numer. Math. 146 (2020) 661–697. [CrossRef] [MathSciNet] [Google Scholar]
- P. Jung, S. Leyendecker, J. Linn and M. Ortiz, A discrete mechanics approach to the Cosserat rod theory—part 1: static equilibria. Int. J. Numer. Methods Eng. 85 (2011) 31–60. [CrossRef] [Google Scholar]
- M. Bergou et al., Discrete elastic rods, in ACM SIGGRAPH 2008 papers. ACM (2008) 1–12. [Google Scholar]
- C. Lestringant, B. Audoly and D.M. Kochmann, A discrete, geometrically exact method for simulating nonlinear, elastic and inelastic beams. Comput. Methods Appl. Mech. Eng. 361 (2020) 112741, 33. [CrossRef] [Google Scholar]
- K. Korner, B. Audoly and K. Bhattacharya, Simple deformation measures for discrete elastic rods and ribbons. Proc. A 477 (2021) Paper No. 20210561, 20. [Google Scholar]
- S. Scholtes, H. Schumacher and M. Wardetzky, Variational convergence of discrete elasticae. IMA J. Numer. Anal. 42 (2022) 300–332. [CrossRef] [MathSciNet] [Google Scholar]
- J.-J. Alibert, A. Della Corte, I. Giorgio and A. Battista, Extensional elastica in large deformation as Γ-limit of a discrete 1D mechanical system. Z. Angew. Math. Phys. 68 (2017) Paper No. 42, 19. [CrossRef] [Google Scholar]
- J.-J. Alibert, A. Della Corte and P. Seppecher, Convergence of Hencky-type discrete beam model to Euler inextensible elastica in large deformation: rigorous proof, in Mathematical Modelling in Solid Mechanics. Vol. 69 of Adv. Struct. Mater. Springer, Singapore (2017) 1–12. [CrossRef] [Google Scholar]
- A.M. Bruckstein, R.J. Holt and A.N. Netravali, Discrete elastica. Appl. Anal. 78 (2001) 453–485. [CrossRef] [MathSciNet] [Google Scholar]
- M.I. Español, D. Golovaty and J. Patrick Wilber, Euler elastica as a Γ-limit of discrete bending energies of one-dimensional chains of atoms. Math. Mech. Solids 23 (2018) 1104–1116. [CrossRef] [MathSciNet] [Google Scholar]
- J.A. Iglesias and A.M. Bruckstein, On the Gamma-convergence of some polygonal curvature functionals. Appl. Anal. 94 (2015) 957–979. [CrossRef] [MathSciNet] [Google Scholar]
- R.L. Bishop, There is more than one way to frame a curve. Amer. Math. Monthly 82 (1975) 246–251. [CrossRef] [MathSciNet] [Google Scholar]
- P. Hornung, Deformation of framed curves with boundary conditions. Calc. Var. Part. Differ. Equ. 60 (2021) Paper No. 87, 26. [CrossRef] [Google Scholar]
- A. Braides, Γ-convergence for beginners. Vol. 22 of Oxford Lecture Series in Mathematics and its Applications. Oxford University Press, Oxford (2002). [Google Scholar]
- A. Braides, Discrete approximation of functionals with jumps and creases, in Homogenization (Naples). Vol. 18 of GAKUTO Internat. Ser. Math. Sci. Appl. (2001) 147–153. [Google Scholar]
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