Influence of chirality on buckling of inextensible rings subject to dead loading

Tuan M. Hoang
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Authors

  • Tuan M. Hoang Institute of Mechanics, VAST, 264 Doi Can, Hanoi, Vietnam

DOI:

https://doi.org/10.15625/0866-7136/20353

Keywords:

elastic ring, special Cosserat rod, buckling, chirality, dead loading

Abstract

A variational approach is studied to understand buckling of inextensible rings made from chiral filaments and subject to dead loading. In opposite to previous literatures in which only in-plane bifurcation is allowed, i.e., the ring deforms only in its plane, in this work we consider both in-plane and out-of-plane bifurcation, i.e., the ring deforms both in its plane and out of its plane. For circular rings made from filaments without chirality, we find that they lose instability via out-of-plane bifurcation at critical values of loading smaller than those published. For circular rings made from filaments with chirality, they lose instability via coupling between in-plane and out-of-plane bifurcation at critical values of loading smaller than those at which bifurcation would happen without chirality. The destabilizing effect of chirality, however, can be reduced by increasing the twisting rigidity relative to the bending rigidity.

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References

[1] M. M. Lévy. Mémoire sur un nouveau cas intégrable du probléme de l’élastique et lune de ses applications. Journal of Pure and Applied Mathematics, 10, (1884), pp. 5–42.

[2] R. Hashemi and R. Avazmohammadi. Surface effects on stability of nanorings under uniform pressure. Journal of Applied Physics, 114, (2013). https://doi.org/10.1063/1.4824818.

[3] D. F. Windenburg and C. Trilling. Collapse by instability of thin cylindrical shells under external pressure. Transactions of the American Society of Mechanical Engineers, 56, (11), (1934), pp. 819–825. https://doi.org/10.1115/1.4019870.

[4] M. R. Eslami. Buckling and postbuckling of beams, plates, and shells. Springer, (2018). https://doi.org/10.1007/978-3-319-62368-9.

[5] G. Carrier. On the buckling of elastic rings. Journal of Applied Mathematics and Physics, 26, (1947), pp. 94–103. https://doi.org/10.1002/sapm194726194.

[6] I. Tadjbakhsh and F. Odeh. Equilibrium states of elastic rings. Journal of Mathematical Analysis and Applications, 18, (1967), pp. 59–74. https://doi.org/10.1016/0022-247x(67)90182-5.

[7] P. Seidel and E. D. Albano. Bifurcation of circular rings under normal concentrated loads. ASME Journal on Applied Mechanics, 40, (1), (1973), pp. 233–238. https://doi.org/10.1115/1.3422932.

[8] L. B. Sills and B. Budiansky. Postbuckling ring analysis. ASME Journal on Applied Mechanics, 45, (1), (1978), pp. 208–210. https://doi.org/10.1115/1.3424235.

[9] L. B. Sills and B. Budiansky. Erratum on postbuckling ring analysis. ASME Journal on Applied Mechanics, 50, (3), (1983).

[10] G. J. Simitses and D. H. Hodges. Fundamentals of structural stability. Butterworth-Heinemann, (2006).

[11] T. Savin, N. A. Kurpios, A. E. Shyer, P. Florescu, H. Liang, L. Mahadevan, and C. J. Tabin. On the growth and form of the gut. Nature, 476, (7358), (2011), pp. 57–62. https://doi.org/10.1038/nature10277.

[12] A. Catte, J. C. Patterson, M. K. Jones, W. G. Jerome, D. Bashtovyy, Z. Su, F. Gu, J. Chen, M. P. Aliste, S. C. Harvey, L. Li, G. Weinstein, and J. P. Segrest. Novel changes in discoidal high density lipoprotein morphology: A molecular dynamics study. Biophysical Journal, 90, (12), (2006), pp. 4345–4360. https://doi.org/10.1529/biophysj.105.071456.

[13] L. Giomi and L. Mahadevan. Minimal surfaces bounded by elastic lines. Proceedings of the Royal Society of London Series A, Mathematical, Physical and Engineering Sciences, 468, (2012), pp. 1851–1864. https://doi.org/10.1098/rspa.2011.0627.

[14] Y.-C. Chen and E. Fried. Stability and bifurcation of a soap film spanning a flexible loop. Journal of Elasticity, 116, (1), (2014), pp. 75–100.

[15] A. Biria and E. Fried. Buckling of a soap film spanning a flexible loop resistant to bending and twisting. Proceedings of the Royal Society of London Series A, Mathematical, Physical and Engineering Sciences, 470, (2172), (2014). https://doi.org/10.1098/rspa.2014.0368.

[16] A. Biria and E. Fried. Theoretical and experimental study of the stability of a soap film spanning a flexible loop. International Journal of Engineering Science, 94, (2015), pp. 86–102. https://doi.org/10.1016/j.ijengsci.2015.05.002.

[17] T. M. Hoang and E. Fried. Influence of a spanning liquid film on the stability and buckling of a circular loop with intrinsic curvature or intrinsic twist density. Mathematics and Mechanics of Solids, 23, (1), (2018), pp. 43–66.

[18] G. Giusteri, P. Franceschini, and E. Fried. Instability paths in the Kirchhoff–Plateau problem. Journal of Nonlinear Science, 26, (4), (2016), pp. 1097–1132. https://doi.org/10.1007/s00332-016-9299-4.

[19] E. D. Albano and P. Seidel. Bifurcation of rings under concentrated centrally directed loads. ASME Journal on Applied Mechanics, 40, (2), (1973), pp. 553–558. https://doi.org/10.1115/1.3423022.

[20] J. Singer and C. D. Babcock. On the buckling of rings under constant directional and centrally directed pressure. Journal of Applied Mechanics, 37, (1), (1970), pp. 215–218. https://doi.org/10.1115/1.3408445.

[21] J. Singer and C. D. Babcock. Erratum on “On the buckling of rings under constant directional and centrally directed pressure”. Journal of Applied Mechanics, 38, (2), (1971).

[22] M. Gaibotti, D. Bigoni, A. Cutolo, M. Fraldi, and A. Piccolroaz. Effects of different loading on the bifurcation of annular elastic rods: Theory vs. experiments. International Journal of Non–Linear Mechanics, 165, (2024). https://doi.org/10.1016/j.ijnonlinmec.2024.104820.

[23] C. G. Merret. Stability of viscoelastic rings under radial loads with applications to nuclear technology. Journal of Applied Mechanics, 82, (2015). https://doi.org/10.1115/1.4030309.

[24] T. M. Hoang. Influence of chirality on buckling and initial postbuckling of inextensible rings subject to central loadings. International Journal of Solids and Structures, 172-173, (2019), pp. 97–109. https://doi.org/10.1016/j.ijsolstr.2019.03.029.

[25] P. N. R. D. Kamien, T. C. Lubensky and C. S. O’Hern. Direct determination of DNA twist-stretch coupling. Europhysics Letters (EPL), 38, (3), (1997), pp. 237–242. https://doi.org/10.1209/epl/i1997-00231-y.

[26] J. D. Moroz and P. Nelson. Torsional directed walks, entropic elasticity, and DNA twist stiffness. Proceedings of the National Academy of Sciences of the United States of America, 94, (1997), pp. 14418–14422. https://doi.org/10.1073/pnas.94.26.14418.

[27] T. J. Healey. Material symmetry and chirality in nonlinearly elastic solids. Mathematics and Mechanics of Solids, 7, (2002), pp. 405–420. https://doi.org/10.1177/108128028482.

[28] T. J. Healey and C. Papdopoulos. Bifurcation of hemitropic elastic rods under axial thrust. Quarterly of Applied Mathematics, LXXI, (2013), pp. 729–753. https://doi.org/10.1090/s0033-569x-2013-01308-7.

[29] B. Đuričković, A. Goriely, and J. H. Maddocks. Twist and stretch of helices explained via the Kirchhoff-Love rod model of elastic filaments. Physical Review Letters, 111, (2013). https://doi.org/10.1103/physrevlett.111.108103.

[30] T. M. Hoang. Postbuckling of chiral elastic rings with intrinsic twist. International Journal of Solids and Structures, 225, (2021). https://doi.org/10.1016/j.ijsolstr.2021.03.020.

[31] W. Helfrich. Elastic theory of helical fibers. Langmuir, 7, (1991), pp. 567–568. https://doi.org/10.1021/la00051a025.

[32] J. F. Marko and E. D. Sigga. Bending and twisting elasticity of DNA. Macromolecules, 27, (1994), pp. 981–988. https://doi.org/10.1021/ma00082a015.

[33] J. F. Marko. Stretching must twist DNA. Europhysics Letters (EPL), 38, (3), (1997), pp. 183–188. https://doi.org/10.1209/epl/i1997-00223-5.

[34] Z. Wei, Z. Haijun, and O.-Y. Zhong-can. Kink instability in circular DNA studied as Helfrich chiral chains. Physical Review E, 58, (1998), pp. 8040–8043. https://doi.org/10.1103/physreve.58.8040.

[35] S. S. Antman. Nonlinear problems of elasticity. Springer, (1995). https://doi.org/10.1007/978-1- 4757-4147-6.

[36] B. Budiansky. Theory of buckling and post-buckling behavior of elastic structures. Advances in Applied Mechanics, 14, (1974), pp. 1–65. https://doi.org/10.1016/s0065-2156(08)70030-9.

[37] M. S. E. Naschie. Influence of loading behavior on the post buckling of circular rings. AIAA Journal, 14, (2), (1975). https://doi.org/10.2514/3.7087.

[38] G. Napoli and A. Goriely. A tale of two nested elastic rings. Proceedings of the Royal Society A, 473, (2017). https://doi.org/10.1098/rspa.2017.0340.

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31-10-2024

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