Euler buckling on curved surfaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866908705118748672 |
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| author | Zhao, Shiheng Haas, Pierre A. |
| author_facet | Zhao, Shiheng Haas, Pierre A. |
| contents | Euler buckling epitomises mechanical instabilities: An inextensible straight elastic line buckles under compression when the compressive force reaches a critical value $F_\ast>0$. Here, we extend this classical, planar instability to the buckling under compression of an inextensible relaxed elastic line on a curved surface. By weakly nonlinear analysis of an asymptotically short elastic line, we reveal that the buckling bifurcation changes fundamentally: The critical force for the lowest buckling mode is $F_\ast=0$ and higher buckling modes disconnect from the undeformed branch to connect in pairs. Solving the buckling problem numerically, we additionally find a new post-buckling instability: A long elastic line on a curved surface snaps through under sufficient compression. Our results thus set the foundations for understanding the buckling instabilities on curved surfaces that pervade the emergence of shape in biology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_04303 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Euler buckling on curved surfaces Zhao, Shiheng Haas, Pierre A. Soft Condensed Matter Biological Physics Euler buckling epitomises mechanical instabilities: An inextensible straight elastic line buckles under compression when the compressive force reaches a critical value $F_\ast>0$. Here, we extend this classical, planar instability to the buckling under compression of an inextensible relaxed elastic line on a curved surface. By weakly nonlinear analysis of an asymptotically short elastic line, we reveal that the buckling bifurcation changes fundamentally: The critical force for the lowest buckling mode is $F_\ast=0$ and higher buckling modes disconnect from the undeformed branch to connect in pairs. Solving the buckling problem numerically, we additionally find a new post-buckling instability: A long elastic line on a curved surface snaps through under sufficient compression. Our results thus set the foundations for understanding the buckling instabilities on curved surfaces that pervade the emergence of shape in biology. |
| title | Euler buckling on curved surfaces |
| topic | Soft Condensed Matter Biological Physics |
| url | https://arxiv.org/abs/2503.04303 |