Dynamic buckling of an inextensible elastic ring: Linear and nonlinear analyses
Slender elastic objects such as a column tend to buckle under loads. While static buckling is well understood as a bifurcation problem, the evolution of shapes during dynamic buckling is much harder to study. Elastic rings under normal pressure have emerged as a theoretical and experimental paradigm...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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American Physical Society
2020
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| _version_ | 1826267823999025152 |
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| author | Kodio, O Goriely, A Vella, D |
| author_facet | Kodio, O Goriely, A Vella, D |
| author_sort | Kodio, O |
| collection | OXFORD |
| description | Slender elastic objects such as a column tend to buckle under loads. While static buckling is well understood as a bifurcation problem, the evolution of shapes during dynamic buckling is much harder to study. Elastic rings under normal pressure have emerged as a theoretical and experimental paradigm for the study of dynamic buckling with controlled loads. Experimentally, an elastic ring is placed within a soap film. When the film outside the ring is removed, surface tension pulls the ring inward, mimicking an external pressurization. Here we present a theoretical analysis of this process by performing a postbifurcation analysis of an elastic ring under pressure. This analysis allows us to understand how inertia, material properties, and loading affect the observed shape. In particular, we combine direct numerical solutions with a postbifurcation asymptotic analysis to show that inertia drives the system towards higher modes that cannot be selected in static buckling. Our theoretical results explain experimental observations that cannot be captured by a standard linear stability analysis.
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| first_indexed | 2024-03-06T21:00:08Z |
| format | Journal article |
| id | oxford-uuid:3a9bae4c-b894-42ac-aa99-61930d25ff4c |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T21:00:08Z |
| publishDate | 2020 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | oxford-uuid:3a9bae4c-b894-42ac-aa99-61930d25ff4c2022-03-26T14:02:38ZDynamic buckling of an inextensible elastic ring: Linear and nonlinear analysesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3a9bae4c-b894-42ac-aa99-61930d25ff4cEnglishSymplectic ElementsAmerican Physical Society2020Kodio, OGoriely, AVella, DSlender elastic objects such as a column tend to buckle under loads. While static buckling is well understood as a bifurcation problem, the evolution of shapes during dynamic buckling is much harder to study. Elastic rings under normal pressure have emerged as a theoretical and experimental paradigm for the study of dynamic buckling with controlled loads. Experimentally, an elastic ring is placed within a soap film. When the film outside the ring is removed, surface tension pulls the ring inward, mimicking an external pressurization. Here we present a theoretical analysis of this process by performing a postbifurcation analysis of an elastic ring under pressure. This analysis allows us to understand how inertia, material properties, and loading affect the observed shape. In particular, we combine direct numerical solutions with a postbifurcation asymptotic analysis to show that inertia drives the system towards higher modes that cannot be selected in static buckling. Our theoretical results explain experimental observations that cannot be captured by a standard linear stability analysis. |
| spellingShingle | Kodio, O Goriely, A Vella, D Dynamic buckling of an inextensible elastic ring: Linear and nonlinear analyses |
| title | Dynamic buckling of an inextensible elastic ring: Linear and nonlinear analyses |
| title_full | Dynamic buckling of an inextensible elastic ring: Linear and nonlinear analyses |
| title_fullStr | Dynamic buckling of an inextensible elastic ring: Linear and nonlinear analyses |
| title_full_unstemmed | Dynamic buckling of an inextensible elastic ring: Linear and nonlinear analyses |
| title_short | Dynamic buckling of an inextensible elastic ring: Linear and nonlinear analyses |
| title_sort | dynamic buckling of an inextensible elastic ring linear and nonlinear analyses |
| work_keys_str_mv | AT kodioo dynamicbucklingofaninextensibleelasticringlinearandnonlinearanalyses AT gorielya dynamicbucklingofaninextensibleelasticringlinearandnonlinearanalyses AT vellad dynamicbucklingofaninextensibleelasticringlinearandnonlinearanalyses |