Growth-induced axial buckling of a slender elastic filament embedded in an isotropic elastic matrix
We investigate the problem of an axially-loaded, isotropic, slender cylinder embedded in a soft, isotropic, outer elastic matrix. The cylinder undergoes uniform axial growth, whilst both the cylinder and surrounding elastic matrix are confined between two rigid plates, so that this growth results in...
| Main Authors: | , , , |
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| Format: | Journal article |
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2013
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| _version_ | 1826276152942002176 |
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| author | O'Keeffe, S Moulton, D Waters, S Goriely, A |
| author_facet | O'Keeffe, S Moulton, D Waters, S Goriely, A |
| author_sort | O'Keeffe, S |
| collection | OXFORD |
| description | We investigate the problem of an axially-loaded, isotropic, slender cylinder embedded in a soft, isotropic, outer elastic matrix. The cylinder undergoes uniform axial growth, whilst both the cylinder and surrounding elastic matrix are confined between two rigid plates, so that this growth results in axial compression of the cylinder. We use two different modelling approaches to estimate the critical axial growth (that is, the amount of axial growth the cylinder is able to sustain before it buckles) and buckling wavelength of the cylinder. The first approach treats the filament and surrounding matrix as a single 3-dimensional elastic body undergoing large deformations, whilst the second approach treats the filament as a planar, elastic rod embedded in an infinite elastic foundation. By comparing the results of these two approaches, we obtain an estimate of the foundation modulus parameter, which characterises the strength of the foundation, in terms of the geometric and material properties of the system. |
| first_indexed | 2024-03-06T23:09:42Z |
| format | Journal article |
| id | oxford-uuid:65078186-a4fa-426a-abe1-bc17acc05961 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T23:09:42Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | oxford-uuid:65078186-a4fa-426a-abe1-bc17acc059612022-03-26T18:22:54ZGrowth-induced axial buckling of a slender elastic filament embedded in an isotropic elastic matrixJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:65078186-a4fa-426a-abe1-bc17acc05961Mathematical Institute - ePrints2013O'Keeffe, SMoulton, DWaters, SGoriely, AWe investigate the problem of an axially-loaded, isotropic, slender cylinder embedded in a soft, isotropic, outer elastic matrix. The cylinder undergoes uniform axial growth, whilst both the cylinder and surrounding elastic matrix are confined between two rigid plates, so that this growth results in axial compression of the cylinder. We use two different modelling approaches to estimate the critical axial growth (that is, the amount of axial growth the cylinder is able to sustain before it buckles) and buckling wavelength of the cylinder. The first approach treats the filament and surrounding matrix as a single 3-dimensional elastic body undergoing large deformations, whilst the second approach treats the filament as a planar, elastic rod embedded in an infinite elastic foundation. By comparing the results of these two approaches, we obtain an estimate of the foundation modulus parameter, which characterises the strength of the foundation, in terms of the geometric and material properties of the system. |
| spellingShingle | O'Keeffe, S Moulton, D Waters, S Goriely, A Growth-induced axial buckling of a slender elastic filament embedded in an isotropic elastic matrix |
| title | Growth-induced axial buckling of a slender elastic filament embedded in an isotropic elastic matrix |
| title_full | Growth-induced axial buckling of a slender elastic filament embedded in an isotropic elastic matrix |
| title_fullStr | Growth-induced axial buckling of a slender elastic filament embedded in an isotropic elastic matrix |
| title_full_unstemmed | Growth-induced axial buckling of a slender elastic filament embedded in an isotropic elastic matrix |
| title_short | Growth-induced axial buckling of a slender elastic filament embedded in an isotropic elastic matrix |
| title_sort | growth induced axial buckling of a slender elastic filament embedded in an isotropic elastic matrix |
| work_keys_str_mv | AT okeeffes growthinducedaxialbucklingofaslenderelasticfilamentembeddedinanisotropicelasticmatrix AT moultond growthinducedaxialbucklingofaslenderelasticfilamentembeddedinanisotropicelasticmatrix AT waterss growthinducedaxialbucklingofaslenderelasticfilamentembeddedinanisotropicelasticmatrix AT gorielya growthinducedaxialbucklingofaslenderelasticfilamentembeddedinanisotropicelasticmatrix |