Axisymmetric bifurcations of thick spherical shells under inflation and compression
Incremental equilibrium equations and corresponding boundary conditions for an isotropic, hyperelastic and incompressible material are summarized and then specialized to a form suitable for the analysis of a spherical shell subject to an internal or an external pressure. A thick-walled spherical she...
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| Format: | Journal article |
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2012
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| _version_ | 1826282702388592640 |
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| author | deBotton, G Bustamante, R Dorfmann, A |
| author_facet | deBotton, G Bustamante, R Dorfmann, A |
| author_sort | deBotton, G |
| collection | OXFORD |
| description | Incremental equilibrium equations and corresponding boundary conditions for an isotropic, hyperelastic and incompressible material are summarized and then specialized to a form suitable for the analysis of a spherical shell subject to an internal or an external pressure. A thick-walled spherical shell during inflation is analyzed using four different material models. Specifically, one and two terms in the Ogden energy formulation, the Gent model and an I1 formulation recently proposed by Lopez-Pamies. We investigate the existence of local pressure maxima and minima and the dependence of the corresponding stretches on the material model and on shell thickness. These results are then used to investigate axisymmetric bifurcations of the inflated shell. The analysis is extended to determine the behavior of a thick-walled spherical shell subject to an external pressure. We find that the results of the two terms Ogden formulation, the Gent and the Lopez-Pamies models are very similar, for the one term Ogden material we identify additional critical stretches, which have not been reported in the literature before. |
| first_indexed | 2024-03-07T00:47:50Z |
| format | Journal article |
| id | oxford-uuid:854d68c1-9402-4052-9c59-d23bd84990ab |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:47:50Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | oxford-uuid:854d68c1-9402-4052-9c59-d23bd84990ab2022-03-26T21:56:44ZAxisymmetric bifurcations of thick spherical shells under inflation and compressionJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:854d68c1-9402-4052-9c59-d23bd84990abMathematical Institute - ePrints2012deBotton, GBustamante, RDorfmann, AIncremental equilibrium equations and corresponding boundary conditions for an isotropic, hyperelastic and incompressible material are summarized and then specialized to a form suitable for the analysis of a spherical shell subject to an internal or an external pressure. A thick-walled spherical shell during inflation is analyzed using four different material models. Specifically, one and two terms in the Ogden energy formulation, the Gent model and an I1 formulation recently proposed by Lopez-Pamies. We investigate the existence of local pressure maxima and minima and the dependence of the corresponding stretches on the material model and on shell thickness. These results are then used to investigate axisymmetric bifurcations of the inflated shell. The analysis is extended to determine the behavior of a thick-walled spherical shell subject to an external pressure. We find that the results of the two terms Ogden formulation, the Gent and the Lopez-Pamies models are very similar, for the one term Ogden material we identify additional critical stretches, which have not been reported in the literature before. |
| spellingShingle | deBotton, G Bustamante, R Dorfmann, A Axisymmetric bifurcations of thick spherical shells under inflation and compression |
| title | Axisymmetric bifurcations of thick spherical shells under inflation and compression |
| title_full | Axisymmetric bifurcations of thick spherical shells under inflation and compression |
| title_fullStr | Axisymmetric bifurcations of thick spherical shells under inflation and compression |
| title_full_unstemmed | Axisymmetric bifurcations of thick spherical shells under inflation and compression |
| title_short | Axisymmetric bifurcations of thick spherical shells under inflation and compression |
| title_sort | axisymmetric bifurcations of thick spherical shells under inflation and compression |
| work_keys_str_mv | AT debottong axisymmetricbifurcationsofthicksphericalshellsunderinflationandcompression AT bustamanter axisymmetricbifurcationsofthicksphericalshellsunderinflationandcompression AT dorfmanna axisymmetricbifurcationsofthicksphericalshellsunderinflationandcompression |