Spontaneous Cavitation in Growing Elastic Membranes
One of the possible effects of volumetric growth in elastic materials is the creation of residual stresses. These stresses are known to change many of the classical properties of the material and have been studied extensively in the context of volumetric growth in biomechanics. Here we consider the...
| Hauptverfasser: | , |
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| Format: | Journal article |
| Sprache: | English |
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2010
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| _version_ | 1826265523647676416 |
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| author | McMahon, J Goriely, A |
| author_facet | McMahon, J Goriely, A |
| author_sort | McMahon, J |
| collection | OXFORD |
| description | One of the possible effects of volumetric growth in elastic materials is the creation of residual stresses. These stresses are known to change many of the classical properties of the material and have been studied extensively in the context of volumetric growth in biomechanics. Here we consider the problem of elastic cavitation in a growing compressible elastic membrane. Growth is taken to be homogeneous but anisotropic, and the membrane is assumed to remain axisymmetric during growth and deformation. We prove that neo-Hookean membranes cannot cavitate, but for Varga elastic materials we find conditions under which the material exhibits spontaneous cavitation in the absence of external loads, in marked distinction from the cavitation problem without growth. © 2010 SAGE Publications. |
| first_indexed | 2024-03-06T20:25:02Z |
| format | Journal article |
| id | oxford-uuid:2f1e8984-1bd6-4d6a-b9d8-fc1192c49a9b |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:25:02Z |
| publishDate | 2010 |
| record_format | dspace |
| spelling | oxford-uuid:2f1e8984-1bd6-4d6a-b9d8-fc1192c49a9b2022-03-26T12:53:13ZSpontaneous Cavitation in Growing Elastic MembranesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:2f1e8984-1bd6-4d6a-b9d8-fc1192c49a9bEnglishSymplectic Elements at Oxford2010McMahon, JGoriely, AOne of the possible effects of volumetric growth in elastic materials is the creation of residual stresses. These stresses are known to change many of the classical properties of the material and have been studied extensively in the context of volumetric growth in biomechanics. Here we consider the problem of elastic cavitation in a growing compressible elastic membrane. Growth is taken to be homogeneous but anisotropic, and the membrane is assumed to remain axisymmetric during growth and deformation. We prove that neo-Hookean membranes cannot cavitate, but for Varga elastic materials we find conditions under which the material exhibits spontaneous cavitation in the absence of external loads, in marked distinction from the cavitation problem without growth. © 2010 SAGE Publications. |
| spellingShingle | McMahon, J Goriely, A Spontaneous Cavitation in Growing Elastic Membranes |
| title | Spontaneous Cavitation in Growing Elastic Membranes |
| title_full | Spontaneous Cavitation in Growing Elastic Membranes |
| title_fullStr | Spontaneous Cavitation in Growing Elastic Membranes |
| title_full_unstemmed | Spontaneous Cavitation in Growing Elastic Membranes |
| title_short | Spontaneous Cavitation in Growing Elastic Membranes |
| title_sort | spontaneous cavitation in growing elastic membranes |
| work_keys_str_mv | AT mcmahonj spontaneouscavitationingrowingelasticmembranes AT gorielya spontaneouscavitationingrowingelasticmembranes |