Likely cavitation in stochastic elasticity
We revisit the classic problem of elastic cavitation within the framework of stochastic elasticity. For the deterministic elastic problem, involving homogeneous isotropic incompressible hyperelastic spheres under radially symmetric tension, there is a critical dead-load traction at which cavitation...
| Main Authors: | , , , |
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| Format: | Journal article |
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Springer Verlag
2018
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| _version_ | 1797099266009726976 |
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| author | Mihai, L Woolley, T Fitt, D Goriely, A |
| author_facet | Mihai, L Woolley, T Fitt, D Goriely, A |
| author_sort | Mihai, L |
| collection | OXFORD |
| description | We revisit the classic problem of elastic cavitation within the framework of stochastic elasticity. For the deterministic elastic problem, involving homogeneous isotropic incompressible hyperelastic spheres under radially symmetric tension, there is a critical dead-load traction at which cavitation can occur for some materials. In addition to the well-known case of stable cavitation postbifurcation at the critical dead load, we show the existence of unstable snap cavitation for some isotropic materials satisfying Baker-Ericksen inequalities. For the stochastic problem, we derive the probability distribution of the deformations after bifurcation. In this case, we find that, due to the probabilistic nature of the material parameters, there is always a competition between the stable and unstable states. Therefore, at a critical load, stable or unstable cavitation occurs with a given probability, and there is also a probability that the cavity may form under smaller or greater loads than the expected critical value. We refer to these phenomena as ‘likely cavitation’. Moreover, we provide examples of homogeneous isotropic incompressible materials exhibiting stable or unstable cavitation together with their stochastic equivalent. |
| first_indexed | 2024-03-07T05:21:19Z |
| format | Journal article |
| id | oxford-uuid:df04dee7-5826-4e59-98aa-1e22b05841f1 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T05:21:19Z |
| publishDate | 2018 |
| publisher | Springer Verlag |
| record_format | dspace |
| spelling | oxford-uuid:df04dee7-5826-4e59-98aa-1e22b05841f12022-03-27T09:36:20ZLikely cavitation in stochastic elasticityJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:df04dee7-5826-4e59-98aa-1e22b05841f1Symplectic Elements at OxfordSpringer Verlag2018Mihai, LWoolley, TFitt, DGoriely, AWe revisit the classic problem of elastic cavitation within the framework of stochastic elasticity. For the deterministic elastic problem, involving homogeneous isotropic incompressible hyperelastic spheres under radially symmetric tension, there is a critical dead-load traction at which cavitation can occur for some materials. In addition to the well-known case of stable cavitation postbifurcation at the critical dead load, we show the existence of unstable snap cavitation for some isotropic materials satisfying Baker-Ericksen inequalities. For the stochastic problem, we derive the probability distribution of the deformations after bifurcation. In this case, we find that, due to the probabilistic nature of the material parameters, there is always a competition between the stable and unstable states. Therefore, at a critical load, stable or unstable cavitation occurs with a given probability, and there is also a probability that the cavity may form under smaller or greater loads than the expected critical value. We refer to these phenomena as ‘likely cavitation’. Moreover, we provide examples of homogeneous isotropic incompressible materials exhibiting stable or unstable cavitation together with their stochastic equivalent. |
| spellingShingle | Mihai, L Woolley, T Fitt, D Goriely, A Likely cavitation in stochastic elasticity |
| title | Likely cavitation in stochastic elasticity |
| title_full | Likely cavitation in stochastic elasticity |
| title_fullStr | Likely cavitation in stochastic elasticity |
| title_full_unstemmed | Likely cavitation in stochastic elasticity |
| title_short | Likely cavitation in stochastic elasticity |
| title_sort | likely cavitation in stochastic elasticity |
| work_keys_str_mv | AT mihail likelycavitationinstochasticelasticity AT woolleyt likelycavitationinstochasticelasticity AT fittd likelycavitationinstochasticelasticity AT gorielya likelycavitationinstochasticelasticity |