Likely equilibria of the stochastic Rivlin cube
The problem of the Rivlin cube is to determine the stability of all homogeneous equilibria of an isotropic incompressible hyperelastic body under equitriaxial dead loads. Here, we consider the stochastic version of this problem where the elastic parameters are random variables following standard pro...
| Váldodahkkit: | , , |
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| Materiálatiipa: | Journal article |
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Royal Society
2019
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| _version_ | 1826268836356161536 |
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| author | Mihai, A Woolley, T Goriely, A |
| author_facet | Mihai, A Woolley, T Goriely, A |
| author_sort | Mihai, A |
| collection | OXFORD |
| description | The problem of the Rivlin cube is to determine the stability of all homogeneous equilibria of an isotropic incompressible hyperelastic body under equitriaxial dead loads. Here, we consider the stochastic version of this problem where the elastic parameters are random variables following standard probability laws. Uncertainties in these parameters may arise, for example, from inherent data variation between different batches of homogeneous samples, or from different experimental tests. As for the deterministic elastic problem, we consider the following questions: what are the likely equilibria and how does their stability depend on the material constitutive law? In addition, for the stochastic model, the problem is to derive the probability distribution of deformations, given the variability of the parameters. |
| first_indexed | 2024-03-06T21:15:41Z |
| format | Journal article |
| id | oxford-uuid:3fb8c410-ec8a-4d30-9ddb-eb13ddccb45f |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:15:41Z |
| publishDate | 2019 |
| publisher | Royal Society |
| record_format | dspace |
| spelling | oxford-uuid:3fb8c410-ec8a-4d30-9ddb-eb13ddccb45f2022-03-26T14:33:41ZLikely equilibria of the stochastic Rivlin cubeJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3fb8c410-ec8a-4d30-9ddb-eb13ddccb45fSymplectic Elements at OxfordRoyal Society2019Mihai, AWoolley, TGoriely, AThe problem of the Rivlin cube is to determine the stability of all homogeneous equilibria of an isotropic incompressible hyperelastic body under equitriaxial dead loads. Here, we consider the stochastic version of this problem where the elastic parameters are random variables following standard probability laws. Uncertainties in these parameters may arise, for example, from inherent data variation between different batches of homogeneous samples, or from different experimental tests. As for the deterministic elastic problem, we consider the following questions: what are the likely equilibria and how does their stability depend on the material constitutive law? In addition, for the stochastic model, the problem is to derive the probability distribution of deformations, given the variability of the parameters. |
| spellingShingle | Mihai, A Woolley, T Goriely, A Likely equilibria of the stochastic Rivlin cube |
| title | Likely equilibria of the stochastic Rivlin cube |
| title_full | Likely equilibria of the stochastic Rivlin cube |
| title_fullStr | Likely equilibria of the stochastic Rivlin cube |
| title_full_unstemmed | Likely equilibria of the stochastic Rivlin cube |
| title_short | Likely equilibria of the stochastic Rivlin cube |
| title_sort | likely equilibria of the stochastic rivlin cube |
| work_keys_str_mv | AT mihaia likelyequilibriaofthestochasticrivlincube AT woolleyt likelyequilibriaofthestochasticrivlincube AT gorielya likelyequilibriaofthestochasticrivlincube |