Controllable deformations in compressible isotropic implicit elasticity
For a given material, controllable deformations are those deformations that can be maintained in the absence of body forces and by applying only boundary tractions. For a given class of materials, universal deformations are those deformations that are controllable for any material within the class....
| Những tác giả chính: | , |
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| Định dạng: | Journal article |
| Ngôn ngữ: | English |
| Được phát hành: |
Springer Nature
2024
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| _version_ | 1826314946986639360 |
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| author | Yavari, A Goriely, A |
| author_facet | Yavari, A Goriely, A |
| author_sort | Yavari, A |
| collection | OXFORD |
| description | For a given material, controllable deformations are those deformations that can be maintained in the absence of body forces and by applying only boundary tractions. For a given class of materials, universal deformations are those deformations that are controllable for any material within the class. In this paper, we characterize the universal deformations in compressible isotropic implicit elasticity defined by solids whose constitutive equations, in terms of the Cauchy stress σ and the left Cauchy-Green strain b, have the implicit form f(σ, b) = 0. We prove that universal deformations are homogeneous. However, an important observation is that, unlike Cauchy (and Green) elasticity, not every homogeneous deformation is constitutively admissible for a given implicit-elastic solid. In other words, the set of universal deformations is material-dependent, yet it remains a subset of homogeneous deformations. |
| first_indexed | 2024-09-25T04:20:58Z |
| format | Journal article |
| id | oxford-uuid:b61255c9-dabe-4ff0-985d-83a3e3150f72 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-12-09T03:17:16Z |
| publishDate | 2024 |
| publisher | Springer Nature |
| record_format | dspace |
| spelling | oxford-uuid:b61255c9-dabe-4ff0-985d-83a3e3150f722024-10-22T12:39:49ZControllable deformations in compressible isotropic implicit elasticityJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:b61255c9-dabe-4ff0-985d-83a3e3150f72EnglishSymplectic ElementsSpringer Nature2024Yavari, AGoriely, AFor a given material, controllable deformations are those deformations that can be maintained in the absence of body forces and by applying only boundary tractions. For a given class of materials, universal deformations are those deformations that are controllable for any material within the class. In this paper, we characterize the universal deformations in compressible isotropic implicit elasticity defined by solids whose constitutive equations, in terms of the Cauchy stress σ and the left Cauchy-Green strain b, have the implicit form f(σ, b) = 0. We prove that universal deformations are homogeneous. However, an important observation is that, unlike Cauchy (and Green) elasticity, not every homogeneous deformation is constitutively admissible for a given implicit-elastic solid. In other words, the set of universal deformations is material-dependent, yet it remains a subset of homogeneous deformations. |
| spellingShingle | Yavari, A Goriely, A Controllable deformations in compressible isotropic implicit elasticity |
| title | Controllable deformations in compressible isotropic implicit elasticity |
| title_full | Controllable deformations in compressible isotropic implicit elasticity |
| title_fullStr | Controllable deformations in compressible isotropic implicit elasticity |
| title_full_unstemmed | Controllable deformations in compressible isotropic implicit elasticity |
| title_short | Controllable deformations in compressible isotropic implicit elasticity |
| title_sort | controllable deformations in compressible isotropic implicit elasticity |
| work_keys_str_mv | AT yavaria controllabledeformationsincompressibleisotropicimplicitelasticity AT gorielya controllabledeformationsincompressibleisotropicimplicitelasticity |