Local minimizers and planar interfaces in a phase-transition model with interfacial energy
Interfacial energy is often incorporated into variational solid-solid phase transition models via a perturbation of the elastic energy functional involving second gradients of the deformation. We study consequences of such higher-gradient terms for local minimizers and for interfaces. First it is sh...
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| Format: | Journal article |
| Language: | English |
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2011
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| _version_ | 1797067793805344768 |
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| author | Ball, J Crooks, E |
| author_facet | Ball, J Crooks, E |
| author_sort | Ball, J |
| collection | OXFORD |
| description | Interfacial energy is often incorporated into variational solid-solid phase transition models via a perturbation of the elastic energy functional involving second gradients of the deformation. We study consequences of such higher-gradient terms for local minimizers and for interfaces. First it is shown that at slightly sub-critical temperatures, a phase which globally minimizes the elastic energy density at super-critical temperatures is an L1-local minimizer of the functional including interfacial energy, whereas it is typically only a W1,∞-local minimizer of the purely elastic functional. The second part deals with the existence and uniqueness of smooth interfaces between different wells of the multi-well elastic energy density. Attention is focussed on so-called planar interfaces, for which the deformation depends on a single direction x · N and the deformation gradient then satisfies a rank-one ansatz of the form Dy(x) = A + u(x · N) ⊗ N, where A and B = A + a ⊗ N are the gradients connected by the interface. © 2010 Springer-Verlag. |
| first_indexed | 2024-03-06T22:01:26Z |
| format | Journal article |
| id | oxford-uuid:4ebacd94-0624-41b3-b2a2-58a29221f088 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T22:01:26Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:4ebacd94-0624-41b3-b2a2-58a29221f0882022-03-26T16:02:56ZLocal minimizers and planar interfaces in a phase-transition model with interfacial energyJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:4ebacd94-0624-41b3-b2a2-58a29221f088EnglishSymplectic Elements at Oxford2011Ball, JCrooks, EInterfacial energy is often incorporated into variational solid-solid phase transition models via a perturbation of the elastic energy functional involving second gradients of the deformation. We study consequences of such higher-gradient terms for local minimizers and for interfaces. First it is shown that at slightly sub-critical temperatures, a phase which globally minimizes the elastic energy density at super-critical temperatures is an L1-local minimizer of the functional including interfacial energy, whereas it is typically only a W1,∞-local minimizer of the purely elastic functional. The second part deals with the existence and uniqueness of smooth interfaces between different wells of the multi-well elastic energy density. Attention is focussed on so-called planar interfaces, for which the deformation depends on a single direction x · N and the deformation gradient then satisfies a rank-one ansatz of the form Dy(x) = A + u(x · N) ⊗ N, where A and B = A + a ⊗ N are the gradients connected by the interface. © 2010 Springer-Verlag. |
| spellingShingle | Ball, J Crooks, E Local minimizers and planar interfaces in a phase-transition model with interfacial energy |
| title | Local minimizers and planar interfaces in a phase-transition model with interfacial energy |
| title_full | Local minimizers and planar interfaces in a phase-transition model with interfacial energy |
| title_fullStr | Local minimizers and planar interfaces in a phase-transition model with interfacial energy |
| title_full_unstemmed | Local minimizers and planar interfaces in a phase-transition model with interfacial energy |
| title_short | Local minimizers and planar interfaces in a phase-transition model with interfacial energy |
| title_sort | local minimizers and planar interfaces in a phase transition model with interfacial energy |
| work_keys_str_mv | AT ballj localminimizersandplanarinterfacesinaphasetransitionmodelwithinterfacialenergy AT crookse localminimizersandplanarinterfacesinaphasetransitionmodelwithinterfacialenergy |