EXISTENCE OF SOLUTIONS TO A REGULARIZED MODEL OF DYNAMIC FRACTURE
Existence and convergence results are proved for a regularized model of dynamic brittle fracture based on the AmbrosioTortorelli approximation. We show that the sequence of solutions to the time-discrete elastodynamics, proposed by Bourdin, Larsen and Richardson as a semidiscrete numerical model for...
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| Format: | Journal article |
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2010
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| _version_ | 1826285433851478016 |
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| author | Larsen, C Ortner, C Suli, E |
| author_facet | Larsen, C Ortner, C Suli, E |
| author_sort | Larsen, C |
| collection | OXFORD |
| description | Existence and convergence results are proved for a regularized model of dynamic brittle fracture based on the AmbrosioTortorelli approximation. We show that the sequence of solutions to the time-discrete elastodynamics, proposed by Bourdin, Larsen and Richardson as a semidiscrete numerical model for dynamic fracture, converges, as the time-step approaches zero, to a solution of the natural time-continuous elastodynamics model, and that this solution satisfies an energy balance. We emphasize that these models do not specify crack paths a priori, but predict them, including such complicated behavior as kinking, crack branching, and so forth, in any spatial dimension. © 2010 World Scientific Publishing Company. |
| first_indexed | 2024-03-07T01:28:46Z |
| format | Journal article |
| id | oxford-uuid:92e00b92-b419-49f1-8d57-6a93dc0b314f |
| institution | University of Oxford |
| last_indexed | 2024-03-07T01:28:46Z |
| publishDate | 2010 |
| record_format | dspace |
| spelling | oxford-uuid:92e00b92-b419-49f1-8d57-6a93dc0b314f2022-03-26T23:28:31ZEXISTENCE OF SOLUTIONS TO A REGULARIZED MODEL OF DYNAMIC FRACTUREJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:92e00b92-b419-49f1-8d57-6a93dc0b314fSymplectic Elements at Oxford2010Larsen, COrtner, CSuli, EExistence and convergence results are proved for a regularized model of dynamic brittle fracture based on the AmbrosioTortorelli approximation. We show that the sequence of solutions to the time-discrete elastodynamics, proposed by Bourdin, Larsen and Richardson as a semidiscrete numerical model for dynamic fracture, converges, as the time-step approaches zero, to a solution of the natural time-continuous elastodynamics model, and that this solution satisfies an energy balance. We emphasize that these models do not specify crack paths a priori, but predict them, including such complicated behavior as kinking, crack branching, and so forth, in any spatial dimension. © 2010 World Scientific Publishing Company. |
| spellingShingle | Larsen, C Ortner, C Suli, E EXISTENCE OF SOLUTIONS TO A REGULARIZED MODEL OF DYNAMIC FRACTURE |
| title | EXISTENCE OF SOLUTIONS TO A REGULARIZED MODEL OF DYNAMIC FRACTURE |
| title_full | EXISTENCE OF SOLUTIONS TO A REGULARIZED MODEL OF DYNAMIC FRACTURE |
| title_fullStr | EXISTENCE OF SOLUTIONS TO A REGULARIZED MODEL OF DYNAMIC FRACTURE |
| title_full_unstemmed | EXISTENCE OF SOLUTIONS TO A REGULARIZED MODEL OF DYNAMIC FRACTURE |
| title_short | EXISTENCE OF SOLUTIONS TO A REGULARIZED MODEL OF DYNAMIC FRACTURE |
| title_sort | existence of solutions to a regularized model of dynamic fracture |
| work_keys_str_mv | AT larsenc existenceofsolutionstoaregularizedmodelofdynamicfracture AT ortnerc existenceofsolutionstoaregularizedmodelofdynamicfracture AT sulie existenceofsolutionstoaregularizedmodelofdynamicfracture |