Inverse membrane problems in elasticity
The inverse elasticity problem of determining the undeformed, deflated, configuration of a nonlinear elastic membrane, given the deformed configuration enclosing an incompressible fluid under known pressure, is considered. It is shown that, in practical cases, it is enough to determine only the unde...
| Main Authors: | , , |
|---|---|
| Format: | Journal article |
| Published: |
2009
|
| _version_ | 1826259929751617536 |
|---|---|
| author | Pathmanathan, P Chapman, S Gavaghan, D |
| author_facet | Pathmanathan, P Chapman, S Gavaghan, D |
| author_sort | Pathmanathan, P |
| collection | OXFORD |
| description | The inverse elasticity problem of determining the undeformed, deflated, configuration of a nonlinear elastic membrane, given the deformed configuration enclosing an incompressible fluid under known pressure, is considered. It is shown that, in practical cases, it is enough to determine only the undeformed metric tensor, and it is also shown how the two- and three-dimensional cases are fundamentally different. For the three-dimensional case, we set up and classify the partial differential equations to be solved, prove existence of an undeformed state given an undeformed metric and study the axisymmetric case in detail |
| first_indexed | 2024-03-06T18:57:36Z |
| format | Journal article |
| id | oxford-uuid:12612ca0-5c85-41c0-848f-de28e507ddf6 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:57:36Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:12612ca0-5c85-41c0-848f-de28e507ddf62022-03-26T10:07:37ZInverse membrane problems in elasticityJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:12612ca0-5c85-41c0-848f-de28e507ddf6Department of Computer Science2009Pathmanathan, PChapman, SGavaghan, DThe inverse elasticity problem of determining the undeformed, deflated, configuration of a nonlinear elastic membrane, given the deformed configuration enclosing an incompressible fluid under known pressure, is considered. It is shown that, in practical cases, it is enough to determine only the undeformed metric tensor, and it is also shown how the two- and three-dimensional cases are fundamentally different. For the three-dimensional case, we set up and classify the partial differential equations to be solved, prove existence of an undeformed state given an undeformed metric and study the axisymmetric case in detail |
| spellingShingle | Pathmanathan, P Chapman, S Gavaghan, D Inverse membrane problems in elasticity |
| title | Inverse membrane problems in elasticity |
| title_full | Inverse membrane problems in elasticity |
| title_fullStr | Inverse membrane problems in elasticity |
| title_full_unstemmed | Inverse membrane problems in elasticity |
| title_short | Inverse membrane problems in elasticity |
| title_sort | inverse membrane problems in elasticity |
| work_keys_str_mv | AT pathmanathanp inversemembraneproblemsinelasticity AT chapmans inversemembraneproblemsinelasticity AT gavaghand inversemembraneproblemsinelasticity |