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- Title
Inverse membrane problems in elasticity.
- Authors
PATHMANATHAN, P.; CHAPMAN, S. J.; GAVAGHAN, D. J.
- Abstract
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.
- Subjects
ELASTICITY; DEFORMATIONS (Mechanics); TENSOR algebra; TENSOR products; PARTIAL differential equations
- Publication
Quarterly Journal of Mechanics & Applied Mathematics, 2009, Vol 62, Issue 1, p67
- ISSN
0033-5614
- Publication type
Article
- DOI
10.1093/qjmam/hbn026