Journal
QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS
Volume 62, Issue 1, Pages 67-87Publisher
OXFORD UNIV PRESS
DOI: 10.1093/qjmam/hbn026
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Funding
- Engineering and Physical Sciences Research Council [EP/D048400/1]
- Engineering and Physical Sciences Research Council [EP/D048400/1] Funding Source: researchfish
- EPSRC [EP/D048400/1] Funding Source: UKRI
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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.
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