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Inverse membrane problems in elasticity

P. Pathmanathan‚ SJ Chapman and DJ Gavaghan

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

ISSN
00335614
Journal
QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS    
Keywords
breast
Month
Feb
Number
1
Pages
67–87
Volume
62
Year
2009