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Determining the finite elasticity reference state from a loaded configuration
Author(s) -
Rajagopal Vijayaraghavan,
Chung JaeHoon,
Bullivant David,
Nielsen Poul M. F.,
Nash Martyn P.
Publication year - 2007
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2045
Subject(s) - elasticity (physics) , finite element method , state (computer science) , mathematics , computer science , structural engineering , engineering , algorithm , physics , thermodynamics
There are a number of situations where the deformed configuration of a body is known and it is necessary to determine the reference state. Previous methods developed to calculate the reference state involve the formulation of the finite elasticity equations in terms of the deformed configuration. This paper demonstrates that the undeformed reference state can be accurately determined from a deformed configuration and the associated loading conditions, by using conventional finite elasticity balance equations together with a solution procedure that treats the reference configuration as the unknowns. The mathematical theory behind the solution method is described, validated with an analytical solution, and verified using experimental studies on gel phantoms. The practical utility of this method is then demonstrated in the field of breast biomechanics. Copyright © 2007 John Wiley & Sons, Ltd.