Determining the finite elasticity reference state from a loaded configuration

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 q 2007 John Wiley & Sons, Ltd