COMPUTATIONAL METHODS FOR INVERSE FINITE ELASTOSTATICS

In the inverse motion problem in finite hyper-elasticity, the classica l formulation relies on conservation laws based on Eshelby's energy-mo mentum tenser. This formulation is shown to be lacking in several rega rds for a particular class of inverse motion problems where the deform ed configuration and Cauchy traction are given and the undeformed conf iguration must be calculated. It is shown that for finite element calc ulations a simple re-examination of the equilibrium equations provides a more suitable finite element formulation. This formulation is also shown to involve only minor changes to existing elements designed for forward motion calculations. Examples illustrating the method in simpl e and complex situations involving a Neo-Hookean material are presente d.