Computational methods for inverse finite elastostatics

In the inverse motion problem in finite hyper-elasticity, the classical formulation relies on conservation laws based on Eshelby's energy-momentum tenser. This formulation is shown to be lacking in several regards for a particular class of inverse motion problems where the deformed configuration and Cauchy traction are given and the undeformed configuration must be calculated. It is shown that for finite element calculations 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 simple and complex situations involving a Neo-Hookean material are presented.