ON THE PERTURBED LAGRANGIAN FORMULATION FOR NEARLY INCOMPRESSIBLE ANDINCOMPRESSIBLE HYPERELASTICITY

A perturbed Lagrangian formulation for nearly incompressible and incom pressible hyperelasticity is developed by performing a conjugate trans formation on the volumetric energy function. The formulation is develo ped without reference to any specific material models or volumetric en ergy functions. Solution existence conditions for general nearly incom pressible hyperelasticity problems and their discrete counterparts are described. A discussion on the convergence of nearly incompressible s olutions to an incompressible solution of continuous as well as discre te hyperelasticity problems is given. The rate of convergence with res pect to the compressibility parameter is shown to be one in several nu merical examples.