On the perturbed Lagrangian formulation for nearly incompressible and incompressible hyperelasticity Original Research Article

A perturbed Lagrangian formulation for nearly incompressible and incompressible hyperelasticity is developed by performing a conjugate transformation on the volumetric energy function. The formulation is developed without reference to any specific material models or volumetric energy functions. Solution existence conditions for general nearly incompressible hyperelasticity problems and their discrete counterparts are described. A discussion on the convergence of nearly incompressible solutions to an incompressible solution of continuous as well as discrete hyperelasticity problems is given. The rate of convergence with respect to the compressibility parameter is shown to be one in several numerical examples.