Js. Chen et al., ON THE PERTURBED LAGRANGIAN FORMULATION FOR NEARLY INCOMPRESSIBLE ANDINCOMPRESSIBLE HYPERELASTICITY, Computer methods in applied mechanics and engineering, 142(3-4), 1997, pp. 335-351
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.