Parametrized variational principles encompassing compressible and incompressible elasticity

Abstract

A parametrized five-field variational principle that can accommodate both compressible and incompressible hyperelasticity is presented. The primary variables are mean and deviatoric stresses, mean and deviatoric strains, and displacements. Through appropriate selection of parameters the functional of this general principle specializes to those previously presented by Atluri-Reissner, Herrmann and Franca.