An energy-momentum conserving algorithm for non-linear hypoelastic constitutive models

This paper presents an extension of the energy momentum conserving algorithm, usually developed for hyperelastic constitutive models, to the hypoelastic constitutive models. For such a material no potential can be de ned, and thus the conservation of the energy is ensured only if the elastic work of the deformation can be restored by the scheme. We propose a new expression of internal forces at the element level which is shown to verify this property. We also demonstrate that the work of plastic deformation is positive and consistent with the material model. Finally several numerical applications are presented