On the use of large time steps with an energy momentum conserving algorithm for non-linear hypoelastic constitutive models

Abstract

This paper presents an extension of the energy momentum conserving algorithm, developed by the authors for hypoelastic constitutive models. For such a material, contrarily to hyperelastic models, no potential can be defined, and thus the conservation of the energy is ensured only if the elastic work of deformation can be restored by the scheme. In a previous paper, we proposed a new expression of internal forces at the finite element level which is shown to verify this property. We also demonstrated that the work of plastic deformation is positive and consistent with the material model. In this paper, the second order terms that were neglected in the previous work are now taken into account. Several numerical applications are presented to demonstrate the necessity of taking these terms into account once large time step sizes are used. The limitations of the Newmark algorithm in the non-linear range are also illustrated.