A New Energy-Dissipative Momentum-Conserving Time Integration Scheme Using the Variational Updates Framework.

Although they are the most widely used time integration algorithms for finite-element discretizations, algorithms based on the Newmark family are numerically stable only for linear
models. To overcome that drawback, researches have recently focused on time integration algorithms stable in the non-linear range, leading to the development of Energy Momentum Conserving Algorithms or EMCA. A new Energy Momentum Conserving Algorithm was recently
presented by the authors for elasto-plastic material models. This algorithm is based on a variational formulation of elasto-plastic updates for which the stress tensor always derives from an incremental potential, even when plastic behavior is considered. In this work this formalism is used to develop Energy-Dissipative Momentum-Conserving time integration algorithms, which
have property of being stable in non-linear range, but also dissipate high-frequency numerical
modes to improve the convergence properties. Using the potential existence of the variational
updates framework, the verification of the numerical dissipation of energy in the non-linear
range can easily be demonstrated.