Energy-dissipative momentum-conserving time-stepping algorithms for finite strain multiplicative plasticity

This paper presents a new energy-dissipative momentum-conserving algorithm for multiplicative models of finite strain plasticity. The proposed scheme preserves exactly the conservation laws of linear and angular momenta, and leads to the exact energy dissipation between the two computed solutions in a given time step. In particular, the energy is exactly conserved if the step is elastic, thus recovering existing energy–momentum-conserving schemes in the purely elastic range. Extensions accommodating a strictly non-negative numerical energy dissipation in the high-frequency to handle the numerical stiffness of the problem are also discussed briefly. These conservation/dissipation properties are proven rigorously in the very nonlinear setting of multiplicative finite strain plasticity. In fact, the analysis drives the design of the new return mapping algorithm proposed to integrate the plastic evolution equations so the above dissipation/conservation properties hold. These analyses account for the spatial discretization of the problem in the context of the finite element method. Several representative numerical simulations are presented to illustrate the performance of the new algorithm.