It was proven mathematically and with simulations that the NICE scheme does not become unstable at normal simulations with explicit FEM programs.
The paper deals with the integration of elasto-plastic constitutive models using recently developed NICE integration scheme. The emphasis is put on the stability of the integration, since this issue was not sufficiently addressed in previous publications of the NICE. Nonlinear boundary value problems are nowadays typically solved numerically using finite element method (FEM) with implicit “static” (e.g. ABAQUS/Standard) or explicit “dynamic” approach (e.g. ABAQUS/Explicit). The NICE scheme was primarily developed for the integration of elasto-plastic constitutive models within explicit integration of a given boundary value problem, as a replacement for traditionally used backward-Euler scheme. The simplicity of the implementation, more than satisfactory accuracy and low time consumption of calculation, certainly outperforms the properties of other available schemes, including properties of the backward-Euler scheme. The only open issue regarding the NICE scheme is its conditional stability, which originates from the integration of evolution equations in a “forward” manner, whereas the backward-Euler scheme exhibits unconditional stability. The aim of this paper is to derive stable time increment for the NICE scheme and to show, that for practical quasi-static applications it is much larger than the stable time increment size given for the integration of dynamic boundary value problem equations.
STARMAN, Bojan, HALILOVIČ, Miroslav, VRH, Marko, ŠTOK, Boris. On the stability of the recently developed NICE integration scheme. V: OÑATE, Eugenio (ur.). Computational Plasticity XII : proceedings of the XII International Conference on Computational Plasticity - Fundamentals and Applications, COMPLAST XII, Barcelona, Spain 3 - 5 September 2013.