NICE - An explicit numerical scheme for efficient integration of nonlinear constitutive equations

The paper presents a simple but efficient new numerical scheme for the integration of nonlinear constitutive equations. Although it can be used for integration of system of algebraic and differential equations in general, the scheme is primarily developed for use with direct solution methods for solving boundary value problems, e.g. explicit dynamic analysis in ABAQUS/Explicit. In the developed explicit scheme, where no iteration needs to be done, the implementation simplicity of the forward-Euler scheme and accuracy of the backward-Euler scheme are successfully combined. Properties of the proposed NICE scheme, which was also implemented into ABAQUS/Explicit via User Material Subroutine (VUMAT) interface platform, are compared with the properties of the classical forward-Euler scheme and backward-Euler scheme. For this purpose two highly nonlinear examples, with the von Mises and GTN material model considered, have been studied. The accuracy of the new scheme is demonstrated to be at least of the same level as experienced by the backward-Euler scheme, if we compare them under condition of the same CPU time consumption. Besides, simplicity of the NICE scheme, which is due to implementation similarity with the classical forward-Euler scheme, is its great advantage.