Improved explicit integration in plasticity

Vrh, Halilovič, Štok
2010

In-depth theoretical basis of the new NICE numerical schemes are presented.

The paper presents a simple but efficient new numerical scheme for the integration of nonlinear constitutive equations, in which the principle reason for inaccuracy of the classical forwardEuler scheme is effectively eliminated. 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. Although deduction of the new integration scheme is general, its implementation for shell applications needs a particular care. Namely, in order to satisfy the zero normal stress condition during the whole integration a throughthickness strain increment has to be adequately chosen in each integration step. In a numerical validation of the proposed integration scheme two constitutive models, the von Mises and GTN material model are applied, and two loading casestudies, a bending of a square plate and stretching of a specimen including onset of necking, are considered. The accuracy of the NICE 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.

VRH, Marko, HALILOVIČ, Miroslav, ŠTOK, Boris. Improved explicit integration in plasticity. Int. j. numer. methods eng., 2010, vol. 81, iss. 7, str. 910-938.