×

Improved explicit integration in plasticity. (English) Zbl 1183.74349

Summary: The article presents a simple but efficient numerical scheme for the integration of non-linear constitutive equations, in which the principal reason for the inaccuracy of the classical explicit schemes, for example forward-Euler scheme, is effectively eliminated. In the newly developed explicit scheme, where there is no need for iteration, the implementation simplicity of the forward-Euler scheme and accuracy of the approach, which is using the backward-Euler scheme to integrate the constitutive equations, are successfully combined. Computational performance of the proposed next increment corrects error (NICE) integration scheme, particularly regarding the accuracy and the CPU time consumption, is first analysed on a case of complex loading of a material point. When comparing it to the forward-Euler, backward-Euler, trapezoidal and midpoint integration schemes, it turns out that because of its capability of a fast and relatively accurate integration of the constitutive equations, the NICE scheme is very convenient for the integration of constitutive models, where a direct solution technique is used to solve a boundary value problem. Although the deduction of the new integration scheme is general, its implementation for shell applications needs 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. The NICE scheme, which was also implemented into ABAQUS/Explicit via User Material Subroutine (VUMAT) interface platform, has been additionally compared with the ABAQUS/Explicit default integration scheme (backward-Euler) and forward-Euler scheme. Two loading case-studies, namely the bending of a square plate and the stretching of a specimen including the onset of necking, are considered with two constitutive models - the von Mises and GTN material model being adopted. Generally, the NICE scheme has demonstrated to be advantageous in cases, where reasonable accuracy and very fast integration of the constitutive model is demanded, which is mostly the case in engineering computations with a direct solution method, for example explicit dynamics and metal forming process simulations.

MSC:

74S20 Finite difference methods applied to problems in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74K25 Shells
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Aravas, On the numerical integration of a class of pressure-dependent plasticity, International Journal for Numerical Methods in Engineering 24 (7) pp 1395– (1987) · Zbl 0613.73029
[2] Ortiz, An analysis of a new class of integration algorithms for elastoplastic constitutive relations, International Journal for Numerical Methods in Engineering 23 pp 353– (1986) · Zbl 0585.73058
[3] Ding, Substepping algorithms with stress correction for the simulation of sheet metal forming process, International Journal of Mechanical Sciences 49 (11) pp 1289– (2007)
[4] Alireza, A framework for numerical integration of crystal elasto-plastic constitutive equations compatible with explicit finite element codes, International Journal of Plasticity 23 pp 1918– (2007)
[5] Sloan, Refined explicit integration of elastoplastic models with automatic error control, Engineering Computations 18 pp 121– (2001)
[6] Potts, A critical assessment of methods of correcting for drift from the yield surface in elasto-plastic finite element analysis, International Journal for Numerical Methods in Engineering 9 pp 149– (1985) · doi:10.1002/nag.1610090204
[7] Mattsson, A method to correct yield surface drift in soil plasticity under mixed control and explicit integration, International Journal for Numerical and Analytical Methods in Geomechanics 21 (3) pp 175– (1998) · Zbl 0896.73046
[8] User’s Manual. ABAQUS Version 6.6. Simulia: Providence, RI, 2006.
[9] Štok, Coupling FEM and BEM for computationally efficient solutions of multi-physics and multi-domain problems, Engineering Computations 22 (5/6) pp 711– (2005) · Zbl 1186.74103
[10] Gurson, Continuum theory of ductile rupture by void nucleation and growth: part 1-yield criteria and flow rules for porous ductile media, Journal of Engineering Materials and Technology 99 pp 2– (1977) · doi:10.1115/1.3443401
[11] Tvergaard, Influence of voids on shear band instabilities under plane strain conditions, International Journal of Fracture 17 pp 389– (1981)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.