On the numerical implementation of elasto-plastic constitutive equations for metal forming
Keywords:elasto-plasticity, time integration, constitutive algorithm
This paper is devoted to the time integration of elasto-plastic constitutive models, in view of their implementation in finite element software for the simulation of metal forming processes. Both implicit and explicit time integration schemes are reviewed and presented in algorithmic form. The incremental kinematics are also treated, so that the proposed algorithms can be used stand-alone, outside a finite element code, or they can serve to implement non-classical incremental kinematics. Full algorithms are provided, along with examples of application to non-monotonic loading for a mild steel and a dual phase steel.
HUGHES, T.J.R., Numerical implementation of constitutive models: rate-independent deviatoric plasticity, in: Theoretical foundations for large-scale computations for non-linear material behavior (eds. S. Nemat-Nasser et al.), Martinus Nijhoff Publishers, Dordrecht, The Netherlands, 1984, pp. 29–57.
KEAVEY, M.A., A canonical form return mapping algorithm for rate independent plasticity, Int. J. Num. Meth. Eng., 53, 6, pp. 1491–1510, 2002.
KEAVEY, M.A., A simplified canonical form algorithm with application to porous metal plasticity, Int. J. Num. Meth. Eng., 65, 5, pp. 679–700, 2006.
SLOAN, S., ABBO, A., SHENG, D., Refined explicit integration of elastoplastic models with automatic error control, Engineering Computations, 18, 1–2, pp. 121–154, 2001.
DING, K.Z., QIN, Q.H., CARDEW-HALL, M., Substepping algorithms with stress correction for the simulation of sheet metal forming process, International Journal of Mechanical Sciences, 49, 11, pp. 1289–1308, 2007.
VRH, M. , HALILOVI?, M. , ŠTOK, B., Improved explicit integration in plasticity, Int. J. Num. Meth. Eng., 81, 7, pp. 910–938, 2010.
KOJIC, M., BATHE, K.J., The ‘effective-stress-function’ algorithm for thermo-elasto-plasticity and creep, Int. J. Num. Meth. Eng., 24, 8, pp. 1509–1532, 1987.
MICARI, F., FRATINI, L., ALBERTI, N., An explicit model for the thermal-mechanical analysis of hot metal forming processes, Annals of the CIRP, 44, 1, pp. 193–196, 1995.
BERGMAN, G., OLDENBURG, M., A finite element model for thermomechanical analysis of sheet metal forming, Int. J. Num. Meth. Eng., 59, 9, pp. 1167–1186, 2004.
SIMO, J., TAYLOR, R., Consistent tangent operators for rate-independent elasto-plasticity. Computer Methods in Applied Mechanics and Engineering, 48, 1, pp. 101–118, 1985.
ORTIZ, M., POPOV, E.P., Accuracy and stability of integration algorithms for elastoplastic constitutive relations, Int. J. Num. Meth. Eng., 21, 9, pp. 1561–1576, 1985.
ALVES, J.L., Simulação numérica do processo de estampagem de chapas metálicas: Modelação mecânica e métodos numéricos, PhD Thesis, University of Minho, Portugal, 2003.
HADDAG, B, Contribution to the modeling of sheet metal forming: application to springback and localization, PhD Thesis, ENSAM Metz, France, 2007.
CHABOCHE, J.L., CAILLETAUD, G., Integration methods for complex plastic constitutive equations, Computer Methods in Applied Mechanics and Engineering, 133, 1–2, pp. 125–155, 1996.
BERVEILLER, M., ZAOUI, A., An extension of the self-consistent scheme to plastically-flowing polycrystals, J. Mech. Phys. Sol., 26, 5–6, pp. 325–344, 1978.
PIPARD, J.M., BALAN, T., ABED-MERAIM, F., LEMOINE, X., Elasto-visco-plastic modeling of mild steels for sheet forming applications over a large range of strain rates, International Journal of Solids and Structures, 50, 16–17, pp. 2691–2700, 2013.
RESENDE, T.C., BALAN, T., BOUVIER, S., ABED-MERAIM, F., SABLIN, S.S., Numerical investigation and experimental validation of a plasticity model for sheet steel forming, Modelling and Simulation in Materials Science and Engineering, 21, 1, doi:10.1088/0965- 0393/21/1/015008, 2013.
FANSI, J., BALAN, T., LEMOINE, X., MAIRE, E., LANDRON, C., BOUAZIZ, O., BEN BETTAIEB, M., HABRAKEN, A.M., Numerical investigation and experimental validation of physically-based advanced GTN model for DP steels, Materials Science and Engineering A, 569, pp. 1–12, 2013.
MANDEL, J., Définition d’un repère privilégié pour l’étude des transformations anélastiques du polycristal, Journal de Mécanique Théorique et Appliquée, 1, pp. 7-23, 1982.
KURODA, M., Interpretation of the behavior of metals under large plastic shear deformations: a macroscopic approach, International Journal of Plasticity, 13, 4, pp. 359-383, 1997.
PEETERS, B., HOFERLIN, E., VAN HOUTTE, P., AERNOUDT, E., Assessment of crystal plasticity based calculation of the lattice spin of polycrystalline metals for FE implementation, International Journal of Plasticity, 17, 6, pp. 819–836, 2001.
DAFALIAS, Y.F., Plastic spin: necessity or redundancy, International Journal of Plasticity, 14, 9, pp. 909–931, 1998.
HAN, C.S., CHOI, Y., LEE, J.K., WAGONER, R.H., A FE formulation for elasto-plastic materials with planar anisotropic yield functions and plastic spin, International Journal of Solids and Structures, 39, 20, pp. 5123–5141, 2002.
DUCHÊNE, L., LELOTTE, T., FLORES, P., BOUVIER, S., HABRAKEN, A.M., Rotation of axes for anisotropic metal in FEM simulations, International Journal of Plasticity, 24, 3, pp. 397–427, 2008.
SALAHOUELHADJ, A., ABED-MERAIM, F., CHALAL, H., BALAN, T., Implementation of the continuum shell finite element SHB8PS for elastic-plastic analysis and application to sheet forming simulation, Archive of Applied Mechanics, 82, 9, pp. 1269–1290, 2012.
TEODOSIU, C., HU, Z., Evolution of the intragranular microstructure at moderate and large strains: Modeling and computational significance. in: Simulation of Materials Processing: Theory, Methods and Applications. Numiform’95 Proceedings, 1995, pp. 173–182.
Copyright (c) 2020 The Romanian Journal of Technical Sciences. Applied Mechanics.
This work is licensed under a Creative Commons Attribution 4.0 International License.