Recent and future developments in finite element metal forming simulation
S. Andrietti1
, J.-L. Chenot1,2, Marc Bernacki2
, P.O. Bouchard2, L. Fourment2, E. Hachem2, E. Perchat1
1Transvalor, 694 Avenue du Dr. Maurice Donat, 06255 Mougins Cedex, France.
2CEMEF, Mines Paristech, B.P. 207, 06904 Sophia Antipolis Cedex, France.
DOI:
https://doi.org/10.7494/cmms.2015.2.0536
Abstract:
After more than 40 years of development, finite element metal forming simulation has reached a high level of maturity. After a short mechanical and thermal introduction, the main scientific and technical developments are briefly described. We consider numerical issues, such as adaptive remeshing or parallel computing coupling phenomena for a more realistic simulation, such as thermal and metallurgical coupling, with a special emphasis on modeling of microstructure evolution, the use of optimization for forming processes or for parameters identification. Finally the main potential future research fields for the next 10 years are outlined: process stability and stochastic approaches, more effective massively parallel computing and extension of the application to generate the whole “virtual factory”.
Cite as:
Andrietti, S., Chenot, J., Bernacki, M., Bouchard, P., Fourment, L., Hachem, E., & Perchat, E. (2015). Recent and future developments in finite element metal forming simulation. Computer Methods in Materials Science, 15(2), 265-293. https://doi.org/10.7494/cmms.2015.2.0536
Article (PDF):

Keywords:
Plasticity, Finite element modeling, Metal forming simulation
Publication dates:
Received: 05.01.2014, accepted: 30.03.2014, published:
References:
Agnoli, A., Bozzolo, N., Logé, R., Franchet, J.-M., Laigo, J., Bernacki, M., 2014, Development of a level set methodology to simulate grain growth in the presence of real secondary phase particles and stored energy – Application to nickel-based superalloy, Comp. Mater. Sci., 89, 233-241.
Archard, J. F., Hirst, W., 1956, The Wear of Metals under Unlubricated Conditions, Proceedings of the Royal Society, A
236, 397-410.
Barlat, F., Lian, J., 1989, Plastic behaviour and stretchability of sheet metals (Part I) A yield function for orthotropic
sheet under plane stress conditions, Int. J. Plasticity, 5, 51-56.
Bernacki, M., Chastel, Y., Coupez, T., Logé, R. E., 2008, Level set framework for the numerical modelling of primary
recrystallization in polycrystalline materials, Scripta Mater., 58, 12, 1129-1132.
Bernacki, M., Resk, H., Coupez, T., Logé, R., 2009, Finite element model of primary recrystallization in polycrystalline aggregates using a level set framework, Simul. Mater. Sci. Eng., 17, 064006, doi:10.1088/0965-
0393/17/6/064006.
Bernacki, M., Loge, R., Coupez, T., 2011, Level set framework for the finite-element modelling of recrystallization and
grain growth in polycrystalline materials, Scripta Mat., 64, 525-528.
Bernard, P., Bag, S., Huang, K., Logé, R. E., 2011, A two-site mean field model of discontinuous dynamic recrystallization, Materials Science and Engineering, A 528, 7357-7367.
Bohatier, C., Chenot, J.-L., 1985, Finite element formulations for non-steady-state large viscoplastic deformation, Int.
. for Numerical Methods in Engineering, 21, 9, 1697-1708.
Bonte, M., Fourment, L., Do, T., van den Boogaard, A., Huétink, J., 2010, Optimization of forging processes
using Finite Element simulations, Structural and Multidisciplinary Optimization, 42, 5, 797-810.
Bossavit, A., 1993, Electromagnétisme en vue de la modélisation, Mathématiques et applications, 14, SpringerVerlag, Paris, France (in French).
Bouchard, P.-O., Bourgeon, L., Fayolle, S. Mocellin, K., 2011, An enhanced Lemaitre model formulation for materials
processing damage computation, Int. J. Mater. Form., 4(3), 299-315.
Brahme, A., Alvi, M. H., Saylor, D., Fridy, J., Rolett, A. D., 2006, 3D reconstruction of microstructure in a commercial purity aluminum, Scripta Mater., 55, 1, 75-80.
Brandt, A., 2002, Multiscale Scientific Computation: Review 2001, in Multiscale and Multi resolution Methods, T.
Barth, T. Chan, and R. Haimes Editors., Springer, Berlin, 3-95.
Brooks, A. N., Hughes, T. J. R., 1982, Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Computer Methods in Applied Mechanics and Engineering, 32, 199-259.
Cao, T.S., Gaillac, A., Montmitonnet, P., Bouchard, P.-O., 2013, Identification methodology and comparison of phenomenological ductile damage models via hybrid numericalexperimental analysis of fracture experiments conducted on a zirconium alloy, International Journal of Solids and Structures, 50, 24, 3989-3999.
Cao, T.-S, Gachet, J.-M, Montmitonnet, P., Bouchard, P.-O., 2014, A Lode-dependent enhanced Lemaitre model for
ductile fracture prediction at low stress triaxiality, Engineering Fracture Mechanics, 124-125, 80-96.
Cao, T.S., Maire, E., Verdu, C., Bobadilla, C., Lasne, P., Montmitonnet P., Bouchard P.-O., 2014b, Characterization of ductile damage for a high carbon steel using 3D X-ray micro-tomography and mechanical tests – Application to the identification of a shear modified GTN model, Computational Materials Science, 84, 175-187.
Cardinaux, D., 2008, Etude et modélisation numérique 3D par éléments finis d’un procédé de traitement thermique de tôles embouties après chauffage par induction : application à un renfort de pied central automobile, PhD Thesis,
Mines Paristech, Sophia-Antipolis, France (in French).
Cardinaux, D., Bay, F., Chastel, Y., 2010, A coupled multiphysics model for induction heat treatment processes,
Computer Methods in Materials Science, 10, 4, 307-312.
Chang, K., Feng, W., Chen, L.Q., 2009, Effect of second-phase particle morphology on grain growth kinetics, Acta Mater., 57, 5229-5236.
Chen, L.-Q., 1995, A novel computer simulation technique for modeling grain growth, Scr. Metall. Mater., 32, 1, 115-
120.
Chen, L.-Q., 2002, Phase-field models for microstructure evolution, Ann. Rev. Mater. Res., 32, 113-140.
Chenot, J.-L., 1984, A velocity approach to finite element calculation of elastoplastic and viscoplastic deformation processes, Engineering Computations, 5, 1, 2-9.
Chenot, J.-L., Béraudo, C., Bernacki, M., Fourment, L., 2014, Finite element simulation of multi material metal forming, 11th International Conference on Technology of Plasticity, Procedia Engineering 10/2014; 81:2427-DOI: 10.1016/j.proeng.2014.10.345.
Chenot, J.L., Fourment, L., Mocellin, K., 2002, Numerical treatment of contact and friction in FE simulation of
forming processes, J. Mater. Process. Technol., 125-126, 45-52.
Chinesta, F., Cueto, E., 2014, Introduction, in PGD-Based Modeling of Materials, Structures and Processes,
ESAFORM Bookseries in material forming, Springer International Publishing, 1-24.
Codina, R., Gonzalez-Ondina, J. M., Diaz-Hernandez, G., Principe, J., 2008, Finite element approximation of the modified Boussinesq equations using a stabilized formulation, International Journal for Numerical Methods in
Fluids, 57, 1249-1268.
Collins, J. B., Levine, H., 1985, Diffuse interface model of diffusion-limited crystal growth, Phys. Rev. B, 31, 9,
6119.
Cornfield, G. C., Johnson, R. H., 1973, Theoretical predictions of plastic flow in hot rolling including the effect of various temperature distributions, J. Iron Steel Inst., 211, 567.
Coupez T., Digonnet H., Ducloux R., 2000, Parallel meshing and remeshing, Applied Mathematical Modelling, 25,
153-157.
Dawson, P. R., 2000, Computational crystal plasticity, Int J. Solids Struct., 37,1-2, 115-130.
Dawson, P. R., Miller, M. P., Han, T.-S., Bernier, J.-L., 2005, An accelerated methodology for the evaluation of
critical properties in polyphased alloys, Metall. Mater. Trans., A 36, 1627-1641.
Delalondre, F., 2008, Simulation and 3-D analysis of adiabatic shear bands in high speed metal forming processes, PhD Mines ParisTech, Sophia-Antipolis, 243 (in French).
Ducloux, R., Barbelet, M., Fourment, L., 2013, Automatic optimization of a complete manufacturing chain, NUMIFORM, AIP Conf. Proc. 1532, 665-670.
Ejday, M., Fourment, L., 2010, Metamodel assisted multiobjective optimization for metal forming applications,
Mécanique & Industries, 11, 3-4, 223-233.
El Khaoulani, R., Bouchard, P.-O., 2012, An anisotropic mesh adaptation strategy for damage and failure in ductile materials, Finite Elements in Analysis and Design, 59, 1-10.
Elsey, M., Esedoglu, S., Smereka, P., 2009, Diffusion generated motion for grain growth in two and three dimensions, J. Comput. Phys., 228, 8015-8033.
Fabiano, A.-L., Logé, R., Bernacki, M., 2014, Assessment of simplified 2D grain growth models from numerical experiments based on a level set framework, Comp. Mater. Sci., 92, 305-312.
Fourment, L., Chenot J. L., 1994, Adaptive remeshing and error control for forming processes, Revue Européenne des
Éléments finis, 3, 2, 247-279.
Fourment, L., Chenot J. L., Mocellin K., 1999, Numerical formulations and algorithms for solving contact problems
in metal forming simulation, International Journal for Numerical Methods in Engineering, 46, 9, 1435-1462.
Fourment, L., Popa, S., Barboza, J., 2004, A Quasi-Symmetric Contact Formulation For 3D Problems. Application To
Prediction Of Tool Deformation In Forging, 8th International Conference on Numerical Methods in Industrial
Forming Processes (NUMIFORM), Columbus, Ohio, AIP Conf. Proc. 712, 2240.
Fourment, L., 2007, Meta-model based optimisation algorithms for robust optimization of 3D forging sequences, in 10th ESAFORM Conference on Material Forming, Pts A and B, E. Cueto and F. Chinesta, Editors, 21-26.
Fourment, L., 2008, A quasi-symmetric formulation for contact between deformable bodies, European Journal of Computational Mechanics, 17, 5-7, 907, 918.
Gachet, J.-M., Delattre, G., Bouchard, P.-O., 2014, Fracture mechanisms under monotonic and non-monotonic low
Lode angle loading, Engineering Fracture Mechanics, 124-125, 121-141.
Galeao, A.C., Do Carmo, E. G. D., 1988, A consistent approximate upwind Petrov-Galerkin method for convectiondominated problems, Computer Methods In Applied Mechanics and Engineering, 68, 1, 83-95. Hill, R., 1948, A theory of the yielding and plastic flow of anisotropic metals. Proc. Roy. Soc., London, 193, 281-297.
Hitti, K., Laure, P., Coupez, T., Silva, L., Bernacki, M., 2013, Precise generation of complex statistical Representative
Volume Elements (REVs) in a finite element context, Comp. Mater. Sci., 61, 224-238.
Gruau, C., Coupez, T., 3D tetrahedral, unstructured and anisotropic mesh generation with adaptation to natural and
multidomain metric, Comp. Meth in Appl. Mech and Engg., 194, 48-49, 4951-4976.
Habraken, A.-M., Cescotto, S., 1998, Contact between deformable solids, the fully coupled approach, Mathematical & Computer Modelling, 28 (4-8), 153-169.
Hachem, E., Jannoun, G., Veysset, J., Henri, M., Pierrot, R., Poitrault I., Massoni E., Coupez T., 2013, Modeling of
heat transfer and turbulent flows inside industrial furnaces, Simulation Modelling Practice and Theory, 30, 35-53.
Hallberg, H., 2013, A modified level set approach to 2D modeling of dynamic recrystallization, Modelling Simul. Mater. Sci. Eng., 21, 8, 085012.
Hallquist, J. O., Goudreau, G. L., Benson, D. J., 1985, Sliding interfaces with contact-impact in large-scale Lagrangian
Computations, Comput. Meth. Appl. Mech. Engng., 51, 1-3, 107-137.
Hirt, G., Kopp, R., Hofmann, O., Franzke, M., Barton, G., 2007, Implementing a high accuracy Multi-Mesh Method for
incremental Bulk Metal Forming, CIRP AnnalsManufacturing Technology, 56, 313-316.
Iwata, K., Osakada, K., Fujino, S., 1972, Analysis of hydrostatic extrusion by the finite element method., Transactions of the ASME, B, 94-2, 697-703.
Jaouen, O., Costes, F., Barbelet, M., Lasne, P., 2014a, From continuous casting to rolling process simulation with a
full 3D powerful software tool, 1st ESTAD & 31st JSI, 7-8 April, Paris.
Jaouen, O., Costes, F., Lasne, P., Fourment, C., Barbelet, M., ,2014b, Numerical simulation of a shell forming, from hollow ingot to the final product, with a powerful software tool, 2nd International Conference on Ingot Casting Rolling & Forging, ICRF2014, Milano.
Jin, Y., Lin, B., Bernacki, M., Rohrer, G.S., Rollett, A.D., Bozzolo N., 2014, Annealing twin development during recrystallization and grain growth in pure nickel, Material Sci. and Engg. A, 597, 295-303.
Karma, A., 2001, Phase-Field Formulation for Quantitative Modeling of Alloy Solidification, Phys. Rev. Lett., 87, 115701.
Kim, N., Machida, S., Koboyashi, S., 1990, Ring rolling process simulation by the three dimensional finite element
method, Int. J. Machine Tools and Manufacture, 30, 569-577.
Khoei, A.R., Gharehbaghi, S.A., 2007, The superconvergence patch recovery technique and data transfer operators in
3D plasticity problems, Finite Elements in Analysis and Design, 43, 8, 630-648.
Ko, K.J., Cha, P.A., Srolovitz, D., Hwang, N.M., 2009, Abnormal grain growth induced by sub-boundary-enhanced
solid-state wetting: Analysis by phase-field model simulations, Acta Mater., 57, 838-845.
Kugler, G., Turk, R., 2004, Modeling the dynamic recrystallization under multi-stage hot deformation, Acta Mater., 52,
15, 4659-4668.
Kumar, S., Fourment, L., Guerdoux, S., 2015, Parallel, secondorder and consistent remeshing transfer operators for
evolving meshes with superconvergence property on surface and volume, Finite Elements in Analysis and
Design, 93, 70–84, DOI: 10.1016/j.finel.2014.09.002.
Launder, B. E., Spalding, D. B., 1974, The numerical computation of turbulent flows, Computer Methods In Applied
Mechanics And Engineering, 3, 2, 269-289.
Lebon, J., Le Quillec, G., Breitkopf, P., Coelho, R. F., Villon, P., 2014, A two-pronged approach for springback
variability assessment using sparse polynomial chaos expansion and multi-level simulations, International
Journal of Material Forming, 7, 3, 275-287.
Lee, C. H., Kobayashi, S., 1973, New Solutions to Rigid-Plastic Deformation Problems Using a Matrix Method, J. Eng.
Ind., 95, 865.
Logé, R., Bernacki, M., Resk, H., Delannay, L., Digonnet, H., Chastel Y., Coupez T., 2008, Linking plastic deformation to recrystallization in metals using digital microstructures, Philosophical Magazine B, 88, 30-32, 3691-3712.
Mahajan, P., Fourment L, Chenot J.-L., 1998, Implicit scheme for contact analysis in non-steady state forming, Engineering Computations, 15, 6-7, 908-924.
Mesri, Y., Zerguine, W., Digonnet, H., Silva, L., Coupez, T., 2008, Dynamic parallel mesh adaption for three dimensional unstructured meshes: Application to interface tracking. Proceeding of the 18th IMR, Springer,195-212.
Militzer, M., 2011, Phase field modeling of microstructure evolution in steels, Cur. Op. Solid St. Mater. Sci., 15,
106-115.
Moelans, N., Wendler, F., Nestler, B., 2009, Comparative study of two phase-field models for grain growth, Comp. Mater. Sci., 46, 479-490.
Mole, N., Chenot, J. –L., Fourment, L., 1996, A velocity based approach including acceleration to the finite element
computation of viscoplastic problems, Int. J. Numer. Methods Engng., 39, 3439-51.
Mukherjee, M., Prahl, U., Bleck, W., 2010, Modelling of microstructure and flow stress evolution during hot forging,
Steel Research Int., 81, 1102-1116.
Nagata, T., 2005, Simple local interpolation of surfaces using normal vectors, Computer Aided Geometric Design, 22,
327-347.Nagai, T., Ohta, S., Kawasaki, K., Okuzono, T., 1990, Computer simulation of cellular pattern growth in two and three dimensions, Phase Trans., 28, 177-211.
Nahshon, K., Hutchinson, J., 2008, Modification of the Gurson model for shear failure, Eur. J. Mech. A/Solids, 27, 1, 1-
17.
Nédélec, J. C., 1986, A new family of mixed finite elements in R3 , Numer. Math., 50, 57-81.
Page, D. L., Sun, Y., Koschan, A. F., Paik, J., Abidi, M. A., 2002, Normal Vector Voting: Crease Detection and Curvature Estimation on Large, Noisy Meshes, Graphical Models, 64, 199-229.
Osher, S., Sethian, J. A., 1988, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton–
Jacobi formulations, J. Comput. Phys., 79, 12-49, doi:10.1016/0021-9991(88)90002-2.
Piekos, K., Tarasiuk, J., Wierzbanowski, K., Bacroix, B., 2008a, Stochastic vertex model of recrystallization, Comp. Mater. Sci., 42, 1, 36-42.
Piekos, K., Tarasiuk, J., Wierzbanowski, K., Bacroix, B., 2008b, Generalized vertex model of recrystallization – Application to polycrystalline copper, Comp. Mater. Sci., 42, 4, 584-594.
Ramadan, M., Fourment, L., Digonnet, H., 2009, A parallel two mesh method for speeding-up progresses with localized deformations: application to cogging, Int. J. of Material Forming, 2, Supplement 1, 581-584.
Resk, H., Delannay, L., Bernacki, M., Coupez, T., Logé, R.E., 2009, Adaptive mesh refinement and automatic remeshing in crystal plasticity finite element simulations, Modelling Simul. Mater. Sci. Eng., 17, 075012.
Rey, B., Mocellin, K., Fourment, L., 2008, A node-nested Galerkin multigrid method for metal forging simulation,
Computing and Visualization in Science, 11, 1, 17-25.
Rollett A.D., Raabe D., 2001, A hybrid model for mesoscopic simulation of recrystallization, Comput. Mater. Sci., 21,
69-78.
Roux, E., 2011, Mechanical joining- Process optimization strategies and identification of materials mechanical behaviors, PhD at Ecole des Mines de Paris, Sophia Antipolis (in French).
Roux, E., Bouchard, P.-O., 2011, Numerical investigation of ductile damage parameters identification: benefit of local measurements, A. J. Kassab, E. A. Divo Editors, the7th International Conference on Inverse Problems in Engineering (ICIPE), May 2011, Orlando, United States. Centecorp Publishing, 221-226.
Roux, E., Bernacki, M., Bouchard, P.-O., 2013, A level set and anisotropic adaptive remeshing strategy for the modeling of void growth under large plastic strain, Computational Materials Science, 68, 32-46.
Roux, E., Shakoor, M., Bernacki, M., Bouchard, P.-O., 2014, A new finite element approach for modelling ductile damage void nucleation and growth – analysis of loading path effect on damage mechanisms, Modelling Simul.
Mater. Sci. Eng., 22, 075001, doi:10.1088/0965-0393/22/7/075001.
Ryckelynck, D., 2009, Hyper-reduction of mechanical models involving internal variables, Int. J. Numer. Meth.
Engng., 77, 1, 75-89.
Saby, M., Bernacki, M., Roux, E., Bouchard, P.-O., 2013, Three-dimensional analysis of real void closure at the
meso-scale during hot metal forming processes, Computational Materials Science, 77, 194-201.
Saby, M., Bernacki, M., Bouchard, P.-O., 2014, Understanding and modeling of void closure mechanisms in hot metal
forming processes: a multiscale approach, 11th International Conference on Technology of Plasticity, ICTP, 19-24 October 2014, Nagoya Congress Center, Nagoya,Japan.
Sethian, J.A., 1996, Level Set Methods, Cambridge University Press, Cambridge.
Song, G., Bjorge, T., Holen, J., Magnussen, B. F., 1997, Simulation of fluid flow and gaseous radiation heat transfer in a natural gas-fired furnace, International Journal of Numerical Methods for Heat and Fluid Flow, 7, 169-182.
Strano, M. A, 2008, Technique for FEM optimization under uncertainty of time-dependent process variables in sheet
metal forming, Int. J. Mater. Form., 1, 13-20.
Surdon, G., Chenot, J.-L., 1987, Finite element calculation of three-dimensional hot forging, Int. J. Numer. Meth.
Eng., 24, 2107-2117.
Syha, M., Weygand, D., 2010, A generalized vertex dynamics model for grain growth in three dimensions, Modelling
Simul. Mater. Sci. Eng., 18, 015010.
Takaki, T., Hisakuni, Y., Hirouchi, T., Yamanaka, A., Tomita, Y., 2009, Multi-phase-field simulations for dynamic recrystallization, Comput. Mater. Sci., 45, 881-888.
Teodorescu, M., Lasne, P., Logé, R., 2007, Modeling recrystallization for 3D multi-pass forming processes, Materials
Science Forum, 558-559, 1201-1206.
Traore, K., Forestier, R., Mocellin, K., Montmitonnet, P., Souchet M., 2001, Three dimensional finite element simulation of ring rolling, Proc. of the 7th International Conference on Numerical Methods in Industrial Forming
Processes NUMIFORM 2001, ed. by K. Mori, A. A. Balkema, 595-600.
Wagoner, R. H., Chenot, J.-L., 2001, Metal forming analysis, Cambridge University Press, Cambridge.
Wang, C., Liu, G., 2003, On the stability of grain structure with initial Weibull grain size distribution, Mater. Lett., 57,
28, 4424-4428.
Wiebenga, J. H., Weiss, M., Rolfe, B., Van Den Boogaard, A. H., 2013, Product defect compensation by robust
ptimization of a cold roll forming process, Journal of Materials Processing Technology, 213, 6, 978-986.
Weygand, D., Brechet, Y., Lepinoux, J., 2001, A vertex simulation of grain growth in 2D and 3D, Adv. Eng. Mater.,
3,1-2, 67-71.
Xu, T., Li, M., 2009, Topological and statistical properties of a constrained Voronoi tessellation, Phil. Mag., 89, 349-
374.
Zabaras, N., Bao, Y., Srikanth, A., Frazier, W. G., 2000, A continuum Lagrangian sensitivity analysis for metal
forming processes with applications to die design problems, Int. J. Numer. Meth. Engng, 48, 679-720.
Zienkiewicz, O. C., Godbole, K., 1974, Flow of Plastic and Visco-Plastic Solids with Special Reference to Extrusion
and Forming Processes, Int. J. Numer. Meth. Eng., 8, 1, 1-16.
Zienkiewicz, O.C., Zhu J.Z., 1992, The superconvergent patch recovery (SPR) and adaptive finite element refinement,
Computer Methods in Applied Mechanics and Engineering, 101, 207-224.