Abstract
In this work, a fully automated adaptive remeshing strategy, based on a tetrahedral element for 3D metal forming processes, was proposed in order to solve problems associated with the severe mesh distortion that occurs during the computation. The main idea is to use the h-type adaptive mesh in combination with an a-posteriori error estimator measured (by the energy norm) on each finite elements to locally control the mesh modification-as-needed. Once a new mesh is generated, all history-dependent variables must be carefully transferred between subsequent meshes. Therefore, several transfer techniques are described and compared. A special attention is given to restore the local mechanical equilibrium of the system with a new methodology. After presenting the necessary adaptive remeshing steps, some 3D analytic and numerical results using the proposed adaptive strategy are given to demonstrate the capabilities of the proposed equilibrated approach and to illustrate some practical characteristics of our remeshing process.
Similar content being viewed by others
References
Diez P, Calderon G (2007) Remeshing criteria and proper error representations for goal oriented h-adaptivity. Comput Methods Appl Mech Engrg 196(4-6):719–733
Ainsworth M, Oden JT (1997) A posteriori error estimation in finite element analysis. Comput Methods Appl Mech Engrg 142(1-2):1–88
Verfurth R (1999) A review of a posteriori error estimation techniques for elasticity problems. Comput Methods Appl Mech Engrg 176(1-4):419–440
Lo SH (1991) Volume discretization into tetrahedra-1. Verification and orientation of boundary surfaces. Comput Struct 39(5):493–500
Lo SH (1991) Volume discretization into tetrahedra-II. 3D triangulation by advancing front approach. Comput Struct 39(5):501–511
Dureisseix D, Bavestrello H (2006) Information transfer between incompatible finite element meshes: application to coupled thermo-viscoelasticity. Comput Methods Appl Mech Engrg 85:6523–6541
Zeramdini B, Robert C, Germain G, Pottier T (2016) Simulation of metal forming processes with a 3D adaptive remeshing procedure. AIP Conf Proceed. https://doi.org/10.1063/1.4963636
Srikanth A, Zabaras N (2000) Shape optimization and preform design in metal forming processes. Comput Methods Appl Mech Engrg 190(13–14):1859–1901
Kumar S, Fourment L, Guerdoux S (2015) Parallel, second-order and consistent remeshing transfer operators for evolving meshes with superconvergence property on surface and volume. Finite Elem Anal Des 93:70–84
Peric D, Hochard C, Dutko M, Owen DRJ (1996) Transfer operators for evolving meshes in small strain elasto-placticity. Comput Methods Appl Mech Engrg 137(3-4):331–344
Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery (SPR) and adaptive finite element. Comput Methods Appl Mech Engrg 101(1-3):207–224
Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimation. Part I: the recovery technique. Internat J Numer Methods Engrg 33(7):1331–1364
Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimation. Part II: error estimates and adaptivity. Internat J Numer Methods Engrg 33(7):1365–1382
Babuška I, Rheinbildt WC (1978) A posteriori error estimates for the finite element method. Internat J Numer Methods Engrg 12(10):1597–1615
Ladevèze P, Coffignal G, Pelle J.P (1986) Accuracy of elastoplastic and dynamic analysis. In Babuška I, Zienkiewicz O.C, Gago J and Oliveira E.R de A, ch.11 Accuracy Estimates and Adaptive Refinements in Finite Element Computations, John Wiley & Sons Ltd pp 181–203
Zienkiewicz OC, Zhu JZ (1987) A simple error estimator and adaptive procedure for practical engineering analysis. Int J Numer Methods Eng 24(2):337–357
Ladevèze P, Pelle J.P (2004) Mastering calculation in linear and nonlinear mechanics, Berlin
Boussetta R, Fourment L (2004) A posteriori error estimation and three-dimensional adaptive remeshing: application to error control of non-steady metal forming simulations. AIP Conf Proc 712:2246–2251
Boussetta R, Coupez T, Fourment L (2006) Adaptive remeshing based on a posteriori error estimation for forging simulation. Comput Methods Appl Mech Engrg 195(48-49):6626–6645
Coorevits P, Bellenger E (2004) Alternative mesh optimality criteria for h-adaptive finite element method. Finite Elem Anal Des 40:2195–1215
Ciarlet P.G (1978) The finite element method for elliptic problems. North-Holland publishing company, Amsterdam, New York, 45, 4
Khoei AR, Gharehbaghi SA, Tabarraie AR, Riahi A (2007) Error estimation, adaptivity and data transfer in enriched plasticity continua to analysis of shear band localization. Appl Math Model 31(6):983–1000
Babuška I, Strouboulis T, Upadhyay CS, Gangaraj SK, Copps K (1994) Validation of a posteriori error estimators by numerical approach. Int J Numer Methods Engrg 37(7):1073–1123
Wiberg NE, Abdulwahab F, Ziukas S (1994) Enhanced superconvergent patch recovery incorporating equilibrium and boundary conditions. Inter J for Numer Methods Engrg 37(20):3417–3440
Liszka T, Orkisz J (1980) The finite differences method at arbitrary irregular grids and its application in applied machanics. Comput Struct 11(1-2):83–95
Liszka T (1984) An interpolation method for an irregular net of nodes. Int J Numer Methods Engrg 20(9):1599–1612
Johnson G.R, Cook W.K (1983) A constitutive model and data for metals subjected to large strains high strain rates and high temperatures. 7th international symposium on Balistics pp 541–547
Ayed Y, Germain G, Ammar A, Furet B (2016) Thermo-mechanical characterization of the Ti17 titanium alloy under extreme loading conditions. Int J Adv Manuf Technol 90:5–8. https://doi.org/10.1007/s00170-016-9476-5
Hu Y, Randolph MF (1998) H-adaptive FE analysis of elasto-plastic non-homogeneous soil with large deformation. Comput Geotech 23(1-2):61–83
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
• Adaptive mesh strategy is developed for 3D metal material processes.
• Different methods recovery techniques are compared.
• Equilibrium method for dynamic explicit scheme is proposed.
• Results are compared with experiments test.
Rights and permissions
About this article
Cite this article
Zeramdini, B., Robert, C., Germain, G. et al. Numerical simulation of metal forming processes with 3D adaptive Remeshing strategy based on a posteriori error estimation. Int J Mater Form 12, 411–428 (2019). https://doi.org/10.1007/s12289-018-1425-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12289-018-1425-4