journal article·2026-06Open access

A scientific benchmark for elasto-plastic constitutive modeling - Part I: micro- and macroscopic experimental data set and benchmark problem

Lorenz Maier, Erik Walz, Michael Hofmann, Joana Rebelo Kornmeier, Rongfei Juan, Junhe Lian, Emad Maawad, Wolfram Volk, Christoph Hartmann

Abstract

Abstract An accurate and diverse set of experimental data is essential for characterizing material behavior across different length scales and for calibrating the respective constitutive models. An independent validation experiment, the MUC-Test, is presented to validate such constitutive models. The benchmark dataset provides raw experimental data that serves as the basis for calibrating constitutive models of varying complexity. The material investigated is a dual-phase steel (DP800HHE). The conducted microscale experiments investigate the material properties at the grain level. These experiments include nanoindentation, electron backscatter diffraction, and in-situ synchrotron measurements to capture the material’s microstructural behavior. These data serve as the basis for generating representative volume elements and for phase-specific calibration of the crystal plasticity models. On the macroscale, a wide range of experiments has been conducted, including tensile, tension-compression, plane-strain, shear, layer-compression, and cyclic tensile tests. This data can be used to calibrate flow curves and yield locus curves. Part I of this benchmark paper series details the experiments and provides data for calibrating both microscopic and macroscopic models. It also introduces the benchmark problem based on the MUC-Test for validation of these models. Dataset https://zenodo.org/records/18431261
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Metallurgy and Material Forming · Metal Forming Simulation Techniques · High-Velocity Impact and Material Behavior

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (66)

Show source-provided references
1. Deng J, Dong W, Socher R et al (2009) ImageNet: A large-scale hierarchical image database. Proc IEEE Conf Comput Vis Pattern Recognit 248–255. https://doi.org/10.1109/CVPR.2009.520684810.1109/CVPR.2009.5206848 ↗
2. Reu PL, Blaysat B, Andó E et al (2022) DIC challenge 2.0: Developing images and guidelines for evaluating accuracy and resolution of 2D analyses: Focus on the metrological efficiency indicator. Exp Mech 62(4):639–654. https://doi.org/10.1007/s11340-021-00806-610.1007/s11340-021-00806-6 ↗
3. Allen M, Oliveira M, Hazra S et al (2016) Benchmark 2 - springback of a Jaguar land rover aluminium. J Phys: Conf Ser 734:022002. https://doi.org/10.1088/1742-6596/734/2/02200210.1088/1742-6596/734/2/022002 ↗
4. Vanhulst M, Lee Y, Steinfels D et al (2025) ESAFORM benchmark 2024: study on the geometric accuracy of a complex shape with single point incremental forming. Int J Mater Form 1810.1007/s12289-025-01928-1 ↗
5. Roll K, Wiegand K, Hora P et al (2008) Benchmark 2—influence of drawbeads on the springback behaviour (S-RAIL-08). In: Proc 7th Int Conf Workshop Numer Simul 3D Sheet Metal Forming Process., Numisheet, Interlaken, Switzerland, pp 1–5
6. Nakamachi E (1993) Guide to the benchmark test-simulation and experiment. J Mater Process Technol
7. Santos AD, Teixeira P (2008) A study on experimental benchmarks and simulation results in sheet metal forming. J Mater Process Technol 199(1–3):327–336. https://doi.org/10.1016/j.jmatprotec.2007.08.03910.1016/j.jmatprotec.2007.08.039 ↗
8. Choi J, Lee J, Bong HJ et al (2018) Advanced constitutive modeling of advanced high strength steel sheets for springback prediction after double stage u-draw bending. Int J Solids Struct 151:152–164. https://doi.org/10.1016/j.ijsolstr.2017.09.030, special Issue with a Selection of Papers from the NUMISHEET 2016 Conference10.1016/j.ijsolstr.2017.09.030 ↗
9. Hu Q, Maier L, Nishiwaki T et al (2024) User friendly FE formulation for anisotropic distortional hardening model based on non-associated flow plasticity and its application to springback prediction. Thin-Walled Struct 202:112142. https://doi.org/10.1016/j.tws.2024.11214210.1016/j.tws.2024.112142 ↗
10. Jourdan F, Jean M, Alart P (1998) An alternative method between implicit and explicit schemes devoted to frictional contact problems in deep drawing simulation. J Mater Process Technol 80–81:257–262. https://doi.org/10.1016/s0924-0136(98)00143-510.1016/s0924-0136(98)00143-5 ↗
11. Pimentel AMF, de Carvalho Martins Alves JL, de Seabra Merendeiro NM et al (2018) Comprehensive benchmark study of commercial sheet metal forming simulation softwares used in the automotive industry. Int J Mater Form 11(6):879–899. https://doi.org/10.1007/s12289-018-1397-410.1007/s12289-018-1397-4 ↗
12. Vallaster E, Wiesenmayer S, Merklein M (2023) Effect of a strain rate dependent material modeling of a steel on the prediction accuracy of a numerical deep drawing process. Prod Eng 18(1):47–60. https://doi.org/10.1007/s11740-023-01222-610.1007/s11740-023-01222-6 ↗
13. van den Boogaard T, Havinga J, Belin A et al (2015) Parameter reduction for the Yld 2004–18p yield criterion. Int J Mater Form 9(2):175–178. https://doi.org/10.1007/s12289-015-1221-310.1007/s12289-015-1221-3 ↗
14. Zhang H, Diehl M, Roters F et al (2016) A virtual laboratory using high resolution crystal plasticity simulations to determine the initial yield surface for sheet metal forming operations. Int J Plast 80:111–138. https://doi.org/10.1016/j.ijplas.2016.01.00210.1016/j.ijplas.2016.01.002 ↗
15. Liu W, Li X, Liu M et al (2024) Virtual laboratory enabled constitutive modelling of dual phase steels. Int J Plast 175:10393010.1016/j.ijplas.2024.103930 ↗
16. Coppieters S, Hakoyama T, Eyckens P et al (2018) On the synergy between physical and virtual sheet metal testing: calibration of anisotropic yield functions using a microstructure-based plasticity model. Int J Mater Form 12(5):741–759. https://doi.org/10.1007/s12289-018-1444-110.1007/s12289-018-1444-1 ↗
17. Jeon B, Lee SY, Lee J et al (2024) Direct application of elasto-visco-plastic self-consistent crystal plasticity model to u-draw bending and springback of dual-phase high strength steel. Int J Plast 181:104098. https://doi.org/10.1016/j.ijplas.2024.10409810.1016/j.ijplas.2024.104098 ↗
18. Maier L, Walz E, Hofmann M et al (2026) A scientific benchmark for elasto-plastic constitutive modeling - Part II: blind predictions, calibration strategies, and benchmark results. Int J Mater Form 19(1):17. https://doi.org/10.1007/s12289-026-01984-110.1007/s12289-026-01984-1 ↗
19. Eder M, Gruber M, Volk W (2022) Validation of material models for sheet metals using new test equipment. Int J Mater Form 15(5). https://doi.org/10.1007/s12289-022-01710-710.1007/s12289-022-01710-7 ↗
20. VDI/VDE-Gesellschaft Mess- und Automatisierungstechnik (2019) VDI/VDE 2626 Blatt 1: Optische Messverfahren - Digitale Bildkorrelation - Grundlagen. Richtlinie, Verein Deutscher Ingenieure e.V., Düsseldorf, Annahmeprüfung und Überwachungsprüfung
21. VDI/VDE-Gesellschaft Mess- und Automatisierungstechnik (2002) VDI/VDE 2634 Blatt 1 - Optische 3D-Messsysteme - Bildgebende Systeme mit punktförmiger Antastung. V., Düsseldorf, Richtlinie, Verein Deutscher Ingenieure e
22. Deutsches Institut für Normung (2009) Din 6892–1: Metallic materials - tensile testing - Part 1: Method of test at room temperature. Standard published by Deutsches Institut für Normung DIN 6892–1:2009
23. Deutsches Institut für Normung (2022) Din 50125: Testing of metallic materials - tensile test pieces. Standard published by Deutsches Institut für Normung DIN 50125:2022–08
24. Vitzthum S, Rebelo Kornmeier J, Hofmann M et al (2022) In-situ analysis of the thermoelastic effect and its relation to the onset of yielding of low carbon steel. Mater Des 219:110753. https://doi.org/10.1016/j.matdes.2022.11075310.1016/j.matdes.2022.110753 ↗
25. Vitzthum S, Rebelo Kornmeier J, Hofmann M et al (2022) In-situ analysis of the elastic-plastic characteristics of high strength dual-phase steel. Mater Sci Eng 857:144097. https://doi.org/10.1016/j.msea.2022.14409710.1016/j.msea.2022.144097 ↗
26. Hartmann C, Vitzthum S, Maier L et al (2024) Model-based evaluation of methods for the determination of the onset of yielding by temperature measurement. In: Proc 14th Int Conf Technol Plast Springer Nature, Cham, pp 447–456. https://doi.org/10.1007/978-3-031-42093-1_4310.1007/978-3-031-42093-1_43 ↗
27. Yoshida F, Uemori T, Fujiwara K (2002) Elastic-plastic behavior of steel sheets under in-plane cyclic tension-compression at large strain. Int J Plast 18(5):633–659. https://doi.org/10.1016/S0749-6419(01)00049-310.1016/S0749-6419(01)00049-3 ↗
28. Kuwabara T (2007) Advances in experiments on metal sheets and tubes in support of constitutive modeling and forming simulations. Int J Plast 23(3):385–419. https://doi.org/10.1016/j.ijplas.2006.06.00310.1016/j.ijplas.2006.06.003 ↗
29. Chaboche J (1986) Time-independent constitutive theories for cyclic plasticity. Int J Plast 2(2):149–188. https://doi.org/10.1016/0749-6419(86)90010-010.1016/0749-6419(86)90010-0 ↗
30. Bauschinger J (1886) Über die veränderung der elastizitätsgrenze und die Festigkeit des Eisens und Stahls durch Strecken und Quetschen, durch erwärmen und abkühlen und durch oftmals wiederholte beanspruchungen. Mitt mech-techn Lab K Techn Hochsch München 13(15). https://mediatum.ub.tum.de/download/993273/993273.pdf
31. Roth CC, Mohr D (2016) Ductile fracture experiments with locally proportional loading histories. Int J Plast 79:328–354. https://doi.org/10.1016/j.ijplas.2015.08.00410.1016/j.ijplas.2015.08.004 ↗
32. International Organization for Standardization (2002) ISO 16808: Metallic materials - sheet and strip - determination of biaxial stress-strain curve by means of bulge test with optical measuring systems. Standard published by International Organization for Standardization ISO 16808:2002–08
33. Lara A, Picas I, Casellas D (2013) Effect of the cutting process on the fatigue behaviour of press hardened and high strength dual phase steels. J Mater Process Technol 213(11):1908–1919. https://doi.org/10.1016/j.jmatprotec.2013.05.00310.1016/j.jmatprotec.2013.05.003 ↗
34. Vegter H, An YG (2008) Mechanical testing for modeling of the material behaviour in forming simulations. Proc 7th Int Conf Workshop Numer Simul 3D Sheet Metal Forming Process, Interlaken, Switzerland pp 55–60
35. Merklein M, Kuppert A (2009) A method for the layer compression test considering the anisotropic material behavior. Int J Mater Form 2:483–486. https://doi.org/10.1007/s12289-009-0592-810.1007/s12289-009-0592-8 ↗
36. International Organization for Standardization (2021) ISO 12004–2: Metallic materials - sheet and strip - determination of forming limit curves. Standard published by International Organization for Standardization ISO 12004:2021–07
37. Volk W, Hora P (2010) New algorithm for a robust user-independent evaluation of beginning instability for the experimental FLC determination. Int J Mater Form 4(3):339–346. https://doi.org/10.1007/s12289-010-1012-910.1007/s12289-010-1012-9 ↗
38. Chang Y (2021) Evidence and effects of heterogeneities in complex phase and dual phase steels. Dissertation, Rheinisch-Westfälische Technische Hochschule Aachen, Aachen, Germany
39. Li X (2018) Microstructure-property relationship in cold rolled complex phase steel. Steel Institute, Rheinisch-Westfälische Technische Hochschule Aachen, Aachen, Germany
40. Liu W, Lian J, Aravas N et al (2020) A strategy for synthetic microstructure generation and crystal plasticity parameter calibration of fine-grain-structured dual-phase steel. Int J Plast 126:102614. https://doi.org/10.1016/j.ijplas.2019.10.00210.1016/j.ijplas.2019.10.002 ↗
41. Black D, Windover D, Henins A et al (2011) Certification of standard reference material 660b10.1154/1.3591064 ↗
42. Hoelzel M, Gan W, Hofmann M et al (2013) Rotatable multifunctional load frames for neutron diffractometers at FRM II–design, specifications and applications. Nucl Instrum Methods Phys Res Sect A Accel Spectrom Det Assoc Equip 711:101–105. https://doi.org/10.1016/j.nima.2013.01.04910.1016/j.nima.2013.01.049 ↗
43. Storm M (2024) Pydidas - Python diffraction data analysis suite. https://doi.org/10.5281/zenodo.1148765210.5281/zenodo.11487652 ↗
44. Randau C, Garbe U, Brokmeier HG (2011) StressTextureCalculator: A software tool to extract texture, strain and microstructure information from area-detector measurements. J Appl Crystallogr 44. https://doi.org/10.1107/S002188981101206410.1107/S0021889811012064 ↗
45. Waterschoot T, Kestens L, De Cooman B (2002) Hot rolling texture development in CMnCrSi dual-phase steels. Metall and Mater Trans A 33:1091–1102. https://doi.org/10.1007/s11661-002-0211-510.1007/s11661-002-0211-5 ↗
46. Bachmann F, Hielscher R, Schaeben H (2010) Texture analysis with MTEX-free and open source software toolbox. In: Solid State Phenom, pp 63–68. https://doi.org/10.4028/www.scientific.net/SSP.160.6310.4028/www.scientific.net/SSP.160.63 ↗
47. Masimov M, Peranio N, Springub B, et al (2010) EBSD study of substructure and texture formation in dual-phase steel sheets for semi-finished products. Solid State Phenom, v160, 251-256 (2010) 160. https://doi.org/10.4028/www.scientific.net/SSP.160.25110.4028/www.scientific.net/SSP.160.251 ↗
48. Maier L, Eder M, Norz R et al (2023) Innovative experimental setup for the investigation of material models with regard to strain hardening behavior. IOP Conf Ser Mater Sci Eng 1284(1):012071. https://doi.org/10.1088/1757-899x/1284/1/01207110.1088/1757-899x/1284/1/012071 ↗
49. Swift H (1952) Plastic instability under plane stress. J Mech Phys Solids 1(1):1–18. https://doi.org/10.1016/0022-5096(52)90002-110.1016/0022-5096(52)90002-1 ↗
50. Hockett J, Sherby O (1975) Large strain deformation of polycrystalline metals at low homologous temperatures. J Mech Phys Solids 23(2):87–98. https://doi.org/10.1016/0022-5096(75)90018-610.1016/0022-5096(75)90018-6 ↗
51. Ludwik P (1909) Elemente der Technologischen Mechanik. Springer. https://doi.org/10.1007/978-3-662-40293-110.1007/978-3-662-40293-1 ↗
52. Ghosh A (1977) Tensile instability and necking in materials with strain hardening and strain-rate hardening. Acta Metall 25(12):1413–1424. https://doi.org/10.1016/0001-6160(77)90072-410.1016/0001-6160(77)90072-4 ↗
53. Voce E (1955) A practical strain hardening function. Metallurgia 51:219–226
54. Mises R (1928) Mechanics of plastic deformation of crystals. Z Angew Math Mech 8:161–18510.1002/zamm.19280080302 ↗
55. Tresca H (1864) On the yield of solids at high pressures. C R Acad Sci 59:754
56. Hill R (1948) A theory of the yielding and plastic flow of anisotropic metals. Proc R Soc Lond 193:281–297
57. Barlat F, Brem J, Yoon J et al (2003) Plane stress yield function for aluminium alloy sheets - Part 1: Theory. Int J Plast 19:297–319. https://doi.org/10.1016/S0749-6419(02)00019-010.1016/S0749-6419(02)00019-0 ↗
58. Banabic D, Balan T, Comsa D (2000) A new yield criterion for orthotropic sheet metals under plane-stress conditions. Proc 7th Conf ‘TPR2000’, Cluj Napoca, Romania pp 217–224
59. Vegter D, van den Boogaard A (2006) A plane stress yield function for anisotropic sheet material by interpolation of biaxial stress states. Int J Plast 22:557–580. https://doi.org/10.1016/j.ijplas.2005.04.00910.1016/j.ijplas.2005.04.009 ↗
60. Roters F, Eisenlohr P, Hantcherli L et al (2010) Over-view of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications. Acta Mater 58(4):1152–1211. https://doi.org/10.1016/j.actamat.2009.10.05810.1016/j.actamat.2009.10.058 ↗
61. Feyel F (2003) A multilevel finite element method (FE2) to describe the response of highly non-linear structures using generalized continua. Comput Methods Appl Mech Eng 192(28):3233–3244. https://doi.org/10.1016/S0045-7825(03)00348-710.1016/S0045-7825(03)00348-7 ↗
62. Ma H, Li Y, Zhang H et al (2022) A virtual laboratory based on full-field crystal plasticity simulation to characterize the multiscale mechanical properties of ahss. Sci Rep 12:5054. https://doi.org/10.1038/s41598-022-09045-810.1038/s41598-022-09045-8 ↗
63. Martinitz L, Hartmann C (2023) An artificial neural network approach on crystal plasticity for material modelling in macroscopic simulations. IOP Conf Ser: Mater Sci Eng 1284(1):012052. https://doi.org/10.1088/1757-899X/1284/1/01205210.1088/1757-899X/1284/1/012052 ↗
64. Hartmann C (2023) Towards machine learning of crystal plasticity by neural networks. In: TMS 2023 152nd Annu Meet & Exhib Suppl Proc Springer Nature, Cham, pp 576–583. https://doi.org/10.1007/978-3-031-22524-6_5110.1007/978-3-031-22524-6_51 ↗
65. Ma A, Roters F (2004) A constitutive model for FCC single crystals based on dislocation densities and its application to uniaxial compression of aluminium single crystals. Acta Mater 52(12):3603–3612. https://doi.org/10.1016/j.actamat.2004.04.01210.1016/j.actamat.2004.04.012 ↗
66. Rice J (1971) Inelastic constitutive relations for solids: an internal variable theory and its application to metal plasticity. J Mech Phys Solids 19:433–455. https://doi.org/10.1016/0022-5096(71)90010-X10.1016/0022-5096(71)90010-X ↗