{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,26]],"date-time":"2026-04-26T05:34:55Z","timestamp":1777181695089,"version":"3.51.4"},"reference-count":110,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2022,7,15]],"date-time":"2022-07-15T00:00:00Z","timestamp":1657843200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,7,15]],"date-time":"2022-07-15T00:00:00Z","timestamp":1657843200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int J Mater Form"],"published-print":{"date-parts":[[2022,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This article details the ESAFORM Benchmark 2021. The deep drawing cup of a 1\u00a0mm thick, AA 6016-T4 sheet with a strong cube texture was simulated by 11 teams relying on phenomenological or crystal plasticity approaches, using commercial or self-developed Finite Element (FE) codes, with solid, continuum or classical shell elements and different contact models. The material characterization (tensile tests, biaxial tensile tests, monotonic and reverse shear tests, EBSD measurements) and the cup forming steps were performed with care (redundancy of measurements). The Benchmark organizers identified some constitutive laws but each team could perform its own identification. The methodology to reach material data is systematically described as well as the final data set. The ability of the constitutive law and of the FE model to predict Lankford and yield stress in different directions is verified. Then, the simulation results such as the earing (number and average height and amplitude), the punch force evolution and thickness in the cup wall are evaluated and analysed. The CPU time, the manpower for each step as well as the required tests versus the final prediction accuracy of more than 20 FE simulations are commented. The article aims to guide students and engineers in their choice of a constitutive law (yield locus, hardening law or plasticity approach) and data set used in the identification, without neglecting the other FE features, such as software, explicit or implicit strategy, element type and contact model.<\/jats:p>","DOI":"10.1007\/s12289-022-01672-w","type":"journal-article","created":{"date-parts":[[2022,7,15]],"date-time":"2022-07-15T10:04:04Z","timestamp":1657879444000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":55,"title":["Analysis of ESAFORM 2021 cup drawing benchmark of an Al alloy, critical factors for accuracy and efficiency of FE simulations"],"prefix":"10.1007","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1838-7939","authenticated-orcid":false,"given":"Anne Marie","family":"Habraken","sequence":"first","affiliation":[]},{"given":"Toros Arda","family":"Aksen","sequence":"additional","affiliation":[]},{"given":"Jos\u00e9 L.","family":"Alves","sequence":"additional","affiliation":[]},{"given":"Rui L.","family":"Amaral","sequence":"additional","affiliation":[]},{"given":"Ehssen","family":"Betaieb","sequence":"additional","affiliation":[]},{"given":"Nitin","family":"Chandola","sequence":"additional","affiliation":[]},{"given":"Luca","family":"Corallo","sequence":"additional","affiliation":[]},{"given":"Daniel J.","family":"Cruz","sequence":"additional","affiliation":[]},{"given":"Laurent","family":"Duch\u00eane","sequence":"additional","affiliation":[]},{"given":"Bernd","family":"Engel","sequence":"additional","affiliation":[]},{"given":"Emre","family":"Esener","sequence":"additional","affiliation":[]},{"given":"Mehmet","family":"Firat","sequence":"additional","affiliation":[]},{"given":"Peter","family":"Frohn-S\u00f6rensen","sequence":"additional","affiliation":[]},{"given":"Jes\u00fas","family":"Gal\u00e1n-L\u00f3pez","sequence":"additional","affiliation":[]},{"given":"Hadi","family":"Ghiabakloo","sequence":"additional","affiliation":[]},{"given":"Leo A. I.","family":"Kestens","sequence":"additional","affiliation":[]},{"given":"Junhe","family":"Lian","sequence":"additional","affiliation":[]},{"given":"Rakesh","family":"Lingam","sequence":"additional","affiliation":[]},{"given":"Wencheng","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Jun","family":"Ma","sequence":"additional","affiliation":[]},{"given":"Lu\u00eds F.","family":"Menezes","sequence":"additional","affiliation":[]},{"given":"Tuan","family":"Nguyen-Minh","sequence":"additional","affiliation":[]},{"given":"Sara S.","family":"Miranda","sequence":"additional","affiliation":[]},{"given":"Diogo M.","family":"Neto","sequence":"additional","affiliation":[]},{"given":"Andr\u00e9 F. G.","family":"Pereira","sequence":"additional","affiliation":[]},{"given":"Pedro A.","family":"Prates","sequence":"additional","affiliation":[]},{"given":"Jonas","family":"Reuter","sequence":"additional","affiliation":[]},{"given":"Benoit","family":"Revil-Baudard","sequence":"additional","affiliation":[]},{"given":"Carlos","family":"Rojas-Ulloa","sequence":"additional","affiliation":[]},{"given":"Bora","family":"Sener","sequence":"additional","affiliation":[]},{"given":"Fuhui","family":"Shen","sequence":"additional","affiliation":[]},{"given":"Albert","family":"Van Bael","sequence":"additional","affiliation":[]},{"given":"Patricia","family":"Verleysen","sequence":"additional","affiliation":[]},{"given":"Frederic","family":"Barlat","sequence":"additional","affiliation":[]},{"given":"Oana","family":"Cazacu","sequence":"additional","affiliation":[]},{"given":"Toshihiko","family":"Kuwabara","sequence":"additional","affiliation":[]},{"given":"Augusto","family":"Lopes","sequence":"additional","affiliation":[]},{"given":"Marta C.","family":"Oliveira","sequence":"additional","affiliation":[]},{"given":"Abel D.","family":"Santos","sequence":"additional","affiliation":[]},{"given":"Gabriela","family":"Vincze","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,7,15]]},"reference":[{"issue":"5","key":"1672_CR1","doi-asserted-by":"publisher","first-page":"373","DOI":"10.1007\/s00607-012-0265-1","volume":"95","author":"F Abed-Meraim","year":"2013","unstructured":"Abed-Meraim F, Trinh V-D, Combescure A (2013) New quadratic solid-shell elements and their evaluation on linear benchmark problems. Computing 95(5):373\u2013394. https:\/\/doi.org\/10.1007\/s00607-012-0265-1","journal-title":"Computing"},{"issue":"6","key":"1672_CR2","doi-asserted-by":"publisher","first-page":"923","DOI":"10.1016\/0001-6160(85)90188-9","volume":"33","author":"RJ Asaro","year":"1985","unstructured":"Asaro RJ, Needleman A (1985) Overview no. 42 texture development and strain hardening in rate dependent polycrystals. Acta Metall 33(6):923\u2013953. https:\/\/doi.org\/10.1016\/0001-6160(85)90188-9","journal-title":"Acta Metall"},{"key":"1672_CR3","doi-asserted-by":"publisher","unstructured":"Bachmann F, Hielscher R, Jupp PE, Pantleon W, Schaeben H, Wegert E (2010) Inferential statistics of electron backscatter diffraction data from within individual crystalline grains. J Appl Crystallogr 43:1338e1355.\u00a0https:\/\/doi.org\/10.1107\/S002188981003027X","DOI":"10.1107\/S002188981003027X"},{"issue":"1","key":"1672_CR4","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/0749-6419(89)90019-3","volume":"5","author":"F Barlat","year":"1989","unstructured":"Barlat F, Lian K (1989) Plastic behavior and stretchability of sheet metals. Part I: a yield function for orthotropic sheets under plane stress conditions. Int J Plast 5(1):51\u201366. https:\/\/doi.org\/10.1016\/0749-6419(89)90019-3","journal-title":"Int J Plast"},{"key":"1672_CR5","doi-asserted-by":"publisher","first-page":"1297","DOI":"10.1016\/S0749-6419(02)00019-0","volume":"19","author":"F Barlat","year":"2003","unstructured":"Barlat F, Brem JC, Yoon JW, Chung K, Dick RE, Lege DJ, Pourboghrat F, Choi SH, Chu E (2003) Plane stress yield function for aluminum alloy sheets\u2014part 1: theory. Int J Plast 19:1297\u20131319. https:\/\/doi.org\/10.1016\/S0749-6419(02)00019-0","journal-title":"Int J Plast"},{"key":"1672_CR6","doi-asserted-by":"crossref","unstructured":"Barlat F, Cazacu O, Zyczkowski M, Banabic D, Yoon J-W (2004) Yield surface plasticity and anisotropy. In: Raabe D, Chen L-Q, Barlat F, Roters F (eds) Continuum scale simulation of engineering materials fundamentals-microstructures-process applications. Wiley-VCH, Berlin, pp 145\u2013185","DOI":"10.1002\/3527603786.ch6"},{"key":"1672_CR7","doi-asserted-by":"publisher","first-page":"1009","DOI":"10.1016\/j.ijplas.2004.06.004","volume":"21","author":"F Barlat","year":"2005","unstructured":"Barlat F, Aretz H, Yoon JW, Karabin ME, Brem JC, Dick RE (2005) Linear transformation - based anisotropic yield functions. Int J Plast 21:1009\u20131039. https:\/\/doi.org\/10.1016\/j.ijplas.2004.06.004","journal-title":"Int J Plast"},{"key":"1672_CR8","first-page":"105","volume":"60","author":"PD Barros","year":"2015","unstructured":"Barros PD, Neto DM, Alves JL, Oliveira MC, Menezes LF (2015) DD3IMP, 3D fully implicit finite element solver: implementation of CB2001 yield criterion. Rom J Tech Sci - Appl Mech 60:105\u2013136","journal-title":"Rom J Tech Sci - Appl Mech"},{"key":"1672_CR9","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1016\/0749-6419(89)90025-9","volume":"5","author":"SB Brown","year":"1989","unstructured":"Brown SB, Kim KH, Anand L (1989) An internal variable constitutive model for hot working of metals. Int J Plast 5:95\u2013130. https:\/\/doi.org\/10.1016\/0749-6419(89)90025-9","journal-title":"Int J Plast"},{"key":"1672_CR10","volume-title":"Texture analysis in material science","author":"HJ Bunge","year":"1982","unstructured":"Bunge HJ (1982) Texture analysis in material science. Butterworths, London"},{"issue":"140","key":"1672_CR11","doi-asserted-by":"publisher","first-page":"200","DOI":"10.1016\/j.ijsolstr.2018.01.036","volume":"139","author":"O Cazacu","year":"2018","unstructured":"Cazacu O (2018) New yield criteria for isotropic and textured metallic materials. Int J Solids Struct 139(140):200\u2013210. https:\/\/doi.org\/10.1016\/j.ijsolstr.2018.01.036","journal-title":"Int J Solids Struct"},{"key":"1672_CR12","doi-asserted-by":"publisher","first-page":"613","DOI":"10.1177\/108128650100600603","volume":"6","author":"O Cazacu","year":"2001","unstructured":"Cazacu O, Barlat F (2001) Generalization of Drucker\u2019s yield criterion to orthotropy. Math Mech Solids 6:613\u2013630. https:\/\/doi.org\/10.1177\/108128650100600603","journal-title":"Math Mech Solids"},{"key":"1672_CR13","unstructured":"Cazacu O, Revil-Baudard B, (2021) Plasticity of Metallic Materials: Modelling and Applications to Metal Forming, Elsevier, 500 pages, ISBN 978\u20130\u201312-817984-0. Nov 2020"},{"key":"1672_CR14","doi-asserted-by":"publisher","first-page":"1171","DOI":"10.1016\/j.ijplas.2005.06.001","volume":"22","author":"O Cazacu","year":"2006","unstructured":"Cazacu O, Plunkett B, Barlat F (2006) Orthotropic yield criterion for hexagonal close packed metals. Int J Plast 22:1171\u20131194. https:\/\/doi.org\/10.1016\/j.ijplas.2005.06.001","journal-title":"Int J Plast"},{"key":"1672_CR15","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1016\/j.ijsolstr.2017.04.006","volume":"151","author":"O Cazacu","year":"2018","unstructured":"Cazacu O, Revil-Baudard B, Chandola N (2018) A yield criterion for cubic single crystals. Int J Solids Struct 151:9\u201319. https:\/\/doi.org\/10.1016\/j.ijsolstr.2017.04.006","journal-title":"Int J Solids Struct"},{"key":"1672_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-92922-4","volume-title":"Plasticity damage couplings: from single crystal to polycrystalline materials","author":"O Cazacu","year":"2019","unstructured":"Cazacu O, Revil-Baudard B, Chandola N (2019) Plasticity damage couplings: from single crystal to polycrystalline materials. Springer, Berlin Heidelberg"},{"key":"1672_CR17","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1016\/0749-6419(86)90010-0","volume":"2","author":"JL Chaboche","year":"1986","unstructured":"Chaboche JL (1986) Time-independent constitutive theories for cyclic plasticity. Int J Plast 2:149\u2013188. https:\/\/doi.org\/10.1016\/0749-6419(86)90010-0","journal-title":"Int J Plast"},{"key":"1672_CR18","doi-asserted-by":"publisher","first-page":"2145","DOI":"10.1007\/s00366-020-00954-8","volume":"37","author":"A Chaker","year":"2021","unstructured":"Chaker A, Koubaa S, Mars J, Vivet A, Dammak F (2021) An efficient ABAQUS solid shell element implementation for low velocity impact analysis of FGM plates. Eng Comput 37:2145\u20132157. https:\/\/doi.org\/10.1007\/s00366-020-00954-8","journal-title":"Eng Comput"},{"key":"1672_CR19","doi-asserted-by":"publisher","first-page":"713","DOI":"10.3390\/met10060713","volume":"10","author":"L Chen","year":"2020","unstructured":"Chen L, Zhang H, Song M (2020) Extension of Barlat\u2019s yield criterion to tension\u2013compression asymmetry: modeling and verification. Metals 10:713. https:\/\/doi.org\/10.3390\/met10060713","journal-title":"Metals"},{"key":"1672_CR20","doi-asserted-by":"publisher","first-page":"571","DOI":"10.1016\/s0749-6419(01)00046-8","volume":"18","author":"BK Chun","year":"2002","unstructured":"Chun BK, Jinn JT, Lee JK (2002) Modeling the Bauschinger effect for sheet metals, part I: theory. Int J Plast 18:571\u2013595. https:\/\/doi.org\/10.1016\/s0749-6419(01)00046-8","journal-title":"Int J Plast"},{"key":"1672_CR21","doi-asserted-by":"publisher","first-page":"861","DOI":"10.1016\/j.ijplas.2004.05.014","volume":"21","author":"MG Lee","year":"2005","unstructured":"Lee MG, Kim D, Kim C, Wenner ML, Chung K (2005) Spring-back evaluation of automotive sheets based on isotropic \u2013 kinematic hardening laws and non-quadratic anisotropic yield functions, part I: theory and formulation. Int J Plast 21:861\u2013882. https:\/\/doi.org\/10.1016\/j.ijplas.2004.05.014","journal-title":"Int J Plast"},{"key":"1672_CR22","doi-asserted-by":"publisher","first-page":"357","DOI":"10.48550\/arXiv.1703.10126","volume":"11","author":"J Co\u00ebr","year":"2018","unstructured":"Co\u00ebr J, Laurent H, Oliveira MC, Manach P-Y, Menezes LF (2018) Detailed experimental and numerical analysis of a cylindrical cup deep drawing: pros and cons of using solid-shell elements. Int J Mater Form 11:357\u2013373. https:\/\/doi.org\/10.48550\/arXiv.1703.10126","journal-title":"Int J Mater Form"},{"key":"1672_CR23","doi-asserted-by":"publisher","first-page":"741","DOI":"10.1007\/s12289-018-1444-1","volume":"12","author":"S Coppieters","year":"2019","unstructured":"Coppieters S, Hakoyama T, Eyckens P, Nakano H, Van Bael A, Debruyne D, Kuwabara T (2019) 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 12:741\u2013759. https:\/\/doi.org\/10.1007\/s12289-018-1444-1","journal-title":"Int J Mater Form"},{"key":"1672_CR24","unstructured":"Coulomb CA (1821). Th\u00e9orie des machines simples en ayant \u00e9gard au frottement de leurs parties et \u00e0 la roideur des cordages. Bachelier"},{"key":"1672_CR25","unstructured":"Danckert J, K. B. Nielsen, P. H\u00f8jbjerg. (1999) Experimental investigation of NUMISHEET\u201999 benchmark test C: (The Aalborg Benchmark test). Proceedings of the NUMISHEET\u201999, 4th International Conference and Workshop on Numerical Simulation of 3D Sheet Forming Processes. In: Gelin JC, Picart P (eds) University of France-Comt\u00e9 and E.N.S.M.M., BURS 1:637\u2013642"},{"key":"1672_CR26","unstructured":"Dick RE, Yoon J-W, Huh H, Bae G. (2011) BM1 \u2212 Earing Evolution during Drawing and Ironing Processes. Part C: Benchmark Problems and Results. Proceedings of the 8th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes, Huh H, Chung K, Han SS, Chung WJ. (Eds.), Kaist Press, 11\u201348"},{"key":"1672_CR27","doi-asserted-by":"publisher","unstructured":"Dick R, Cardoso R, Paulino M, Yoon JW. (2013) Benchmark 4 - Wrinkling during cup drawing. AIP Conference Proceedings 1567, NUMISHEET 2014, The 9th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes, 262\u2013327. https:\/\/doi.org\/10.1063\/1.4849984","DOI":"10.1063\/1.4849984"},{"key":"1672_CR28","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1115\/1.4010009","volume":"16","author":"DC Drucker","year":"1949","unstructured":"Drucker DC (1949) Relation of experiments to mathematical theories of plasticity. J Appl Mech 16:349\u2013357. https:\/\/doi.org\/10.1115\/1.4010009","journal-title":"J Appl Mech"},{"key":"1672_CR29","unstructured":"Duch\u00eane L (2003) FEM study of metal sheets with a texture based, local description of the yield locus. Ph. D. Thesis, Uliege, Li\u00e8ge, Belgium, available from http:\/\/hdl.handle.net\/2268\/135058"},{"issue":"1226","key":"1672_CR30","doi-asserted-by":"publisher","first-page":"376","DOI":"10.1098\/rspa.1957.0133","volume":"241","author":"JD Eshelby","year":"1957","unstructured":"Eshelby JD (1957) The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proceedings of the royal society of London. Series A Math Physical Sci 241(1226):376\u2013396. https:\/\/doi.org\/10.1098\/rspa.1957.0133","journal-title":"Series A Math Physical Sci"},{"key":"1672_CR31","doi-asserted-by":"publisher","unstructured":"Frohn-S\u00f6rensen P, Cislo C, Paschke H, Stockinger M, Engel B (2021) Dry friction under pressure variation of PACVD TiN surfaces on selected automotive sheet metals for the application in unlubricated metal forming. Wear 476:203750. https:\/\/doi.org\/10.1016\/j.wear.2021.203750","DOI":"10.1016\/j.wear.2021.203750"},{"key":"1672_CR32","doi-asserted-by":"publisher","unstructured":"Gal\u00e1n J, Verleysen P, Lebensohn RA (2014) An improved algorithm for the polycrystal viscoplastic self-consistent model and its integration with implicit finite element schemes. Model Simul Mater Sci Eng 22(5):055023.\u00a0https:\/\/doi.org\/10.1088\/0965-0393\/22\/5\/055023","DOI":"10.1088\/0965-0393\/22\/5\/055023"},{"issue":"9","key":"1672_CR33","doi-asserted-by":"publisher","first-page":"819","DOI":"10.3390\/cryst10090819","volume":"10","author":"J Gal\u00e1n-L\u00f3pez","year":"2020","unstructured":"Gal\u00e1n-L\u00f3pez J, Hidalgo J (2020) Use of the correlation between grain size and crystallographic orientation in crystal plasticity simulations: application to AISI 420 stainless steel. Crystals 10(9):819. https:\/\/doi.org\/10.3390\/cryst10090819","journal-title":"Crystals"},{"key":"1672_CR34","doi-asserted-by":"crossref","unstructured":"Galdos L, Otegi N, Mendiguren J, Trinidad J, Saenz de Argando\u00f1a E (2021) Contact pressure, sliding velocity and viscosity dependent friction behavior of lubricants used in tube hydroforming processes. Paper presented at ESAFORM 2021. 24th International Conference on Material Forming, Li\u00e8ge, Belgique. https:\/\/popups.uliege.be\/esaform21\/index.php?id=2081","DOI":"10.25518\/esaform21.2081"},{"key":"1672_CR35","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/j.commatsci.2012.05.056","volume":"66","author":"J Gawad","year":"2013","unstructured":"Gawad J, Van Bael A, Eyckens P, Samaey G, Van Houtte P, Roose D (2013) Hierarchical multi-scale modeling of texture induced plastic anisotropy in sheet forming. Comput Mater Sci 66:65\u201383. https:\/\/doi.org\/10.1016\/j.commatsci.2012.05.056","journal-title":"Comput Mater Sci"},{"key":"1672_CR36","unstructured":"Gelin JC, Picart P. (1999) Benchmark problems and results. Proceedings of the NUMISHEET\u201999, 4th International Conference and Workshop on Numerical Simulation of 3D Sheet Forming Processes, Gelin JC, Picart P (Eds.), University of France-Comt\u00e9 and E.N.S.M.M., BURS (Eds.), 2:751\u2013928, ISBN: 2\u201384449\u2013001-8"},{"key":"1672_CR37","doi-asserted-by":"publisher","unstructured":"Gorji MB, Mozaffar M, Heidenreich JN, Cao J, Mohr D (2020) On the potential of recurrent neural networks for modeling path dependent plasticity. J Mech Physics Solids 143:103972.\u00a0https:\/\/doi.org\/10.1016\/j.jmps.2020.103972","DOI":"10.1016\/j.jmps.2020.103972"},{"key":"1672_CR38","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1016\/j.cirp.2008.03.042","volume":"57","author":"P Groche","year":"2008","unstructured":"Groche P, Nitzsche G, Elsen A (2008) Adhesive wear in deep drawing of aluminum sheets. CIRP Ann - Manuf Technol 57:295\u2013298. https:\/\/doi.org\/10.1016\/j.cirp.2008.03.042","journal-title":"CIRP Ann - Manuf Technol"},{"issue":"1","key":"1672_CR39","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1186\/2193-9772-3-5","volume":"3","author":"MA Groeber","year":"2014","unstructured":"Groeber MA, Jackson MA (2014) DREAM. 3D: a digital representation environment for the analysis of microstructure in 3D. Integr Mater Manuf Innov 3(1):56\u201372. https:\/\/doi.org\/10.1186\/2193-9772-3-5","journal-title":"Integr Mater Manuf Innov"},{"key":"1672_CR40","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/BF02736210","volume":"11","author":"A Habraken","year":"2004","unstructured":"Habraken A (2004) Modelling the plastic anisotropy of metals. Arch Comp Methods Eng 11:3\u201396. https:\/\/doi.org\/10.1007\/BF02736210","journal-title":"Arch Comp Methods Eng"},{"key":"1672_CR41","doi-asserted-by":"publisher","first-page":"1525","DOI":"10.1016\/j.ijplas.2003.11.006","volume":"20","author":"AM Habraken","year":"2004","unstructured":"Habraken AM, Duch\u00eane L (2004) Anisotropic elasto-plastic finite element analysis using a stress\u2013strain interpolation method based on a polycrystalline model. Int J Plast 20:1525\u20131560. https:\/\/doi.org\/10.1016\/j.ijplas.2003.11.006","journal-title":"Int J Plast"},{"key":"1672_CR42","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmatprotec.2019.116449","volume":"277","author":"F Han","year":"2020","unstructured":"Han F, Diehl M, Roters F (2020) Raabe D (2020) using spectral-based representative volume element crystal plasticity simulations to predict yield surface evolution during large scale forming simulations. J Mater Proc Tech 277:116449. https:\/\/doi.org\/10.1016\/j.jmatprotec.2019.116449","journal-title":"J Mater Proc Tech"},{"issue":"9","key":"1672_CR43","first-page":"1376","volume":"81","author":"Y Hanabusa","year":"2010","unstructured":"Hanabusa Y, Takizawa H, Kuwabara T (2010) Evaluation of accuracy of stress measurements determined in biaxial stress tests with cruciform specimen using numerical method. Steel Res Int 81(9):1376\u20131379","journal-title":"Steel Res Int"},{"key":"1672_CR44","doi-asserted-by":"publisher","first-page":"961","DOI":"10.1016\/j.jmatprotec.2012.12.007","volume":"213","author":"Y Hanabusa","year":"2013","unstructured":"Hanabusa Y, Takizawa H, Kuwabara T (2013) Numerical verification of a biaxial tensile test method using a cruciform specimen. J Mater Process Technol 213:961. https:\/\/doi.org\/10.1016\/j.jmatprotec.2012.12.007","journal-title":"J Mater Process Technol"},{"key":"1672_CR45","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1115\/1.4010900","volume":"21","author":"AV Hershey","year":"1954","unstructured":"Hershey AV (1954) The plasticity of an isotropic aggregate of anisotropic face centred cubic crystals. J Appl Mech 21:241\u2013249. https:\/\/doi.org\/10.1115\/1.4010900","journal-title":"J Appl Mech"},{"issue":"1033","key":"1672_CR46","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1098\/rspa.1948.0045","volume":"193A","author":"R Hill","year":"1948","unstructured":"Hill R (1948) A theory of the yielding and plastic flow of anisotropic metals. Proc R Soc Lond Ser A 193A(1033):281\u2013297. https:\/\/doi.org\/10.1098\/rspa.1948.0045","journal-title":"Proc R Soc Lond Ser A"},{"key":"1672_CR47","volume-title":"Multiscale friction modeling for sheet metal forming","author":"J Hol","year":"2013","unstructured":"Hol J (2013) Multiscale friction modeling for sheet metal forming. PhD Thesis University of Twente, Enschede"},{"issue":"1","key":"1672_CR48","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1016\/j.matt.2020.04.019","volume":"3","author":"YC Hsu","year":"2020","unstructured":"Hsu YC, Yu C-H, Buehler MJ (2020) Using Deep learning to predict fracture patterns in crystalline solids. Matter 3(1):197\u2013211","journal-title":"Matter"},{"key":"1672_CR49","unstructured":"Hutchinson WB, Lindh E & Bate P (1999) On the determination of textures from discrete orientation measurements. Proc. IICOTOM 12th McGill University, Montreal, Canada, August 9-13, Ed. by Jerzy A. Szpunar in NRC Research Press, 35\u201339"},{"issue":"2010","key":"1672_CR50","doi-asserted-by":"publisher","first-page":"2223","DOI":"10.1016\/j.ijsolstr.2010.04.017","volume":"47","author":"K Inal","year":"2010","unstructured":"Inal K, Mishra RK, Cazacu O (2010) Forming simulation of aluminum sheets using an anisotropic yield function coupled with crystal plasticity theory. Int J Solids Struct 47(2010):2223\u20132233. https:\/\/doi.org\/10.1016\/j.ijsolstr.2010.04.017","journal-title":"Int J Solids Struct"},{"key":"1672_CR51","doi-asserted-by":"crossref","unstructured":"Inoue T, Takizawa H, Kuwabara T, Nomura S. (2018) Benchmark 2 \u2013 Cup drawing of anisotropic thick steel sheet, NUMISHEET 2018, 11th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes, J Phys: Conf Ser 1063, Hama T, Kuroda M, Kuwabara T, Takahashi S, Yamanaka A (Eds.), 59\u2013127","DOI":"10.1088\/1742-6596\/1063\/1\/011001"},{"key":"1672_CR52","unstructured":"ISO 16842 (2014) Metallic materials \u2014 Sheet and strip \u2014 Biaxial tensile testing method using a cruciform test piece"},{"issue":"1\u20134","key":"1672_CR53","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1016\/0924-0136(94)01371-7","volume":"50","author":"L Kaiping","year":"1995","unstructured":"Kaiping L, Habraken A, Bruneel H (1995) Simulation of square cup deep drawing with different finite elements. J Mater Process Technol 50(1\u20134):81\u201391 https:\/\/doi.org\/10.1016\/0924-0136(94)01371-7","journal-title":"J Mater Process Technol"},{"key":"1672_CR54","doi-asserted-by":"publisher","first-page":"1859","DOI":"10.1016\/0022-5096(93)90073-O","volume":"41","author":"AP Karafillis","year":"1993","unstructured":"Karafillis AP, Boyce MC (1993) A general anisotropic yield criterion using bounds and a transformation weighting tensor. J Mech Phys Solids 41:1859\u20131886. https:\/\/doi.org\/10.1016\/0022-5096(93)90073-O","journal-title":"J Mech Phys Solids"},{"issue":"2020","key":"1672_CR55","doi-asserted-by":"publisher","first-page":"085005","DOI":"10.1088\/1361-651X\/abb8e2","volume":"28","author":"M Kasemer","year":"2020","unstructured":"Kasemer M, Falkinger G, G., Roters F. (2020) A numerical study of the influence of crystal plasticity modeling parameters on the plastic anisotropy of rolled aluminum sheet modelling Simul. Mater Sci Eng 28(2020):085005. https:\/\/doi.org\/10.1088\/1361-651X\/abb8e2","journal-title":"Mater Sci Eng"},{"key":"1672_CR56","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1016\/0924-0136(96)02336-9","volume":"60","author":"M Kawka","year":"1996","unstructured":"Kawka M, Makinouchi A (1996) Plastic anisotropy in FEM analysis using degenerated solid element. J Mater Process Technol 60:239\u2013242. https:\/\/doi.org\/10.1016\/0924-0136(96)02336-9","journal-title":"J Mater Process Technol"},{"key":"1672_CR57","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1016\/j.simpat.2015.02.007","volume":"53","author":"A Khalfallah","year":"2015","unstructured":"Khalfallah A, Alves JL, Oliveira MC, Menezes LF (2015) Influence of the characteristics of the experimental data set used to identify anisotropy parameters. Simul Model Pract Theory 53:15\u201344. https:\/\/doi.org\/10.1016\/j.simpat.2015.02.007","journal-title":"Simul Model Pract Theory"},{"key":"1672_CR58","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/j.ijplas.2012.12.003","volume":"45","author":"T Kuwabara","year":"2013","unstructured":"Kuwabara T, Sugawara F (2013) Multiaxial tube expansion test method for measurement of sheet metal deformation behavior under biaxial tension for a large strain range. Int J Plast 45:103\u2013118. https:\/\/doi.org\/10.1016\/j.ijplas.2012.12.003","journal-title":"Int J Plast"},{"key":"1672_CR59","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1016\/j.ijplas.2016.10.002","volume":"93","author":"T Kuwabara","year":"2017","unstructured":"Kuwabara T, Mori T, Asano M, Hakoyama T, Barlat F (2017) Material modeling of 6016-O and 6016-T4 aluminum alloy sheets and application to hole expansion forming simulation. Int J Plast 93:164\u2013186. https:\/\/doi.org\/10.1016\/j.ijplas.2016.10.002","journal-title":"Int J Plast"},{"issue":"9","key":"1672_CR60","doi-asserted-by":"publisher","first-page":"2611","DOI":"10.1016\/0956-7151(93)90130-K","volume":"41","author":"RA Lebensohn","year":"1993","unstructured":"Lebensohn RA, Tom\u00e9 CN (1993) A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: application to zirconium alloys. Acta Metall Mater 41(9):2611\u20132624. https:\/\/doi.org\/10.1016\/0956-7151(93)90130-K","journal-title":"Acta Metall Mater"},{"key":"1672_CR61","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1016\/j.ijplas.2015.04.005","volume":"71","author":"JY Lee","year":"2015","unstructured":"Lee JY, Barlat F, Lee MG (2015) Constitutive and friction modeling for accurate springback analysis of advanced high strength steel sheets. Int J Plast 71:113\u2013135. https:\/\/doi.org\/10.1016\/j.ijplas.2015.04.005","journal-title":"Int J Plast"},{"key":"1672_CR62","doi-asserted-by":"crossref","unstructured":"Levenberg K (1944) A method for the solution of certain nonlinear problems. Q Appl Math 2:164\u2013168.\u00a0https:\/\/www.jstor.org\/stable\/43633451","DOI":"10.1090\/qam\/10666"},{"key":"1672_CR63","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1016\/j.ijsolstr.2017.04.007","volume":"151","author":"J Lian","year":"2018","unstructured":"Lian J, Shen F, Jia X, Ahn D-C, Chae D-C, M\u00fcnstermann S, Bleck W (2018) An evolving non-associated Hill48 plasticity model accounting for anisotropic hardening and r-value evolution and its application to forming limit prediction. Int J Solids Struct 151:20\u201344. https:\/\/doi.org\/10.1016\/j.ijsolstr.2017.04.007","journal-title":"Int J Solids Struct"},{"key":"1672_CR64","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1016\/j.ijsolstr.2020.02.008","volume":"193\u2013194","author":"W Liu","year":"2020","unstructured":"Liu W, Chen BK, Pang Y, Najafzadeh A (2020) A 3D phenomenological yield function with both in and out-of-plane mechanical anisotropy using full-field crystal plasticity spectral method for modelling sheet metal forming of strong textured aluminum alloy. Int J Solids Struct 193\u2013194:117\u2013133. https:\/\/doi.org\/10.1016\/j.ijsolstr.2020.02.008","journal-title":"Int J Solids Struct"},{"key":"1672_CR65","unstructured":"Livermore Software Technology Corporation (LSTC). (2015) Ls-Dyna\u00ae Keyword User\u2019s Manual Volume II-Material Models pp. 286\u2013302"},{"key":"1672_CR66","doi-asserted-by":"publisher","first-page":"657","DOI":"10.1007\/s00170-018-1985-y","volume":"97","author":"J Ma","year":"2018","unstructured":"Ma J, Li H, Wang D et al (2018) Tribological behaviors in titanium sheet and tube forming at elevated temperatures: evaluation and modeling. Int J Adv Manuf Technol 97:657\u2013674. https:\/\/doi.org\/10.1007\/s00170-018-1985-y","journal-title":"Int J Adv Manuf Technol"},{"key":"1672_CR67","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/0924-0136(96)02303-5","volume":"60","author":"A Makinouchi","year":"1996","unstructured":"Makinouchi A (1996) Sheet metal forming simulation in industry. J Mater Process Technol 60:19\u201326. https:\/\/doi.org\/10.1016\/0924-0136(96)02303-5","journal-title":"J Mater Process Technol"},{"key":"1672_CR68","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1088\/1742-6596\/734\/2\/022003","volume":"734","author":"P-Y Manach","year":"2016","unstructured":"Manach P-Y, Co\u00ebr J, J\u00e9gat A, Laurent H, Yoon JW (2016) Benchmark 3 \u2013 Springback of an Al-mg alloy in warm forming conditions. Proceedings of NUMISHEET 2016, 10th international conference and workshop on numerical simulation of 3D sheet metal forming processes. J Physics: Conf Series, R Cardoso, OB Adetosro (Eds) 734:1\u201325. https:\/\/doi.org\/10.1088\/1742-6596\/734\/2\/022003","journal-title":"J Physics: Conf Series, R Cardoso, OB Adetosro (Eds)"},{"key":"1672_CR69","doi-asserted-by":"publisher","first-page":"012026","DOI":"10.1088\/1757-899X\/967\/1\/012026","volume":"967","author":"W Muhammad","year":"2020","unstructured":"Muhammad W, Brahme AP, Kang J, Eyr E, Wilkinson DS, Inal K (2020) A method to incorporate grain boundary strength and its effects on plastic deformation in FCC Polycrystals. IOP Conf Ser: Mater Sci Eng 967:012026. https:\/\/doi.org\/10.1088\/1757-899X\/967\/1\/012026","journal-title":"IOP Conf Ser: Mater Sci Eng"},{"key":"1672_CR70","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1016\/j.jmatprotec.2017.12.023","volume":"255","author":"CV Nielsen","year":"2018","unstructured":"Nielsen CV, Bay N (2018) Review of friction modeling in metal forming processes. J Mater Process Technol 255:234\u2013241. https:\/\/doi.org\/10.1016\/j.jmatprotec.2017.12.023","journal-title":"J Mater Process Technol"},{"key":"1672_CR71","doi-asserted-by":"publisher","first-page":"1951","DOI":"10.1016\/0001-6160(83)90014-7","volume":"31","author":"D Peirce","year":"1983","unstructured":"Peirce D, Asaro RJ, Needleman A (1983) Material rate dependence and localized deformation in crystalline solids. Acta Metall 31:1951\u20131976. https:\/\/doi.org\/10.1016\/0001-6160(83)90014-7","journal-title":"Acta Metall"},{"issue":"5","key":"1672_CR72","doi-asserted-by":"publisher","first-page":"847","DOI":"10.1016\/j.ijplas.2007.07.013","volume":"24","author":"B Plunkett","year":"2008","unstructured":"Plunkett B, Cazacu O, Barlat F (2008) Orthotropic yield criteria for description of the anisotropy in tension and compression of sheet metals. Int J Plast 24(5):847\u2013866. https:\/\/doi.org\/10.1016\/j.ijplas.2007.07.013","journal-title":"Int J Plast"},{"key":"1672_CR73","doi-asserted-by":"publisher","first-page":"444","DOI":"10.1016\/j.acme.2013.04.010","volume":"13","author":"P Pres","year":"2013","unstructured":"Pres P, Stembalski M, Skoczynski W (2013) Determination of the friction coefficient as a function of sliding speed and normal pressure for steel C45 and steel 40 HM. Arch Civ Mech Eng 13:444\u2013448. https:\/\/doi.org\/10.1016\/j.acme.2013.04.010","journal-title":"Arch Civ Mech Eng"},{"key":"1672_CR74","doi-asserted-by":"publisher","first-page":"012027","DOI":"10.1088\/1742-6596\/896\/1\/012027","volume":"896","author":"V Recklin","year":"2017","unstructured":"Recklin V, Dietrich F, Groche P (2017) In-situ-measurement of the friction coefficient in the deep drawing process. J Phys Conf Ser 896:012027. https:\/\/doi.org\/10.1088\/1742-6596\/896\/1\/012027","journal-title":"J Phys Conf Ser"},{"key":"1672_CR75","doi-asserted-by":"publisher","first-page":"1152","DOI":"10.1016\/j.actamat.2009.10.058","volume":"58","author":"F Roters","year":"2010","unstructured":"Roters F, Eisenlohr P, Hantcherli L et al (2010) Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: theory, experiments, applications. Acta Mater 58:1152\u20131211. https:\/\/doi.org\/10.1016\/j.actamat.2009.10.058","journal-title":"Acta Mater"},{"key":"1672_CR76","doi-asserted-by":"publisher","first-page":"420","DOI":"10.1016\/j.commatsci.2018.04.030","volume":"158","author":"F Roters","year":"2019","unstructured":"Roters F, Diehl M, Shanthraj P et al (2019) DAMASK \u2013 the D\u00fcsseldorf advanced material simulation kit for modeling multi-physics crystal plasticity, thermal, and damage phenomena from the single crystal up to the component scale. Comput Mater Sci 158:420\u2013478. https:\/\/doi.org\/10.1016\/j.commatsci.2018.04.030","journal-title":"Comput Mater Sci"},{"key":"1672_CR77","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1038\/s41524-018-0094-7","volume":"4","author":"A Rovinelli","year":"2018","unstructured":"Rovinelli A, Sangid MD, Proudhon H et al (2018) Using machine learning and a data-driven approach to identify the small fatigue crack driving force in polycrystalline materials. Npj Comput Mater 4:35. https:\/\/doi.org\/10.1038\/s41524-018-0094-7","journal-title":"Npj Comput Mater"},{"key":"1672_CR78","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1007\/BF03024331","volume":"19","author":"EB Saff","year":"1997","unstructured":"Saff EB, Kuijlaars ABJ (1997) Distributing many points on a sphere. Math Intell 19:5\u201311. https:\/\/doi.org\/10.1007\/BF03024331","journal-title":"Math Intell"},{"issue":"10","key":"1672_CR79","doi-asserted-by":"publisher","first-page":"1322","DOI":"10.1002\/nme.2653","volume":"80","author":"M Schwarze","year":"2009","unstructured":"Schwarze M, Reese S (2009) A reduced integration solid-shell finite element based on the eas and the ans concept-geometrically linear problems. Isnt J Numer Meth Eng 80(10):1322\u20131355. https:\/\/doi.org\/10.1002\/nme.2653","journal-title":"Isnt J Numer Meth Eng"},{"issue":"181","key":"1672_CR80","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s42452-021-04206-2","volume":"3","author":"B Sener","year":"2021","unstructured":"Sener B, Esener E, Firat M (2021) Modeling plastic anisotropy evolution of AISI 304 steel sheets by a polynomial yield function. SN Appl Sci 3(181):1\u201312. https:\/\/doi.org\/10.1007\/s42452-021-04206-2","journal-title":"SN Appl Sci"},{"key":"1672_CR81","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1016\/J.IJPLAS.2014.02.006","volume":"66","author":"P Shanthraj","year":"2015","unstructured":"Shanthraj P, Eisenlohr P, Diehl M, Roters F (2015) Numerically robust spectral methods for crystal plasticity simulations of heterogeneous materials. Int J Plast 66:31\u201345. https:\/\/doi.org\/10.1016\/J.IJPLAS.2014.02.006","journal-title":"Int J Plast"},{"key":"1672_CR82","doi-asserted-by":"publisher","unstructured":"Shen F, M\u00fcnstermann S, Lian J (2021) Forming limit prediction by the Marciniak\u2013Kuczynski model coupled with the evolving non-associated Hill48 plasticity model. J Mater Process Technol 287:116384.\u00a0https:\/\/doi.org\/10.1016\/j.jmatprotec.2019.116384","DOI":"10.1016\/j.jmatprotec.2019.116384"},{"key":"1672_CR83","doi-asserted-by":"publisher","first-page":"106554","DOI":"10.1016\/j.triboint.2020.106554","volume":"153","author":"M Shisode","year":"2021","unstructured":"Shisode M, Hazrati J, Mishra T et al (2021a) Modeling boundary friction of coated sheets in sheet metal forming. Tribol Int 153:106554. https:\/\/doi.org\/10.1016\/j.triboint.2020.106554","journal-title":"Tribol Int"},{"issue":"2","key":"1672_CR84","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1007\/s12289-016-1330-7","volume":"11","author":"D Shore","year":"2018","unstructured":"Shore D, Leo K, Jurij S, Van Houtte P, Van Bael A (2018) Process parameter influence on texture heterogeneity in asymmetric rolling of aluminum sheet alloys. Int J Mater Form 11(2):297\u2013309. https:\/\/doi.org\/10.1007\/s12289-016-1330-7","journal-title":"Int J Mater Form"},{"key":"1672_CR85","volume-title":"Friction modelling in sheet metal forming simulations: application and validation on an u-bend product, 8th forming technology forum 2015: advanced constitutive models in sheet metal forming, 135\u2013142","author":"M Sigvant","year":"2015","unstructured":"Sigvant, M., Hol, J., & Chezan, T. (2015). Friction modelling in sheet metal forming simulations: application and validation on an u-bend product, 8th forming technology forum 2015: advanced constitutive models in sheet metal forming, 135\u2013142"},{"key":"1672_CR86","unstructured":"Soare SC, (2007). On the use of homogeneous polynomials to develop anisotropic yield functions with applications to sheet forming. University of Florida, Department of Mechanical and Aerospace Engineering. Ph.D. Thesis"},{"key":"1672_CR87","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1098\/rspa.1976.0027","volume":"348","author":"Society TR","year":"1976","unstructured":"Society TR (1976) Bounds and self-consistent estimates for creep of polycrystalline materials. Proc R Soc London A Math Phys Sci 348:101\u2013127. https:\/\/doi.org\/10.1098\/rspa.1976.0027","journal-title":"Proc R Soc London A Math Phys Sci"},{"key":"1672_CR88","unstructured":"Sou (2019) Desenvolvimento de um Sistema de Controlo e Aquisi\u00e7\u00e3o de Dados para M\u00e1quina Universal de Ensaios de Chapas Met\u00e1licas (in portuguese), Jo\u00e3o Paulo Sousa, MSc thesis (pp.46), Faculty of Engineering, University of Porto"},{"key":"1672_CR89","doi-asserted-by":"publisher","first-page":"1777","DOI":"10.1016\/j.ijplas.2009.02.003","volume":"25","author":"TB Stoughton","year":"2009","unstructured":"Stoughton TB, Yoon JW (2009) Anisotropic hardening and non-associated flow in proportional loading of sheet metals. Int J Plast 25:1777\u20131817. https:\/\/doi.org\/10.1016\/j.ijplas.2009.02.003","journal-title":"Int J Plast"},{"issue":"1","key":"1672_CR90","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0022-5096(52)90002-1","volume":"1","author":"HW Swift","year":"1952","unstructured":"Swift HW (1952) Plastic instability under plane stress. J Mech Physics Solids 1(1):1\u201318. https:\/\/doi.org\/10.1016\/0022-5096(52)90002-1","journal-title":"J Mech Physics Solids"},{"key":"1672_CR91","first-page":"307","volume":"62","author":"GI Taylor","year":"1938","unstructured":"Taylor GI (1938) Plastic strain in metals. J Inst Met 62:307\u2013324","journal-title":"J Inst Met"},{"key":"1672_CR92","unstructured":"Thi\u00e9baut C, Voltz C, Platon R. (1999) Limiting drawing height test with hydroforming. Proceedings of the NUMISHEET\u201999, 4th International Conference and Workshop on Numerical Simulation of 3D Sheet Forming Processes, Gelin JC, Picart P (Eds.), University of France-Comt\u00e9 and E.N.S.M.M., BURS (Eds.), 1:631\u2013636, ISBN: 2\u201384449\u2013001-8"},{"issue":"10","key":"1672_CR93","doi-asserted-by":"publisher","first-page":"1637","DOI":"10.1016\/0001-6160(84)90222-0","volume":"32","author":"C Tome","year":"1984","unstructured":"Tome C, Canova GR, Kocks UF, Christodoulou N, Jonas JJ (1984) The relation between macroscopic and microscopic strain hardening in FCC polycrystals. Acta Metall 32(10):1637\u20131653. https:\/\/doi.org\/10.1016\/0001-6160(84)90222-0","journal-title":"Acta Metall"},{"issue":"4","key":"1672_CR94","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1155\/TSM.19.229","volume":"19","author":"L Toth","year":"1992","unstructured":"Toth L, Van Houtte P (1992) Discretization techniques for orientation distribution-functions. Text Microstruct 19(4):229\u2013244. https:\/\/doi.org\/10.1155\/TSM.19.229","journal-title":"Text Microstruct"},{"key":"1672_CR95","doi-asserted-by":"publisher","first-page":"590","DOI":"10.2507\/IJSIMM16(4)3.392","volume":"16","author":"T Trzepiecinski","year":"2017","unstructured":"Trzepiecinski T, Lemu HG, Fejkiel R (2017) Numerical simulation of effect of friction directionality on forming of anisotropic sheets. Int J Simul Model 16:590\u2013602. https:\/\/doi.org\/10.2507\/IJSIMM16(4)3.392","journal-title":"Int J Simul Model"},{"key":"1672_CR96","unstructured":"Van Houtte, P. (1995). MTM-FHM Software, Ver. 2. User Manual"},{"issue":"6","key":"1672_CR97","first-page":"702","volume":"80","author":"P Van Houtte","year":"2004","unstructured":"Van Houtte P, Li S, Engler O (2004) Modelling deformation texture of aluminium alloys using grain interaction models. Aluminium 80(6):702\u2013706","journal-title":"Aluminium"},{"issue":"3","key":"1672_CR98","doi-asserted-by":"publisher","first-page":"589","DOI":"10.1016\/j.ijplas.2004.04.011","volume":"21","author":"P Van Houtte","year":"2005","unstructured":"Van Houtte P, Li S, Seefeldt M, Delannay L (2005) Deformation texture prediction: from the Taylor model to the advanced Lamel model. Int J Plast 21(3):589\u2013624. https:\/\/doi.org\/10.1016\/j.ijplas.2004.04.011","journal-title":"Int J Plast"},{"issue":"2","key":"1672_CR99","doi-asserted-by":"publisher","first-page":"332","DOI":"10.1016\/j.ijplas.2008.02.001","volume":"25","author":"P Van Houtte","year":"2009","unstructured":"Van Houtte P, Yerra SK, Van Bael A (2009) The facet method: a hierarchical multilevel modelling scheme for anisotropic convex plastic potentials. Int J Plast 25(2):332\u2013360. https:\/\/doi.org\/10.1016\/j.ijplas.2008.02.001","journal-title":"Int J Plast"},{"issue":"11","key":"1672_CR100","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1007\/s11837-011-0189-9","volume":"63","author":"P Van Houtte","year":"2011","unstructured":"Van Houtte P, Gawad J, Eyckens P, Van Bael B, Samaey G, Roose D (2011) A full-field strategy to take texture-induced anisotropy into account during FE simulations of metal forming processes. JOM 63(11):37\u201343. https:\/\/doi.org\/10.1007\/s11837-011-0189-9","journal-title":"JOM"},{"key":"1672_CR101","doi-asserted-by":"publisher","first-page":"4475","DOI":"10.1007\/s11661-013-1895-4","volume":"A44","author":"G Vincze","year":"2013","unstructured":"Vincze G, Barlat F, Rauch EF, Tome CN, Butuc MC, Gr\u00e1cio JJ (2013) Experiments and modeling of low carbon steel sheet subjected to double strain path changes. Metall Mater Trans A A44:4475\u20134479. https:\/\/doi.org\/10.1007\/s11661-013-1895-4","journal-title":"Metall Mater Trans A"},{"key":"1672_CR102","doi-asserted-by":"publisher","first-page":"032111","DOI":"10.1088\/1742-6596\/734\/3\/032111","volume":"734","author":"G Vincze","year":"2016","unstructured":"Vincze G, Butuc MC, Barlat F (2016) \u201cMechanical behavior of TWIP steel under shear loading\u201d, Numisheet 2016, IOP publishing. J Phys Conf Ser 734:032111 pp. 1-4","journal-title":"J Phys Conf Ser"},{"key":"1672_CR103","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1007\/s12289-011-1038-7","volume":"4","author":"IN Vladimirov","year":"2011","unstructured":"Vladimirov IN, Pietryga MP, Reese S (2011) On the influence of kinematic hardening on plastic anisotropy in the context of finite strain plasticity. Int J Mater Form 4:255. https:\/\/doi.org\/10.1007\/s12289-011-1038-7","journal-title":"Int J Mater Form"},{"key":"1672_CR104","first-page":"537","volume":"74","author":"E Voce","year":"1948","unstructured":"Voce E (1948) The relationship between stress and strain for homogeneous deformation. J Inst Met 74:537\u2013562","journal-title":"J Inst Met"},{"key":"1672_CR105","doi-asserted-by":"publisher","unstructured":"Watson M, Dick R, Helen Huang Y, Lockley A, Cardoso R, Santos A. (2016) Benchmark 1 \u2013 Failure Prediction after Cup Drawing, Reverse Redrawing and Expansion. Proceedings of NUMISHEET 2016, 10th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes, Journal of Physics: Conference Series, R. Cardoso, O.B. Adetosro (Eds.), 734:1\u201385. https:\/\/doi.org\/10.1088\/1742-6596\/734\/2\/022001","DOI":"10.1088\/1742-6596\/734\/2\/022001"},{"key":"1672_CR106","doi-asserted-by":"publisher","first-page":"113234","DOI":"10.1016\/j.cma.2020.113234","volume":"369","author":"L Wu","year":"2020","unstructured":"Wu L, Nguyen VD, Kilingar NG, Noels L (2020) A recurrent neural network-accelerated multi-scale model for elasto-plastic heterogeneous materials subjected to random cyclic and non-proportional loading paths. Comput Methods Appl Mech Eng 369:113234. https:\/\/doi.org\/10.1016\/j.cma.2020.113234","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1672_CR107","doi-asserted-by":"publisher","unstructured":"Yamanaka A, Kamijyo R, Koenuma K et al (2020) Deep neural network approach to estimate biaxial stress-strain curves of sheet metals. Mater Des 195:108970.\u00a0https:\/\/doi.org\/10.1016\/j.matdes.2020.108970","DOI":"10.1016\/j.matdes.2020.108970"},{"key":"1672_CR108","unstructured":"Yang D-Y, Soo Ik O, Kim HHEYH. (2002) Benchmark Results of test A - Deep Drawing of a Cylindrical Cup, Proceedings of the NUMISHEET 2002, 5th International Conference and Workshop on Numerical Simulation of 3D Sheet Forming Processes - Verification of Simulation with Experiment, Yang DY, Soo Ik O, Kim HHEYH (Eds.) 2:677\u2013756.\u00a0October 21-25"},{"key":"1672_CR109","doi-asserted-by":"publisher","first-page":"1165","DOI":"10.1016\/j.ijplas.2011.01.002","volume":"27","author":"JW Yoon","year":"2011","unstructured":"Yoon JW, Dick RE, Barlat F (2011) A new analytical theory for earing generated from anisotropic plasticity. Int J Plast 27:1165\u20131184. https:\/\/doi.org\/10.1016\/j.ijplas.2011.01.002","journal-title":"Int J Plast"},{"issue":"2","key":"1672_CR110","doi-asserted-by":"publisher","first-page":"607","DOI":"10.1115\/1.3422732","volume":"39","author":"WFA Hosford","year":"1972","unstructured":"Hosford WFA (1972) Generalized isotropic yield criterion. J Appl Mech 39(2):607\u2013609. https:\/\/doi.org\/10.1115\/1.3422732","journal-title":"J Appl Mech"}],"container-title":["International Journal of Material Forming"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12289-022-01672-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12289-022-01672-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12289-022-01672-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,12]],"date-time":"2022-09-12T14:23:50Z","timestamp":1662992630000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12289-022-01672-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,15]]},"references-count":110,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2022,9]]}},"alternative-id":["1672"],"URL":"https:\/\/doi.org\/10.1007\/s12289-022-01672-w","relation":{},"ISSN":["1960-6206","1960-6214"],"issn-type":[{"value":"1960-6206","type":"print"},{"value":"1960-6214","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,7,15]]},"assertion":[{"value":"5 January 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 February 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 July 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"61"}}