Modelling and simulation of metal additive manufacturing processes with particle methods: A review

References

• Standard A. Standard terminology for additive manufacturing technologies. ASTM Int F2792-12a. 2012;10.04:1–9.
   Google Scholar
• Gibson I, Rosen D, Stucker B, et al. Additive manufacturing technologies. Vol. 17. Cham (Switzerland): Springer; 2021.
   Google Scholar
• Wohlers T. Wohlers report. Wohlers Associates Inc; 2014.
   Google Scholar
• King W, Anderson AT, Ferencz RM, et al. Overview of modelling and simulation of metal powder bed fusion process at Lawrence Livermore National Laboratory. Mater Sci Technol. 2015;31(8):957–968. doi: 10.1179/1743284714Y.0000000728
   Web of Science ®Google Scholar
• Galantucci LM, Guerra MG, Dassisti M, et al. Additive manufacturing: new trends in the 4th industrial revolution. In: Proceedings of the 4th International Conference on the Industry 4.0 Model for Advanced Manufacturing: AMP 4; Springer; 2019. p. 153–169.
   Google Scholar
• Mehrpouya M, Dehghanghadikolaei A, Fotovvati B, et al. The potential of additive manufacturing in the smart factory industrial 4.0: a review. Appl Sci. 2019;9(18):3865. doi: 10.3390/app9183865
   Google Scholar
• Koenig B. Toyota using AI, 3D printing as tools. 2022.
   Google Scholar
• Campbell I, Diegel O, Kowen J, et al. Wohlers report 2018: 3D printing and additive manufacturing state of the industry: annual worldwide progress report. 2018.
   Google Scholar
• King WE, Anderson AT, Ferencz RM, et al. Laser powder bed fusion additive manufacturing of metals; physics, computational, and materials challenges. Appl Phys Rev. 2015 Dec;2(4):041304. doi: 10.1063/1.4937809
   Web of Science ®Google Scholar
• Yan W, Lin S, Kafka OL, et al. Modeling process-structure-property relationships for additive manufacturing. Front Mech Eng. 2018;13(4):482–492. doi: 10.1007/s11465-018-0505-y
   Web of Science ®Google Scholar
• Yadroitsev I. Selective laser melting: direct manufacturing of 3D-objects by selective laser melting of metal powders. Saint-Etienne: LAP Lambert Academic Publishing; 2009.
   Google Scholar
• Nie P, Ojo O, Li Z. Numerical modeling of microstructure evolution during laser additive manufacturing of a nickel-based superalloy. Acta Mater. 2014;77:85–95. doi: 10.1016/j.actamat.2014.05.039
   Web of Science ®Google Scholar
• Sahoo S, Chou K. Phase-field simulation of microstructure evolution of Ti–6Al–4V in electron beam additive manufacturing process. Addit Manuf. 2016;9:14–24.
   Web of Science ®Google Scholar
• Khairallah SA, Anderson A. Mesoscopic simulation model of selective laser melting of stainless steel powder. J Mater Process Technol. 2014;214(11):2627–2636. doi: 10.1016/j.jmatprotec.2014.06.001
   Web of Science ®Google Scholar
• Heeling T, Cloots M, Wegener K. Melt pool simulation for the evaluation of process parameters in selective laser melting. Addit Manuf. 2017;14:116–125.
   Web of Science ®Google Scholar
• Wang Z, Denlinger E, Michaleris P, et al. Residual stress mapping in inconel 625 fabricated through additive manufacturing: method for neutron diffraction measurements to validate thermomechanical model predictions. Mater Des. 2017;113:169–177. doi: 10.1016/j.matdes.2016.10.003
   Web of Science ®Google Scholar
• Williams RJ, Davies CM, Hooper PA. A pragmatic part scale model for residual stress and distortion prediction in powder bed fusion. Addit Manuf. 2018;22:416–425.
   Web of Science ®Google Scholar
• Verma R, Kumar P, Jayaganthan R, et al. Extended finite element simulation on tensile, fracture toughness and fatigue crack growth behaviour of additively manufactured Ti6Al4V alloy. Theoret Appl Fract Mech. 2022;117:103163. doi: 10.1016/j.tafmec.2021.103163
   Web of Science ®Google Scholar
• Markl M, Körner C. Multiscale modeling of powder bed–based additive manufacturing. Annu Rev Mater Res. 2016;46(1):93–123. doi: 10.1146/matsci.2016.46.issue-1
   Google Scholar
• Meier C, Penny RW, Zou Y, et al. Thermophysical phenomena in metal additive manufacturing by selective laser melting: fundamentals, modeling, simulation, and experimentation. Ann Rev Heat Transf. 2017;20(1):241–316. doi: 10.1615/AnnualRevHeatTransfer.v20
   Google Scholar
• Francois MM, Sun A, King WE, et al. Modeling of additive manufacturing processes for metals: challenges and opportunities. Curr Opin Solid State Mater Sci. 2017;21(4):198–206. doi: 10.1016/j.cossms.2016.12.001
   Web of Science ®Google Scholar
• Wei H, Mukherjee T, Zhang W, et al. Mechanistic models for additive manufacturing of metallic components. Prog Mater Sci. 2021;116:100703. doi: 10.1016/j.pmatsci.2020.100703
   Web of Science ®Google Scholar
• Luo Z, Zhao Y. A survey of finite element analysis of temperature and thermal stress fields in powder bed fusion additive manufacturing. Addit Manuf. 2018;21:318–332.
   Web of Science ®Google Scholar
• Bayat M, Dong W, Thorborg J, et al. A review of multi-scale and multi-physics simulations of metal additive manufacturing processes with focus on modeling strategies. Addit Manuf. 2021;47:102278.
   Web of Science ®Google Scholar
• Li E, Zhou Z, Wang L, et al. Particle scale modelling of powder recoating and melt pool dynamics in laser powder bed fusion additive manufacturing: a review. Powder Technol. 2022;409:117789. doi: 10.1016/j.powtec.2022.117789
   Web of Science ®Google Scholar
• Wirth F. Process understanding, modeling and predictive simulation of laser cladding. Zurich (Switzerland): ETH Zurich; 2018.
   Google Scholar
• Cook PS, Murphy AB. Simulation of melt pool behaviour during additive manufacturing: underlying physics and progress. Addit Manuf. 2020 Jan;31:100909.
   Web of Science ®Google Scholar
• Steen WM, Mazumder J. Laser material processing. London: Springer-Verlag London Ltd; 2010.
   Google Scholar
• Gu DD, Meiners W, Wissenbach K, et al. Laser additive manufacturing of metallic components: materials, processes and mechanisms. Int Mater Rev. 2012;57(3):133–164. doi: 10.1179/1743280411Y.0000000014
   Web of Science ®Google Scholar
• Khairallah SA, Anderson AT, Rubenchik A, et al. Laser powder-bed fusion additive manufacturing: physics of complex melt flow and formation mechanisms of pores, spatter, and denudation zones. Acta Mater. 2016;108:36–45. doi: 10.1016/j.actamat.2016.02.014
   Web of Science ®Google Scholar
• Brackbill JU, Kothe DB, Zemach C. A continuum method for modeling surface tension. J Comput Phys. 1992;100(2):335–354. doi: 10.1016/0021-9991(92)90240-Y
   Web of Science ®Google Scholar
• Chow T. Wetting of rough surfaces. J Phys Condens Matter. 1998;10(27):L445–L451. doi: 10.1088/0953-8984/10/27/001.
   Web of Science ®Google Scholar
• Semak V, Matsunawa A. The role of recoil pressure in energy balance during laser materials processing. J Phys D: Appl Phys. 1997;30(18):2541–2552. doi: 10.1088/0022-3727/30/18/008
   Web of Science ®Google Scholar
• Klassen A, Scharowsky T, Körner C. Evaporation model for beam based additive manufacturing using free surface lattice boltzmann methods. J Phys D Appl Phys. 2014;47(27):275303. doi: 10.1088/0022-3727/47/27/275303
   Web of Science ®Google Scholar
• Klassen A, Forster VE, Körner C. A multi-component evaporation model for beam melting processes. Model Simul Mater Sci Eng. 2017;25(2):025003. doi: 10.1088/1361-651X/aa5289
   Web of Science ®Google Scholar
• Weirather J, Rozov V, Wille M, et al. A smoothed particle hydrodynamics model for laser beam melting of Ni-based alloy 718. Comput Math Appl. 2019;78(7):2377–2394.
   Web of Science ®Google Scholar
• Gusarov A, Yadroitsev I, Bertrand P, et al. Model of radiation and heat transfer in laser-powder interaction zone at selective laser melting. ASME J Heat Transf. 2009;131(7):1–10. doi: 10.1115/1.3109245
   Web of Science ®Google Scholar
• Hashemi H, Sliepcevich C. A numerical method for solving two-dimensional problems of heat conduction with change of phase. Chem Eng Prog Symp Ser. 1967;63:34–41.
   Google Scholar
• Kaufman L, Bernstein H. Computer calculation of phase diagrams. with special reference to refractory metals. 1970.
   Google Scholar
• Ganeriwala R, Zohdi TI. A coupled discrete element-finite difference model of selective laser sintering. Granul Matter. 2016;18(2):21. doi: 10.1007/s10035-016-0626-0
   Web of Science ®Google Scholar
• Marshall P. Austenitic stainless steels: microstructure and mechanical properties. 1984.
   Google Scholar
• Russell M, Souto-Iglesias A, Zohdi T. Numerical simulation of laser fusion additive manufacturing processes using the SPH method. Comput Methods Appl Mech Eng. 2018;341:163–187. doi: 10.1016/j.cma.2018.06.033
   Web of Science ®Google Scholar
• Mills KC. Recommended values of thermophysical properties for selected commercial alloys. Cambridge (England): Woodhead Publishing; 2002.
   Google Scholar
• Sahoo P, Debroy T, McNallan M. Surface tension of binary metal–surface active solute systems under conditions relevant to welding metallurgy. Metall Trans B. 1988;19(3):483–491. doi: 10.1007/BF02657748
   Web of Science ®Google Scholar
• He X, Fuerschbach P, DebRoy T. Heat transfer and fluid flow during laser spot welding of 304 stainless steel. J Phys D Appl Phys. 2003;36(12):1388–1398. doi: 10.1088/0022-3727/36/12/306
   Web of Science ®Google Scholar
• Wessels H, Weißenfels C, Wriggers P. Metal particle fusion analysis for additive manufacturing using the stabilized optimal transportation meshfree method. Comput Methods Appl Mech Eng. 2018;339:91–114. doi: 10.1016/j.cma.2018.04.042
   Web of Science ®Google Scholar
• Wessels H. Thermo-mechanical modeling for selective laser melting. Institut für Kontinuumsmechanik, Gottfried Wilhelm Leibniz Universität Hannover. 2019.
   Google Scholar
• Chawla T, Graff D, Borg R, et al. Thermophysical properties of mixed oxide fuel and stainless steel type 316 for use in transition phase analysis. Nuclear Eng Des. 1981;67(1):57–74. doi: 10.1016/0029-5493(81)90155-2
   Web of Science ®Google Scholar
• Goldak JA, Akhlaghi M. Computational welding mechanics. New York (NY): Springer Science & Business Media; 2005.
   Google Scholar
• Karditsas PJ, Baptiste M-J. Thermal and structural properties of fusion related materials. UKAEA Government Division; 1995. (Tech. rep.).
   Google Scholar
• Hodge N, Ferencz R, Solberg J. Implementation of a thermomechanical model for the simulation of selective laser melting. Comput Mech. 2014;54(1):33–51. doi: 10.1007/s00466-014-1024-2
   Web of Science ®Google Scholar
• Neira-Arce A. Thermal modeling and simulation of electron beam melting for rapid prototyping on Ti6Al4V alloys. Ann Arbor (MI): ProQuest LLC; 2012.
   Google Scholar
• Andreotta R, Ladani L, Brindley W. Finite element simulation of laser additive melting and solidification of inconel 718 with experimentally tested thermal properties. Finite Elem Anal Des. 2017;135:36–43. doi: 10.1016/j.finel.2017.07.002
   Web of Science ®Google Scholar
• Chen H, Wei Q, Wen S, et al. Flow behavior of powder particles in layering process of selective laser melting: numerical modeling and experimental verification based on discrete element method. Int J Mach Tools Manuf. 2017;123:146–159. doi: 10.1016/j.ijmachtools.2017.08.004
   Web of Science ®Google Scholar
• You Y, Zhao Y. Discrete element modelling of ellipsoidal particles using super-ellipsoids and multi-spheres: a comparative study. Powder Technol. 2018;331:179–191. doi: 10.1016/j.powtec.2018.03.017
   Web of Science ®Google Scholar
• Spierings AB, Voegtlin M, Bauer T, et al. Powder flowability characterisation methodology for powder-bed-based metal additive manufacturing. Progress Addit Manuf. 2016;1(1–2):9–20. doi: 10.1007/s40964-015-0001-4
   Google Scholar
• Dai L, Chan Y, Vastola G, et al. Characterizing the intrinsic properties of powder–a combined discrete element analysis and hall flowmeter testing study. Adv Powder Technol. 2021;32(1):80–87. doi: 10.1016/j.apt.2020.11.015
   Web of Science ®Google Scholar
• Nguyen QB, Nai MLS, Zhu Z, et al. Characteristics of inconel powders for powder-bed additive manufacturing. Engineering. 2017;3(5):695–700. doi: 10.1016/J.ENG.2017.05.012
   Web of Science ®Google Scholar
• Tan Y, Zhang J, Li X, et al. Comprehensive evaluation of powder flowability for additive manufacturing using principal component analysis. Powder Technol. 2021;393:154–164. doi: 10.1016/j.powtec.2021.07.069
   Web of Science ®Google Scholar
• Lumay G, Boschini F, Traina K, et al. Measuring the flowing properties of powders and grains. Powder Technol. 2012;224:19–27. doi: 10.1016/j.powtec.2012.02.015
   Web of Science ®Google Scholar
• Cordova L, Chen Z. Impact of powder recoating speed on built properties in PBF-LB process. Procedia CIRP. 2022;115:125–129. doi: 10.1016/j.procir.2022.10.061
   Google Scholar
• Zhang Z, Ge P, Li T, et al. Electromagnetic wave-based analysis of laser–particle interactions in directed energy deposition additive manufacturing. Addit Manuf. 2020;34:101284.
   Web of Science ®Google Scholar
• Yao X, Zhang Z. Laser-particle interaction-based heat source model of laser powder bed fusion additive manufacturing. Opt Laser Technol. 2022;155:108402. doi: 10.1016/j.optlastec.2022.108402
   Web of Science ®Google Scholar
• Zhang Z, Ge P, Li J, et al. Laser–particle interaction-based analysis of powder particle effects on temperatures and distortions in directed energy deposition additive manufacturing. J Therm Stresses. 2021;44(9):1068–1095. doi: 10.1080/01495739.2021.1954572
   Web of Science ®Google Scholar
• Yao X, Li J, Wang Y, et al. Experimental and numerical studies of nozzle effect on powder flow behaviors in directed energy deposition additive manufacturing. Int J Mech Sci. 2021;210:106740. doi: 10.1016/j.ijmecsci.2021.106740
   Web of Science ®Google Scholar
• Gao X, Yao X, Niu F, et al. The influence of nozzle geometry on powder flow behaviors in directed energy deposition additive manufacturing. Adv Powder Technol. 2022;33(3):103487. doi: 10.1016/j.apt.2022.103487
   Web of Science ®Google Scholar
• Zohdi TI. Additive particle deposition and selective laser processing-a computational manufacturing framework. Comput Mech. 2014 Jul;54(1):171–191. doi: 10.1007/s00466-014-1012-6
   Web of Science ®Google Scholar
• Zohdi T. Computation of the coupled thermo-optical scattering properties of random particulate systems. Comput Methods Appl Mech Eng. 2006;195(41–43):5813–5830. doi: 10.1016/j.cma.2005.04.023
   Web of Science ®Google Scholar
• Zaeh MF, Branner G. Investigations on residual stresses and deformations in selective laser melting. Prod Eng. 2010;4(1):35–45. doi: 10.1007/s11740-009-0192-y
   Google Scholar
• Körner C, Attar E, Heinl P. Mesoscopic simulation of selective beam melting processes. Comp Part Mech. 2011;6:978–987.
   Google Scholar
• Panwisawas C, Qiu C, Anderson MJ, et al. Mesoscale modelling of selective laser melting: thermal fluid dynamics and microstructural evolution. Comput Mater Sci. 2017;126:479–490. doi: 10.1016/j.commatsci.2016.10.011
   Web of Science ®Google Scholar
• Zohdi TI. Rapid simulation of laser processing of discrete particulate materials. Arch Comput Methods Eng. 2013;20(4):309–325. doi: 10.1007/s11831-013-9092-6
   Web of Science ®Google Scholar
• Qiu C, Panwisawas C, Ward M, et al. On the role of melt flow into the surface structure and porosity development during selective laser melting. Acta Mater. 2015;96:72–79. doi: 10.1016/j.actamat.2015.06.004
   Web of Science ®Google Scholar
• Panwisawas C, Sovani Y, Turner RP, et al. Modelling of thermal fluid dynamics for fusion welding. J Mater Process Technol. 2018;252:176–182. doi: 10.1016/j.jmatprotec.2017.09.019
   Web of Science ®Google Scholar
• Yan W, Smith J, Ge W, et al. Multiscale modeling of electron beam and substrate interaction: a new heat source model. Comput Mech. 2015;56(2):265–276. doi: 10.1007/s00466-015-1170-1
   Web of Science ®Google Scholar
• Zohdi T. On the optical thickness of disordered particulate media. Mech Mater. 2006;38(8–10):969–981. doi: 10.1016/j.mechmat.2005.06.025
   Web of Science ®Google Scholar
• Zacarias M, Malacara-Hernández D, Malacara-Hernández Z. Handbook of optical design. Boca Raton (FL): CRC Press; 2003.
   Google Scholar
• Yan W, Ge W, Qian Y, et al. Multi-physics modeling of single/multiple-track defect mechanisms in electron beam selective melting. Acta Mater. 2017;134:324–333. doi: 10.1016/j.actamat.2017.05.061
   Web of Science ®Google Scholar
• Yan W, Lin S, Kafka OL, et al. Data-driven multi-scale multi-physics models to derive process–structure–property relationships for additive manufacturing. Comput Mech. 2018;61(5):521–541. doi: 10.1007/s00466-018-1539-z
   Web of Science ®Google Scholar
• Ki H, Mazumder J, Mohanty PS. Modeling of laser keyhole welding: part I. Mathematical modeling, numerical methodology, role of recoil pressure, multiple reflections, and free surface evolution. Metall Mater Trans A. 2002;33(6):1817–1830. doi: 10.1007/s11661-002-0190-6
   Web of Science ®Google Scholar
• Otto A, Koch H, Vazquez RG. Multiphysical simulation of laser material processing. Phys Proc. 2012;39:843–852. doi: 10.1016/j.phpro.2012.10.109
   Google Scholar
• Gürtler F, Karg M, Dobler M, et al. Influence of powder distribution on process stability in laser beam melting: analysis of melt pool dynamics by numerical simulations. In: International Solid Freeform Fabrication Symposium; Austin (TX). 2014. p. 1099–1117.
   Google Scholar
• Lee Y, Zhang W. Modeling of heat transfer, fluid flow and solidification microstructure of nickel-base superalloy fabricated by laser powder bed fusion. Addit Manuf. 2016;12:178–188.
   Web of Science ®Google Scholar
• Liu B, Fang G, Lei L, et al. A new ray tracing heat source model for mesoscale CFD simulation of selective laser melting (SLM). Appl Math Model. 2020;79:506–520. doi: 10.1016/j.apm.2019.10.049
   Web of Science ®Google Scholar
• Hu H, Eberhard P. Thermomechanically coupled conduction mode laser welding simulations using smoothed particle hydrodynamics. Comput Particle Mech. 2017;4(4):473–486. doi: 10.1007/s40571-016-0140-5
   Web of Science ®Google Scholar
• Wessels H, Bode T, Weißenfels C, et al. Investigation of heat source modeling for selective laser melting. Comput Mech. 2019 May;63(5):949–970. doi: 10.1007/s00466-018-1631-4
   Web of Science ®Google Scholar
• Gürtler F-J, Karg M, Leitz K-H, et al. Simulation of laser beam melting of steel powders using the three-dimensional volume of fluid method. Phys Procedia. 2013;41:881–886. doi: 10.1016/j.phpro.2013.03.162
   Google Scholar
• Megahed M, Mindt H-W, N'Dri N, et al. Metal additive-manufacturing process and residual stress modeling. Integ Mater Manuf Innov. 2016;5(1):61–93. doi: 10.1186/s40192-016-0047-2
   Google Scholar
• Liu M, Liu G. Smoothed particle hydrodynamics (sph): an overview and recent developments. Arch Comput Methods Eng. 2010;17(1):25–76. doi: 10.1007/s11831-010-9040-7
   Web of Science ®Google Scholar
• Shadloo MS, Oger G, Le Touzé D. Smoothed particle hydrodynamics method for fluid flows, towards industrial applications: motivations, current state, and challenges. Comput Fluids. 2016;136:11–34. doi: 10.1016/j.compfluid.2016.05.029
   Web of Science ®Google Scholar
• Violeau D, Rogers BD. Smoothed particle hydrodynamics (sph) for free-surface flows: past, present and future. J Hydraul Res. 2016;54(1):1–26. doi: 10.1080/00221686.2015.1119209
   Web of Science ®Google Scholar
• Fürstenau J-P, Wessels H, Weißenfels C, et al. Generating virtual process maps of slm using powder-scale sph simulations. Comput Part Mech. 2020;7(4):655–677. doi: 10.1007/s40571-019-00296-3
   Web of Science ®Google Scholar
• Fan Z, Wang H, Huang Z, et al. A lagrangian meshfree mesoscale simulation of powder bed fusion additive manufacturing of metals. Int J Numer Methods Eng. 2021;122(2):483–514. doi: 10.1002/nme.v122.2
   Web of Science ®Google Scholar
• Dao MH, Lou J. Simulations of laser assisted additive manufacturing by smoothed particle hydrodynamics. Comput Methods Appl Mech Eng. 2021;373:113491. doi: 10.1016/j.cma.2020.113491
   Web of Science ®Google Scholar
• Dao MH, Lou J. Simulations of directed energy deposition additive manufacturing process by smoothed particle hydrodynamics methods. Int J Adv Manuf Technol. 2022;120(7-8):4755–4774. doi: 10.1007/s00170-022-09050-1
   Web of Science ®Google Scholar
• Meier C, Fuchs SL, Hart AJ, et al. A novel smoothed particle hydrodynamics formulation for thermo-capillary phase change problems with focus on metal additive manufacturing melt pool modeling. Comput Methods Appl Mech Eng. 2021;381:113812. doi: 10.1016/j.cma.2021.113812
   Web of Science ®Google Scholar
• Fuchs SL, Praegla PM, Cyron CJ, et al. A versatile sph modeling framework for coupled microfluid-powder dynamics in additive manufacturing: binder jetting, material jetting, directed energy deposition and powder bed fusion. Eng Comput. 2022;38:4853–4877. doi: 10.1007/s00366-022-01724-4
   Google Scholar
• Körner C, Attar E, Heinl P. Mesoscopic simulation of selective beam melting processes. J Mater Process Technol. 2011;211(6):978–987. doi: 10.1016/j.jmatprotec.2010.12.016
   Web of Science ®Google Scholar
• Maeshima T, Kim Y, Zohdi TI. Particle-scale numerical modeling of thermo-mechanical phenomena for additive manufacturing using the material point method. Comput Part Mech. 2021;8(3):613–623. doi: 10.1007/s40571-020-00358-x
   Web of Science ®Google Scholar
• Cundall PA, Strack OD. A discrete numerical model for granular assemblies. Geotechnique. 1979;29(1):47–65. doi: 10.1680/geot.1979.29.1.47
   Web of Science ®Google Scholar
• Monaghan J. Sph and riemann solvers. J Comput Phys. 1997;136(2):298–307. doi: 10.1006/jcph.1997.5732
   Web of Science ®Google Scholar
• Lucy LB. A numerical approach to the testing of the fission hypothesis. Astron J. 1977;82:1013–1024. doi: 10.1086/112164
   Web of Science ®Google Scholar
• Liu G-R, Liu MB. Smoothed particle hydrodynamics: a meshfree particle method. Singapore: World Scientific; 2003.
   Google Scholar
• Afrasiabi M, Roethlin M, Wegener K. Contemporary meshfree methods for three dimensional heat conduction problems. Arch Comput Methods Eng. 2020 Nov;27(5):1413–1447. doi: 10.1007/s11831-019-09355-7
   Web of Science ®Google Scholar
• Li B, Habbal F, Ortiz M. Optimal transportation meshfree approximation schemes for fluid and plastic flows. Int J Numer Methods Eng. 2010;83(12):1541–1579. doi: 10.1002/nme.2869
   Web of Science ®Google Scholar
• Weißenfels C, Wriggers P. Stabilization algorithm for the optimal transportation meshfree approximation scheme. Comput Methods Appl Mech Eng. 2018;329:421–443. doi: 10.1016/j.cma.2017.09.031
   Web of Science ®Google Scholar
• Wang H, Liao H, Fan Z, et al. The hot optimal transportation meshfree (hotm) method for materials under extreme dynamic thermomechanical conditions. Comput Methods Appl Mech Eng. 2020;364:112958. doi: 10.1016/j.cma.2020.112958
   Web of Science ®Google Scholar
• Chen H, Wei Q, Zhang Y, et al. Powder-spreading mechanisms in powder-bed-based additive manufacturing: experiments and computational modeling. Acta Mater. 2019;179:158–171. doi: 10.1016/j.actamat.2019.08.030
   Web of Science ®Google Scholar
• Han Q, Gu H, Setchi R. Discrete element simulation of powder layer thickness in laser additive manufacturing. Powder Technol. 2019;352:91–102. doi: 10.1016/j.powtec.2019.04.057
   Web of Science ®Google Scholar
• Meier C, Weissbach R, Weinberg J, et al. Critical influences of particle size and adhesion on the powder layer uniformity in metal additive manufacturing. J Mater Process Technol. 2019;266:484–501. doi: 10.1016/j.jmatprotec.2018.10.037
   Web of Science ®Google Scholar
• Dai L, Chan Y, Vastola G, et al. Discrete element simulation of powder flow in revolution powder analyser: effects of shape factor, friction and adhesion. Powder Technol. 2022;408:117790. doi: 10.1016/j.powtec.2022.117790
   Web of Science ®Google Scholar
• Yim S, Bian H, Aoyagi K, et al. Spreading behavior of Ti48Al2Cr2Nb powders in powder bed fusion additive manufacturing process: experimental and discrete element method study. Addit Manuf. 2022;49:102489.
   Web of Science ®Google Scholar
• Lee Y, Gurnon AK, Bodner D, et al. Effect of particle spreading dynamics on powder bed quality in metal additive manufacturing. Integ Mater Manuf Innovat. 2020;9(4):410–422. doi: 10.1007/s40192-020-00193-1
   Web of Science ®Google Scholar
• Ganesan VV, Amerinatanzi A, Jain A. Discrete element modeling (DEM) simulations of powder bed densification using horizontal compactors in metal additive manufacturing. Powder Technol. 2022;405:117557. doi: 10.1016/j.powtec.2022.117557
   Web of Science ®Google Scholar
• Sehhat MH, Mahdianikhotbesara A. Powder spreading in laser-powder bed fusion process. Granul Matter. 2021;23(4):89. doi: 10.1007/s10035-021-01162-x
   Web of Science ®Google Scholar
• Lee Y, Nandwana P, Zhang W. Dynamic simulation of powder packing structure for powder bed additive manufacturing. Int J Adv Manuf Technol. 2018;96(1-4):1507–1520. doi: 10.1007/s00170-018-1697-3
   Web of Science ®Google Scholar
• Nan W, Pasha M, Bonakdar T, et al. Jamming during particle spreading in additive manufacturing. Powder Technol. 2018;338:253–262. doi: 10.1016/j.powtec.2018.07.030
   Web of Science ®Google Scholar
• Nan W, Ghadiri M. Numerical simulation of powder flow during spreading in additive manufacturing. Powder Technol. 2019;342:801–807. doi: 10.1016/j.powtec.2018.10.056
   Web of Science ®Google Scholar
• Fouda YM, Bayly AE. A dem study of powder spreading in additive layer manufacturing. Granul Matter. 2020;22(1):1–18. doi: 10.1007/s10035-019-0971-x
   Web of Science ®Google Scholar
• Yim S, Bian H, Aoyagi K, et al. Effect of powder morphology on flowability and spreading behavior in powder bed fusion additive manufacturing process: a particle-scale modeling study. Addit Manuf. 2023;72:103612.
   Web of Science ®Google Scholar
• Bouabbou A, Vaudreuil S. Numerical modelling of SS316L powder flowability for laser powder-bed fusion. Arch Mater Sci Eng. 2023;120(1):22–29. doi: 10.5604/18972764
   Google Scholar
• Yan Z, Wilkinson SK, Stitt EH, et al. Investigating mixing and segregation using discrete element modelling (DEM) in the freeman FT4 rheometer. Int J Pharm. 2016;513(1–2):38–48. doi: 10.1016/j.ijpharm.2016.08.065
   PubMedGoogle Scholar
• Wilkinson S, Turnbull S, Yan Z, et al. A parametric evaluation of powder flowability using a freeman rheometer through statistical and sensitivity analysis: a discrete element method (DEM) study. Comput Chem Eng. 2017;97:161–174. doi: 10.1016/j.compchemeng.2016.11.034
   Web of Science ®Google Scholar
• Steuben JC, Iliopoulos AP, Michopoulos JG. Discrete element modeling of particle-based additive manufacturing processes. Comput Methods Appl Mech Eng. 2016;305:537–561. doi: 10.1016/j.cma.2016.02.023
   Web of Science ®Google Scholar
• Yan W, Qian Y, Ge W, et al. Meso-scale modeling of multiple-layer fabrication process in selective electron beam melting: inter-layer/track voids formation. Mater Des. 2018;141:210–219. doi: 10.1016/j.matdes.2017.12.031
   Web of Science ®Google Scholar
• Chen H, Sun Y, Yuan W, et al. A review on discrete element method simulation in laser powder bed fusion additive manufacturing. Chin J Mech Eng Addit Manuf Front. 2022;1:100017.
   Google Scholar
• Ma H, Zhou L, Liu Z, et al. A review of recent development for the cfd-dem investigations of non-spherical particles. Powder Technol. 2022;412:117972. doi: 10.1016/j.powtec.2022.117972
   Web of Science ®Google Scholar
• Rong D, Horio M. Dem simulation of char combustion in a fluidized bed. In: Second International Conference on CFD in the Minerals and Process Industries CSIRO; Melbourne, Australia; 1999. p. 65–70.
   Google Scholar
• Zhou Z, Yu A, Zulli P. A new computational method for studying heat transfer in fluid bed reactors. Powder Technol. 2010;197(1–2):102–110. doi: 10.1016/j.powtec.2009.09.002
   Web of Science ®Google Scholar
• Peng Z, Doroodchi E, Moghtaderi B. Heat transfer modelling in discrete element method (dem)-based simulations of thermal processes: theory and model development. Prog Energy Combust Sci. 2020;79:100847. doi: 10.1016/j.pecs.2020.100847
   Web of Science ®Google Scholar
• Liu S, Liu J, Chen J, et al. Influence of surface tension on the molten pool morphology in laser melting. Int J Therm Sci. 2019;146:106075. doi: 10.1016/j.ijthermalsci.2019.106075
   Web of Science ®Google Scholar
• Afrasiabi M, Lüthi C, Bambach M, et al. Multi-resolution sph simulation of a laser powder bed fusion additive manufacturing process. Appl Sci. 2021;11(7):1. doi: 10.3390/app11072962
   Google Scholar
• Afrasiabi M, Lüthi C, Bambach M, et al. Smoothed particle hydrodynamics modeling of the multi-layer laser powder bed fusion process. Procedia CIRP. 2022;107:276–282. doi: 10.1016/j.procir.2022.04.045
   Google Scholar
• Liu S, Liu J, Qi L, et al. Simulation of the temperature distribution and solidified bead in single-pass selective laser melting using a mesh-free method. J Appl Phys. 2019;126(13):133104. doi: 10.1063/1.5096041
   Web of Science ®Google Scholar
• Qiu Y, Niu X, Song T, et al. Three-dimensional numerical simulation of selective laser melting process based on sph method. J Manuf Process. 2021;71:224–236. doi: 10.1016/j.jmapro.2021.09.018
   Web of Science ®Google Scholar
• Meier C, Fuchs SL, Much N, et al. Physics-based modeling and predictive simulation of powder bed fusion additive manufacturing across length scales. GAMM-Mitteilungen. 2021;44(3):e202100014. doi: 10.1002/gamm.v44.3
   Google Scholar
• Park CY, Zohdi TI. Numerical modeling of thermo-mechanically induced stress in substrates for droplet-based additive manufacturing processes. J Manuf Sci Eng. 2019;141(6):061001. doi: 10.1115/1.4043254
   Web of Science ®Google Scholar
• Trautmann M, Hertel M, Füssel U. Numerical simulation of TIG weld pool dynamics using smoothed particle hydrodynamics. Int J Heat Mass Transf. 2017;115:842–853. doi: 10.1016/j.ijheatmasstransfer.2017.08.060
   Web of Science ®Google Scholar
• Afrasiabi M, Keller D, Lüthi C, et al. Effect of process parameters on melt pool geometry in laser powder bed fusion of metals: a numerical investigation. Procedia CIRP. 2022;113:378–384. doi: 10.1016/j.procir.2022.09.187
   Google Scholar
• Lüthi C, Afrasiabi M, Bambach M. An adaptive smoothed particle hydrodynamics (SPH) scheme for efficient melt pool simulations in additive manufacturing. Comput Math Appl. 2023;139:7–27.
   Web of Science ®Google Scholar
• Fan Z, Li B. Meshfree simulations for additive manufacturing process of metals. Integr Mater Manuf Innov. 2019;8(2):144–153. doi: 10.1007/s40192-019-00131-w
   Web of Science ®Google Scholar
• Wessels H, Bode T, Weißenfels C, et al. Investigation of heat source modeling for selective laser melting. Comput Mech. 2019;63(5):949–970. doi: 10.1007/s00466-018-1631-4
   Web of Science ®Google Scholar
• He X, Luo L-S. A priori derivation of the lattice Boltzmann equation. Phys Rev E. 1997;55(6):R6333–R6336. doi: 10.1103/PhysRevE.55.R6333
   Web of Science ®Google Scholar
• Ammer R, Markl M, Ljungblad U, et al. Simulating fast electron beam melting with a parallel thermal free surface lattice Boltzmann method. Comput Math Appl. 2014;67(2):318–330. doi: 10.1016/j.camwa.2013.10.001
   Web of Science ®Google Scholar
• Miyanaji H, Zhang S, Yang L. A new physics-based model for equilibrium saturation determination in binder jetting additive manufacturing process. Int J Mach Tools Manuf. 2018;124:1–11. doi: 10.1016/j.ijmachtools.2017.09.001
   Web of Science ®Google Scholar
• Deng H, Huang Y, Wu S, et al. Binder jetting additive manufacturing: three-dimensional simulation of micro-meter droplet impact and penetration into powder bed. J Manuf Process. 2022;74:365–373. doi: 10.1016/j.jmapro.2021.12.019
   Web of Science ®Google Scholar
• Yang Z, Zhang Y, Yan W. High-fidelity modeling of binder-powder interactions in binder jetting: binder flow and powder dynamics. Acta Mater. 2023;260:119298. doi: 10.1016/j.actamat.2023.119298
   Web of Science ®Google Scholar
• Wimmer A, Yalvac B, Zoeller C, et al. Experimental and numerical investigations of in situ alloying during powder bed fusion of metals using a laser beam. Metals. 2021;11(11):1842. doi: 10.3390/met11111842
   Web of Science ®Google Scholar
• Flow-3D A. FlOW-3D am. [Accessed 2023 July 10].
   Google Scholar
• Pryor RW. Multiphysics modeling using COMSOL 5 and MATLAB. Mercury learning and information. 2021.
   Google Scholar
• De Vaucorbeil A, Nguyen VP, Sinaie S, et al. Material point method after 25 years: theory, implementation, and applications. Adv Appl Mech. 2020;53:185–398. doi: 10.1016/bs.aams.2019.11.001
   Web of Science ®Google Scholar
• Oñate E, Idelsohn SR, Del Pin F, et al. The particle finite element method–an overview. Int J Comput Methods. 2004;01(02):267–307. doi: 10.1142/S0219876204000204
   Google Scholar
• Zhang D, Rodriguez J, Ye X, et al. A particle finite element method for additive manufacturing simulations. J Comput Inf Sci Eng. 2023;23(5):051008. doi: 10.1115/1.4062143
   Web of Science ®Google Scholar
• Chen J, Beraun J, Carney T. A corrective smoothed particle method for boundary value problems in heat conduction. Int J Numer Methods Eng. 1999;46(2):231–252. doi: 10.1002/(ISSN)1097-0207
   Web of Science ®Google Scholar
• Liu WK, Jun S, Zhang YF. Reproducing kernel particle methods. Int J Numer Methods Fluids. 1995;20(8-9):1081–1106. doi: 10.1002/fld.v20:8/9
   Web of Science ®Google Scholar
• Fatehi R, Manzari M. Error estimation in smoothed particle hydrodynamics and a new scheme for second derivatives. Comput Math Appl. 2011;61(2):482–498.
   Web of Science ®Google Scholar
• Afrasiabi M, Wegener K. 3D thermal simulation of a laser drilling process with meshfree methods. J Manuf Mater Process. 2020 Jun;4:58.
   Google Scholar
• Yu T, Zhao J. Semi-coupled resolved CFD–DEM simulation of powder-based selective laser melting for additive manufacturing. Comput Methods Appl Mech Eng. 2021;377:113707. doi: 10.1016/j.cma.2021.113707
   Web of Science ®Google Scholar
• Vignjevic R, Reveles JR, Campbell J. SPH in a total lagrangian formalism. CMC-Tech Sci Press. 2006;4(3):181.
   Google Scholar
• Islam MRI, Peng C. A total lagrangian sph method for modelling damage and failure in solids. Int J Mech Sci. 2019;157–158:498–511. doi: 10.1016/j.ijmecsci.2019.05.003
   Web of Science ®Google Scholar
• Wang L, Xu F, Yang Y. An improved total lagrangian SPH method for modeling solid deformation and damage. Eng Anal Bound Elem. 2021;133:286–302. doi: 10.1016/j.enganabound.2021.09.010
   Web of Science ®Google Scholar
• Hu X, Adams NA. An incompressible multi-phase SPH method. J Comput Phys. 2007;227(1):264–278. doi: 10.1016/j.jcp.2007.07.013
   Web of Science ®Google Scholar
• Yu T, Zhao J. Quantitative simulation of selective laser melting of metals enabled by new high-fidelity multiphase, multiphysics computational tool. Comput Methods Appl Mech Eng. 2022;399:115422. doi: 10.1016/j.cma.2022.115422
   Web of Science ®Google Scholar
• Cummins S, Cleary PW, Delaney G, et al. A coupled dem/sph computational model to simulate microstructure evolution in Ti-6Al-4V laser powder bed fusion processes. Metals. 2021;11(6):858. doi: 10.3390/met11060858
   Web of Science ®Google Scholar
• Cao L, Guan W. Simulation and analysis of LPBF multi-layer single-track forming process under different particle size distributions. Int J Adv Manuf Technol. 2021;114(7-8):2141–2157. doi: 10.1007/s00170-021-06987-7
   Web of Science ®Google Scholar
• Mehrpouya M, Tuma D, Vaneker T, et al. Multimaterial powder bed fusion techniques. Rapid Prototyp J. 2022;28(11):1–19. doi: 10.1108/RPJ-01-2022-0014
   Web of Science ®Google Scholar
• Wang D, Liu L, Deng G, et al. Recent progress on additive manufacturing of multi-material structures with laser powder bed fusion. Virtual Phys Prototyp. 2022;17(2):329–365. doi: 10.1080/17452759.2022.2028343
   Web of Science ®Google Scholar
• Feenstra D, Banerjee R, Fraser H, et al. Critical review of the state of the art in multi-material fabrication via directed energy deposition. Curr Opin Solid State Mater Sci. 2021;25(4):100924. doi: 10.1016/j.cossms.2021.100924
   Web of Science ®Google Scholar
• Tang C, Yao L, Du H. Computational framework for the simulation of multi material laser powder bed fusion. Int J Heat Mass Transf. 2022;191:122855. doi: 10.1016/j.ijheatmasstransfer.2022.122855
   Web of Science ®Google Scholar
• Li W, Kishore M, Zhang R, et al. Comprehensive studies of SS316L/IN718 functionally gradient material fabricated with directed energy deposition: multi-physics & multi-materials modelling and experimental validation. Addit Manuf. 2023;61:103358.
   Web of Science ®Google Scholar
• Küng VE, Scherr R, Markl M, et al. Multi-material model for the simulation of powder bed fusion additive manufacturing. Comput Mater Sci. 2021;194:110415. doi: 10.1016/j.commatsci.2021.110415
   Web of Science ®Google Scholar
• Zhu Q, Liu Z, Yan J. Machine learning for metal additive manufacturing: predicting temperature and melt pool fluid dynamics using physics-informed neural networks. Comput Mech. 2021;67:619–635. doi: 10.1007/s00466-020-01952-9
   Web of Science ®Google Scholar
• Hemmasian A, Ogoke F, Akbari P, et al. Surrogate modeling of melt pool temperature field using deep learning. Addit Manuf Lett. 2023;5:100123. doi: 10.1016/j.addlet.2023.100123
   Google Scholar