Abstract
One of the major barriers that hinder the realization of significant potential of metal-based additive manufacturing (AM) techniques is the variation in the quality of the manufactured parts. Uncertainty quantification (UQ) and uncertainty management (UM) can resolve this challenge based on the modeling and simulation of the AM process. This paper reviews the research state of the art and discusses needs and opportunities in the UQ/UM of the AM processes, with a focus on laser powder bed fusion AM. The major methods and models of laser powder bed fusion AM process are summarized first. The current research work in UQ of AM processes is then reviewed. Based on the review of AM process models and current UQ approaches for the AM process, this paper presents insights into how the current state of the art UQ and UM techniques can be applied to AM to improve the product quality. Future research needs in UQ and UM of AM are also discussed. Laser sintering of metal nanoparticles, which is part of the micro-AM process, is used as an example to illustrate the application of UQ and UM in the AM.
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References
Standard A (2012) F2792. 2012. Standard terminology for additive manufacturing technologies, ASTM F2792-10e1
Huang Y, Leu MC, Mazumder J, Donmez A (2015) Additive manufacturing: current state, future potential, gaps and needs, and recommendations. J Manuf Sci Eng 137(1):014001
Vaezi M, Seitz H, Yang S (2013) A review on 3D micro-additive manufacturing technologies. Int J Adv Manuf Technol 67(5–8):1721–1754
Wohler T (2013) “Additive manufacturing and 3D printing—state of the industry annual worldwide progress report 2014, Wohler’s associates,” Inc., Fort Collins, CO
Zhang X, Jiang X, Sun C (1999) Micro-stereolithography of polymeric and ceramic microstructures. Sensors Actuators A Phys 77(2):149–156
Mireles J, Kim H-C, Lee IH, Espalin D, Medina F, MacDonald E, Wicker R (2013) Development of a fused deposition modeling system for low melting temperature metal alloys. J Electron Packag 135(1):011008
Klosterman D, Chartoff R, Graves G, Osborne N, Priore B (1998) Interfacial characteristics of composites fabricated by laminated object manufacturing. Compos A: Appl Sci Manuf 29(9):1165–1174
Lü L, Fuh JYH, Wong Y-S (2001) “Selective laser sintering,” Laser-Induced Materials and Processes for Rapid Prototyping, Springer, pp. 89–142
Kruth J-P, Froyen L, Van Vaerenbergh J, Mercelis P, Rombouts M, Lauwers B (2004) Selective laser melting of iron-based powder. J Mater Process Technol 149(1):616–622
Dinda G, Dasgupta A, Mazumder J (2009) Laser aided direct metal deposition of Inconel 625 superalloy: microstructural evolution and thermal stability. Mater Sci Eng A 509(1):98–104
Tang L, Ruan J, Landers RG, Liou F (2008) Variable powder flow rate control in laser metal deposition processes. J Manuf Sci Eng 130(4):041016
Morgan R, Sutcliffe C, O'neill W (2004) Density analysis of direct metal laser re-melted 316L stainless steel cubic primitives. J Mater Sci 39(4):1195–1205
Tapia G, Elwany A (2014) A review on process monitoring and control in metal-based additive manufacturing. J Manuf Sci Eng 136(6):060801
Hu Z, Mahadevan S, Du X “Uncertainty quantification in time-dependent reliability analysis in the presence of parametric uncertainty,” ASCE-ASME J Risk Uncertain Eng Syst, B: Mech Eng
Xiu D, Karniadakis GE (2002) The Wiener–Askey polynomial chaos for stochastic differential equations. SIAM J Sci Comput 24(2):619–644
Bichon BJ, Eldred MS, Swiler LP, Mahadevan S, McFarland JM (2008) Efficient global reliability analysis for nonlinear implicit performance functions. AIAA J 46(10):2459–2468
Kamath C, (2016) “Data mining and statistical inference in selective laser melting,” The International Journal of Advanced Manufacturing Technology, pp. 1-19.
Lopez F, Witherell P, Lane B (2016) Identifying uncertainty in laser powder bed fusion additive manufacturing models. Journal of Mechanical Design 138(11):114502
Moser D, Beaman J, Fish S, Murthy J (2014) "Multi-layer computational modeling of selective laser sintering processes." ASME 2014 International Mechanical Engineering Congress and Exposition, Volume 2A: Advanced Manufacturing. Montreal, Quebec, Canada, November 14–20, Paper No. IMECE2014-37535, pp. V02AT02A008; 11 pages
Turner JA, Babu SS, Blue C (2015) “Advanced Simulation for Additive Manufacturing: Meeting Challenges Through Collaboration (Workshop Report for U.S. DOE/EERE/AMO),”, Oak Ridge National Laboratory, ORNL Report TM-2015/324, Sep, 2015
Mellor S, Hao L, Zhang D (2014) Additive manufacturing: a framework for implementation. Int J Prod Econ 149:194–201
Baumers M, Tuck C, Bourell D, Sreenivasan R, Hague R (2011) "Sustainability of additive manufacturing: measuring the energy consumption of the laser sintering process," Proceedings of the Institution of Mechanical Engineers. Part B: Journal of Engineering Manufacture 225(12):2228–2239
Paul R, Anand S (2012) Process energy analysis and optimization in selective laser sintering. J Manuf Syst 31(4):429–437
Nelson JC, Xue S, Barlow JW, Beaman JJ, Marcus HL, Bourell DL (1993) Model of the selective laser sintering of bisphenol-A polycarbonate. Ind Eng Chem Res 32(10):2305–2317
Zäh MF, Lutzmann S (2010) Modelling and simulation of electron beam melting. Prod Eng 4(1):15–23
Rubenchik A, Wu S, Mitchell S, Golosker I, LeBlanc M, Peterson N (2015) Direct measurements of temperature-dependent laser absorptivity of metal powders. Appl Opt 54(24):7230–7233
King W, Anderson A, Ferencz R, Hodge N, Kamath C, Khairallah S, Rubenchik A (2015) Laser powder bed fusion additive manufacturing of metals; physics, computational, and materials challenges. Appl Phys Rev 2(4):041304
Markl M, Körner C (2016) Multi-scale modeling of powder-bed-based additive manufacturing. Annu Rev Mater Res 46:1–34
Wang X, Kruth J (2000) “Energy absorption and penetration in selective laser sintering: a ray tracing model.”, In Proceedings of the International Conference on Mathematical Modeling and Computer Simulation of Metal Technologies, Ariel, Israel, November 13-15, MMT (pp. 673-682)
Boley C, Khairallah S, Rubenchik A (2015) Calculation of laser absorption by metal powders in additive manufacturing. Appl Opt 54(9):2477–2482
Meakin P, Jullien R (1987) Restructuring effects in the rain model for random deposition. J Phys 48(10):1651–1662
Mishra B, Rajamani RK (1992) The discrete element method for the simulation of ball mills. Appl Math Model 16(11):598–604
Kloss C, Goniva C (2011) LIGGGHTS—open source discrete element simulations of granular materials based on Lammps. Supplemental Proceedings: Materials Fabrication, Properties, Characterization, and Modeling 2:781–788
Dou X, Mao Y, Zhang Y (2014) Effects of contact force model and size distribution on microsized granular packing. J Manuf Sci Eng 136(2):021003
Xiang Z, Yin M, Deng Z, Mei X, Yin G (2016) Simulation of forming process of powder bed for additive manufacturing. J Manuf Sci Eng 138(8):081002
Herbold, E., Walton, O., and Homel, M., 2015, “Simulation of powder layer deposition in additive manufacturing processes using the discrete element method,” Lawrence Livermore National Lab.(LLNL), Livermore, CA (United States).
Parteli EJR. (2013) "DEM simulation of particles of complex shapes using the multisphere method: application for additive manufacturing." In AIP Conference Proceedings, vol. 1542, no. 1, pp. 185-188. AIP, doi: 10.1063/1.4811898
Alexander FJ, Chen S, Sterling J (1993) Lattice Boltzmann thermohydrodynamics. Phys Rev E 47(4):R2249
Khairallah SA, Anderson A (2014) Mesoscopic simulation model of selective laser melting of stainless steel powder. J Mater Process Technol 214(11):2627–2636
Devesse W, De Baere D, Guillaume P (2014) The isotherm migration method in spherical coordinates with a moving heat source. Int J Heat Mass Transf 75:726–735
Jasak, H., Jemcov, A., and Tukovic, Z., “OpenFOAM: a C++ library for complex physics simulations,” Proc. International Workshop on Coupled Methods in Numerical Dynamics, IUC Dubrovnik, Croatia, pp. 1–20.
Klassen A, Scharowsky T, Körner C (2014) Evaporation model for beam based additive manufacturing using free surface lattice Boltzmann methods. J Phys D Appl Phys 47(27):275303
Gürtler F-J, Karg M, Leitz K-H, Schmidt M (2013) Simulation of laser beam melting of steel powders using the three-dimensional volume of fluid method. Phys Procedia 41:881–886
McClelland MA, Maienschein JL, Nichols AL, Wardell JF, Atwood AI, Curran PO (2002) “ALE3D Model Predictions and Materials Characterization for the Cookoff Response of PBXN-109”, (No. UCRL-JC-145756). Lawrence Livermore National Lab., CA (US)
Qi Y, Çağın T, Kimura Y, Goddard WA III (1999) Molecular-dynamics simulations of glass formation and crystallization in binary liquid metals: Cu-Ag and Cu-Ni. Phys Rev B 59(5):3527
Rappaz M, Gandin C-A (1993) Probabilistic modelling of microstructure formation in solidification processes. Acta Metall Mater 41(2):345–360
Zhang J, Liou F, Seufzer W, Taminger K (2016) A coupled finite element cellular automaton model to predict thermal history and grain morphology of Ti-6Al-4V during direct metal deposition (DMD). Additive Manufac 11:32–39
Liou, F., Newkirk, J., Fan, Z., Sparks, T., Chen, X., Fletcher, K., Zhang, J., Zhang, Y., Kumar, K. S., and Karnati, S., 2015, Multiscale and multiphysics modeling of additive manufacturing of advanced materials
Amine T, Newkirk JW, Liou F (2015) Methodology for studying effect of cooling rate during laser deposition on microstructure. J Mater Eng Perform 24(8):3129–3136
Denlinger, E. R., Heigel, J. C., and Michaleris, P., 2014, Residual stress and distortion modeling of electron beam direct manufacturing Ti-6Al-4V. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, p. 0954405414539494.
Mercelis P, Kruth J-P (2006) Residual stresses in selective laser sintering and selective laser melting. Rapid Prototyp J 12(5):254–265
Liu H (2014) “Numerical analysis of thermal stress and deformation in multi-layer laser metal deposition process.”, Department of Mechanical and Aerospace Engineering, Missouri University of Science and Technology, master’s dissertation, Rolla, Missouri
Ding D, Pan Z, Cuiuri D, Li H (2015) Wire-feed additive manufacturing of metal components: technologies, developments and future interests. Int J Adv Manuf Technol 81(1–4):465–481
Megahed M, Mindt H-W, N’Dri N, Duan H, Desmaison O (2016) Metal additive-manufacturing process and residual stress modeling. Integrat Mater Manuf Innov 5(1):1–33
Paul R, Anand S (2015) A combined energy and error optimization method for metal powder based additive manufacturing processes. Rapid Prototyp J 21(3):301–312
Xu X, Meteyer S, Perry N, Zhao YF (2015) Energy consumption model of binder-jetting additive manufacturing processes. Int J Prod Res 53(23):7005–7015
Meteyer S, Xu X, Perry N, Zhao YF (2014) Energy and material flow analysis of binder-jetting additive manufacturing processes. Procedia CIRP 15:19–25
Garg, A., Lam, J. S. L., and Savalani, M., 2015, “Energy component in the density of selective laser melting fabricated prototype,” The International Journal of Advanced Manufacturing Technology, pp. 1-9.
Paul R (2013) “Modeling and optimization of powder based additive manufacturing (AM) processes.”, Department of Mechanical Engineering, University of Cincinnati, Ph.D. Dissertation
Sreenivasan R, Goel A, Bourell D (2010) Sustainability issues in laser-based additive manufacturing. Phys Procedia 5:81–90
Körner C, Attar E, Heinl P (2011) Mesoscopic simulation of selective beam melting processes. J Mater Process Technol 211(6):978–987
Mahale TR (2009) “Electron beam melting of advanced materials and structures.”, Department of Industrial Engineering, North Carolina State University, Ph.D. Dissertation
Gusarov A, Kruth J-P (2005) Modelling of radiation transfer in metallic powders at laser treatment. Int J Heat Mass Transf 48(16):3423–3434
Gusarov A, Yadroitsev I, Bertrand P, Smurov I (2007) Heat transfer modelling and stability analysis of selective laser melting. Appl Surf Sci 254(4):975–979
Wang X, Laoui T, Bonse J, Kruth J-P, Lauwers B, Froyen L (2002) Direct selective laser sintering of hard metal powders: experimental study and simulation. Int J Adv Manuf Technol 19(5):351–357
Sisto A, Kamath C (2013)” Ensemble Feature Selection in Scientific Data Analysis”, Lawrence Livermore National Laboratory (LLNL), Livermore, CA, report number: No. LLNL-TR-644160
Tolochko NK, Khlopkov YV, Mozzharov SE, Ignatiev MB, Laoui T, Titov VI (2000) Absorptance of powder materials suitable for laser sintering. Rapid Prototyp J 6(3):155–161
Shi Y, Zhang Y (2008) “Simulation of random packing of spherical particles with different size distributions.”, ASME 2006 International Mechanical Engineering Congress and Exposition, Heat Transfer, Volume 3, Chicago, Illinois, USA, November 5 – 10, Paper No. IMECE2006-15271, pp. 539-544; 6 pages
Parteli EJ, Pöschel T (2016) Particle-based simulation of powder application in additive manufacturing. Powder Technol 288:96–102
N'Dri, N., Mindt, H. W., Shula, B., Megahed, M., Peralta, A., Kantzos, P., and Neumann, J., 2015, “DMLS process modelling & validation,” TMS2015 Supplemental Proceedings, pp. 389-396.
Körner C, Pohl T, Rüde U, Thürey N, Zeiser T (2006) “Parallel lattice Boltzmann methods for CFD applications.”, In Numerical Solution of Partial Differential Equations on Parallel Computers, Lecture Notes in Computational Science and Engineering, vol 51. Springer, Berlin, Heidelberg, pp. 439-466
Ammer R, Markl M, Ljungblad U, Körner C, Rüde U (2014) Simulating fast electron beam melting with a parallel thermal free surface lattice Boltzmann method. Comput Math Appl 67(2):318–330
Mindt H, Megahed M, Perlata A, Neumann J (2015) "DMLM models-numerical assessment of porosity," proceedings from the 22nd International Symposium on Air Breathing Engines, Phoenix, AZ, Oct, pp. 25-30
Jahanshahi M, Sanati M, Babaei Z (2008) Optimization of parameters for the fabrication of gelatin nanoparticles by the Taguchi robust design method. J Appl Stat 35(12):1345–1353
Boettinger WJ, Warren JA, Beckermann C, Karma A (2002) Phase-field simulation of solidification. Mater Res 32(1):163
Beckermann C, Diepers H-J, Steinbach I, Karma A, Tong X (1999) Modeling melt convection in phase-field simulations of solidification. J Comput Phys 154(2):468–496
Dai K, Shaw L (2006) Parametric studies of multi-material laser densification. Mater Sci Eng A 430(1):221–229
Zaeh MF, Branner G (2010) Investigations on residual stresses and deformations in selective laser melting. Prod Eng 4(1):35–45
Cohen, D. L., 2010, “Additive manufacturing of functional constructs under process uncertainty,” Cornell University
Delgado J, Ciurana J, Rodríguez CA (2012) Influence of process parameters on part quality and mechanical properties for DMLS and SLM with iron-based materials. Int J Adv Manuf Technol 60(5–8):601–610
Raghunath N, Pandey PM (2007) Improving accuracy through shrinkage modelling by using Taguchi method in selective laser sintering. Int J Mach Tools Manuf 47(6):985–995
Garg A, Tai K, Savalani M (2014) State-of-the-art in empirical modelling of rapid prototyping processes. Rapid Prototyp J 20(2):164–178
Schaaf K (1999) "Uncertainty and sensitivity analysis of the heat transfer mechanisms in the lower head.", Proceedings of the OECD/CSNI Workshop on in-vessel core debris retention and coolability, Garching, 3rd-6th March, Paper No. NEA-CSNI-R--1998-18
Swiler, L. P., Eldred, M. S., and Adams, B. M., 2015, Dakota: bridging advanced scalable uncertainty quantification algorithms with production deployment
Anderson A (2015) "Development of Physics-Based Numerical Models for Uncertainty Quantification of Selective Laser Melting Processes-2015 Annual Progress Report," Lawrence Livermore National Laboratory (LLNL), Livermore, CA, report number: LLNL-TR-678006
Adamczak S, Bochnia J, Kaczmarska B (2014) Estimating the uncertainty of tensile strength measurement for a photocured material produced by additive manufacturing. Metrol Measur Syst 21(3):553–560
Ma, L., Fong, J., Lane, B., Moylan, S., Filliben, J., Heckert, A., and Levine, L., “Using design of experiments in finite element modeling to identify critical variables for laser powder bed fusion,” Proc. International Solid Freeform Fabrication Symposium, Laboratory for Freeform Fabrication and the University of Texas Austin, TX, USA
Loughnane, G. T., 2015, “A framework for uncertainty quantification in microstructural characterization with application to additive manufacturing of Ti-6Al-4V,” Wright State University
Park S-I, Rosen DW, Choi S-k, Duty CE (2014) Effective mechanical properties of lattice material fabricated by material extrusion additive manufacturing. Additive Manufac 1:12–23
Cai G, Mahadevan S (2016)” Uncertainty Quantification of Manufacturing Process Effects on Macro-scale Material Properties”. International Journal for Multiscale Computational Engineering, 14(3), DOI: 10.1615/IntJMultCompEng.2016015552
Haldar A, Mahadevan S (2000) Probability, reliability, and statistical methods in engineering design. Wiley, New York
Sankararaman S, Ling Y, Mahadevan S (2011) Uncertainty quantification and model validation of fatigue crack growth prediction. Eng Fract Mech 78(7):1487–1504
Devathi, H., Hu, Z., and Mahadevan, S., 2016, “Snap-through buckling reliability analysis under spatiotemporal variability and epistemic uncertainty,” AIAA J, pp 3981–3993.
Mahadevan S, Zhang R, Smith N (2001) Bayesian networks for system reliability reassessment. Struct Saf 23(3):231–251
Zhang R, Mahadevan S (2000) Model uncertainty and Bayesian updating in reliability-based inspection. Struct Saf 22(2):145–160
Du X (2008) Unified uncertainty analysis by the first order reliability method. Journal of Mechanical Design 130(9):091401
Sankararaman S, Mahadevan S (2011) Likelihood-based representation of epistemic uncertainty due to sparse point data and/or interval data. Reliab Eng Syst Saf 96(7):814–824
Hu Z, Du X (2015) A random field approach to reliability analysis with random and interval variables. ASCE-ASME J Risk Uncertain Eng Syst B: Mech Eng 1(4):041005
Richardson LF (1911) “The approximate arithmetical solution by finite differences of physical problems involving differential equations, with an application to the stresses in a masonry dam,” Philosophical Transactions of the Royal Society of London. Ser A, Contain Papers Math Phys Char 210:307–357
Celik I, Karatekin O (1997) Numerical experiments on application of Richardson extrapolation with nonuniform grids. J Fluids Eng 119(3):584–590
Kennedy MC, O'Hagan A (2001) Bayesian calibration of computer models. J Royal Stat Soc: Ser B (Stat Methodol) 63(3):425–464
Jones DR, Schonlau M, Welch WJ (1998) Efficient global optimization of expensive black-box functions. J Glob Optim 13(4):455–492
Suykens JA, Vandewalle J (1999) Least squares support vector machine classifiers. Neural Process Lett 9(3):293–300
Rasmussen CE, Williams CK (2006) Gaussian processes for machine learning (Vol. 1). Cambridge: MIT press
Santner TJ, Williams BJ, Notz WI (2013) “The design and analysis of computer experiments.”, Springer Series in Statistics, Springer Science & Business Media New York, DOI 10.1007/978-1-4757-3799-8
Lophaven SN, Nielsen HB, Søndergaard J (2002) “DACE-A Matlab Kriging Toolbox, Version 2.0,” Technical University of Denmark, Technical. Report No. IMM-TR-2002-12
Ganapathysubramanian B, Zabaras N (2007) Sparse grid collocation schemes for stochastic natural convection problems. J Comput Phys 225(1):652–685
Hampton J, Doostan A (2015) Compressive sampling of polynomial chaos expansions: convergence analysis and sampling strategies. J Comput Phys 280:363–386
Hu Z, Mahadevan S (2016) Global sensitivity analysis-enhanced surrogate (GSAS) modeling for reliability analysis. Struct Multidiscip Optim 53(3):501–521
Sankararaman S, Mahadevan S (2012) Likelihood-based approach to multidisciplinary analysis under uncertainty. J Mech Des 134(3):031008
Committee, A. S., 1998, “AIAA guide for the verification and validation of computational fluid dynamics simulations (G-077-1998),” AIAA
Ling Y, Mahadevan S (2013) Quantitative model validation techniques: new insights. Reliab Eng Syst Saf 111:217–231
Rebba R, Mahadevan S, Huang S (2006) Validation and error estimation of computational models. Reliab Eng Syst Saf 91(10):1390–1397
Kleijnen JP (1995) Verification and validation of simulation models. Eur J Oper Res 82(1):145–162
Drignei D, Mourelatos ZP, Kokkolaras M, Pandey V (2014) Reallocation of testing resources in validating optimal designs using local domains. Struct Multidiscip Optim 50(5):825–838
Ferson S, Oberkampf WL, Ginzburg L (2008) Model validation and predictive capability for the thermal challenge problem. Comput Methods Appl Mech Eng 197(29):2408–2430
Rebba R, Mahadevan S (2008) Computational methods for model reliability assessment. Reliab Eng Syst Saf 93(8):1197–1207
Li C, Mahadevan S (2016) An efficient modularized sample-based method to estimate the first-order Sobol′ index. Reliab Eng Syst Saf 153:110–121
Chen W, Jin R, Sudjianto A (2005) Analytical variance-based global sensitivity analysis in simulation-based design under uncertainty. J Mech Des 127(5):875–886
Sudret B (2008) Global sensitivity analysis using polynomial chaos expansions. Reliab Eng Syst Saf 93(7):964–979
Computers and Information in Engineering Conference. Volume 1A: 36th Computers and Information in Engineering Conference Charlotte, North Carolina, USA, August 21–24, Paper No. DETC2016-59671, pp. V01AT02A023; 10 pages doi:10.1115/DETC2016-59671
Hu Z, Ao D, Mahadevan S (2017) Calibration experimental design considering field response and model uncertainty. Computer Methods in Applied Mechanics and Engineering 318:92–119
Ao D, Hu Z, Mahadevan S (2017) Design of validation experiments for life prediction models. Reliability Engineering & System Safety 165:22–33
Nath P, Hu Z, Mahadevan S (2017) Sensor placement for calibration of spatially varying model parameters. Journal of Computational Physics 343:150–169
Sankararaman S, McLemore K, Mahadevan S, Bradford SC, Peterson LD (2013) Test resource allocation in hierarchical systems using Bayesian networks. AIAA J 51(3):537–550
Mullins J, Mahadevan S (2014) Variable-fidelity model selection for stochastic simulation. Reliab Eng Syst Saf 131:40–52
Jiang X, Mahadevan S (2006) Bayesian cross-entropy methodology for optimal design of validation experiments. Meas Sci Technol 17(7):1895
Sankararaman S, Mahadevan S (2015) Integration of model verification, validation, and calibration for uncertainty quantification in engineering systems. Reliab Eng Syst Saf 138:194–209
Du X, Chen W (2004) Sequential optimization and reliability assessment method for efficient probabilistic design. J Mech Des 126(2):225–233
Zaman K, McDonald M, Mahadevan S, Green L (2011) Robustness-based design optimization under data uncertainty. Struct Multidiscip Optim 44(2):183–197
Zaman, K., and Mahadevan, S., 2016, Reliability-based design optimization of multidisciplinary system under aleatory and epistemic uncertainty. Struct Multidiscip Optim, pp. 1-19
Rangavajhala S, Mahadevan S (2013) Design optimization for robustness in multiple performance functions. Struct Multidiscip Optim 47(4):523–538
Du X, Sudjianto A, Chen W (2004) An integrated framework for optimization under uncertainty using inverse reliability strategy. J Mech Des 126(4):562–570
Plimpton, S., Crozier, P., and Thompson, A., 2007, “LAMMPS-large-scale atomic/molecular massively parallel simulator,” Sandia National Laboratories, 18
Mendelev M, Han S, Srolovitz D, Ackland G, Sun D, Asta M (2003) Development of new interatomic potentials appropriate for crystalline and liquid iron. Philos Mag 83(35):3977–3994
Ackland G, Bacon D, Calder A, Harry T (1997) Computer simulation of point defect properties in dilute Fe–Cu alloy using a many-body interatomic potential. Philos Mag A 75(3):713–732
Biersack J, Ziegler J (1982) Refined universal potentials in atomic collisions. Nucl Inst Methods Phys Res A 194(1):93–100
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Hu, Z., Mahadevan, S. Uncertainty quantification and management in additive manufacturing: current status, needs, and opportunities. Int J Adv Manuf Technol 93, 2855–2874 (2017). https://doi.org/10.1007/s00170-017-0703-5
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DOI: https://doi.org/10.1007/s00170-017-0703-5