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Computational Modeling and Sub-Grid Scale Stabilization of Incompressibility and Convection in the Numerical Simulation of Friction Stir Welding Processes

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Abstract

This paper deals with the computational modeling and sub-grid scale stabilization of incompressibility and convection in the numerical simulation of the material flow around the probe tool in a friction stir welding (FSW) process. Within the paradigmatic framework of the multiscale stabilization methods, suitable pressure and convective derivative of the temperature sub-grid scale stabilized coupled thermomechanical formulations have been developed using an Eulerian description. Norton-Hoff and Sheppard-Wright thermo-rigid-viscoplastic constitutive material models have been considered. Constitutive equations for the sub-grid scale models have been proposed and an approximation of the sub-grid scale variables has been given. In particular, algebraic sub-grid scale (ASGS) and orthogonal sub-grid scale (OSGS) methods for mixed velocity, pressure and temperature P1/P1/P1 linear elements have been considered. Furthermore, it has been shown that well known classical stabilized formulations, such as the Galerkin least-squares (GLS) for incompressible (or quasi-incompressible) problems or the Streamline Upwind/Petrov-Galerkin (SUPG) method for convection dominant problems, can be recovered as particular cases of the multiscale stabilization framework considered. Using a product formula algorithm for the solution of the coupled thermomechanical problem, the resulting algebraic system of equations has been solved using a staggered procedure in which a mechanical problem, defined by the linear momentum balance equation, under quasi-static conditions, and the incompressibility equation, is solved first at constant temperature. Then a thermal problem, defined by the energy balance equation, is solved keeping constant the mechanical variables, i.e. velocity and pressure. The computational model has been implemented in an enhanced version of the finite element software COMET, developed by the authors at the International Center for Numerical Methods in Engineering (CIMNE). Two numerical examples have been considered. The first one deals with the numerical simulation of a coupled thermomechanical flow in a 2D rectangular domain. Steady-state and transient conditions have been considered. The goal of this numerical example has been the comparison between different sub-grid scale stabilization methods for the velocity and temperature equations. In particular, using a GLS stabilization method for the pressure equation, a comparison between SUPG and OSGS convective stabilization methods has been performed. Additionally, using a SUPG stabilization method for the temperature equation, a comparison between GLS and OSGS pressure stabilization methods has been done. The second example deals with the 3D numerical simulation of a representative FSW process. Numerical results obtained have been compared with experimental results available in the literature. A good agreement on the temperature distribution has been obtained and predicted peak temperatures compare well, both in value and position, with the experimental results available.

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References

  1. Agelet de Saracibar C (1998) Numerical analysis of coupled thermomechanical contact problems. Computational model and applications. Arch Comput Methods Mech 5:243–301. doi:10.1007/BF02897875

    Article  MathSciNet  Google Scholar 

  2. Agelet de Saracibar C, Cervera M, Chiumenti M (1999) On the formulation of coupled thermoplastic problems with phase-change. Int J Plast 15:1–34. doi:10.1016/S0749-6419(98)00055-2

    Article  MATH  Google Scholar 

  3. Agelet de Saracibar C, Cervera M, Chiumenti M (2001) On the constitutive modeling of coupled thermomechanical phase-change problems. Int J Plast 17:1565–1622. doi:10.1016/S0749-6419(00)00094-2

    Article  MATH  Google Scholar 

  4. Agelet de Saracibar C, Chiumenti M, Valverde Q, Cervera M (2004) On the orthogonal sub-grid scale pressure stabilization of small and finite deformation J2 plasticity, In: Agelet de Saracibar C (ed) Monograph series on computational methods in forming processes, monograph no. 2, CIMNE, Barcelona, Spain

  5. Agelet de Saracibar C, Chiumenti M, Valverde Q, Cervera M (2006) On the orthogonal sub-grid scale pressure stabilization of finite deformation J2 plasticity. Comput Methods Appl Mech Eng 195:1224–1251. doi:10.1016/j.cma.2005.04.007

    Article  MATH  Google Scholar 

  6. Agelet de Saracibar C, Chiumenti M, Santiago D, Dialami N, Lombera G (2010) On the numerical modeling of FSW processes. In: Proceedings of the international symposium on plasticity and its current applications, plasticity 2010, St. Kitts, St. Kitts and Nevis, January 3–8

  7. Agelet de Saracibar C, Chiumenti M, Santiago D, Cervera M, Dialami N, Lombera G (2010) A computational model for the numerical simulation of FSW processes. In: Barlat F, Moon YH, Lee MG (eds) NUMIFORM 2010: proceedings of the 10th international conference on numerical methods in industrial forming processes, Dedicated to Professor O. C. Zienkiewicz (1921–2009), Pohang, South Korea, 13–17 June 2010, AIP Conference Proceedings, vol 1252, 2010, pp. 81–88. doi:10.1063/1.3457640

  8. Agelet de Saracibar C, Chiumenti M, Cervera M, Dialami N, Santiago D, Lombera G (2011) Advances in the numerical simulation of 3D FSW processes. In: Proceedings of the international symposium on plasticity and its current applications, plasticity 2011, Puerto Vallarta, Mexico, January 3–8

  9. Agelet de Saracibar C, López R, Ducoeur B, Chiumenti M, de Meester B (2013) Un modelo numérico para la simulación de disolución de precipitados en aleaciones de aluminio con endurecimiento utilizando redes neuronales. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en la Ingeniería 29(1):29–37. doi:10.1016/j.rimni.2012.02.003

    Article  Google Scholar 

  10. Armero F, Simo JC (1991) A new unconditionally stable fractional step method for non-linear coupled thermomechanical problems. Int J Numer Methods Eng 35:737–766. doi:10.1002/nme.1620350408

    Article  MathSciNet  Google Scholar 

  11. Armero F, Simo JC (1992) Product formula algorithms for nonlinear coupled thermo-plasticity: formulation and non-linear stability analysis, SUDAM Report #92-4. Division of Applied Mechanics, Stanford University, Palo Alto, CA, USA, Department of Mechanical Engineering

  12. Armero F, Simo JC (2003) A priori stability estimates and unconditionally stable product formula algorithms for non-linear coupled thermoplasticity. Int J Plast 9(6):749–782

    Article  Google Scholar 

  13. Askari A, Silling S, London B, Mahoney M (2003) Modeling and analysis of friction stir welding processes. In: Proceedings of the 4th International Symposium on Friction Stir Welding (4ISFSW), GKSS Workshop, Park City, Utah, USA, May 14–16

  14. Avila M, Principe J, Codina R (2010) Finite element dynamical sub-grid scale approximation of low Mach number flow equations. In: Dvorkin E, Goldschmit M, Storti M (eds) Proceedings of the Asociación Argentina de Mecánica Computacional, Buenos Aires, Argentina, 15–18 Noviembre 2010, Mecánica Computacional, vol XXIX, pp 7967–7983

  15. Bendzsak G, North T, Smith C (2000) An experimentally validated 3D model for friction stir welding. In: Proceedings of the 2nd International Symposium on Friction Stir Welding (2ISFSW), Gothenburg, Sweden, June 27–29

  16. Bendzsak G, North T, Smith C (2000) Material properties relevant to 3-D FSW modeling. In: Proceedings of the 2nd International Symposium on Friction Stir Welding (2ISFSW), Gothenburg, Sweden, June 27–29

  17. Brezzi F, Fortin M (1991) Mixed and hybrid finite element methods. Springer Series in Computational Mathematics, vol 15. Springer, New York

  18. Buffa G, Hua J, Shivpuri R, Fratini L (2006) A continuum-based fem model for friction stir welding—model development. Mater Sci Eng A 419:389–396. doi:10.1016/j.msea.2005.09.040

    Article  Google Scholar 

  19. Bussetta P, Dialami N, Boman R, Chiumenti M, Agelet de Saracibar C, Cervera M, Ponthot JP (2013) Comparison of a fluid and a solid approach for the numerical simulation of friction stir welding with a non-cylindrical pin. In: Proceedings of the international conference on coupled problems in engineering 2013, Santa Eulalia, Ibiza, Spain, June 17–19

  20. Bussetta P, Dialami N, Boman R, Chiumenti M, Agelet de Saracibar C, Cervera M, Ponthot JP (2013) Numerical simulation of friction stir welding process with different pin geometries based on a combined ALE/remeshing formulation. Steel Research International. doi:10.1002/srin.201300182

  21. Cervera M, Agelet de Saracibar C, Chiumenti M (2002) COMET—a coupled mechanical and thermal analysis code. Data Input Manual. Version 5.0, Technical Report IT-308, CIMNE, Barcelona, Spain, http://www.cimne.com/comet

  22. Cervera M, Chiumenti M, Valverde Q, Agelet de Saracibar C (2003) Mixed linear/linear simplicial elements for incompressible elasticity and plasticity. Comput Methods Appl Mech Eng 192:5249–5263. doi:10.1016/j.cma.2003.07.007

    Article  MATH  Google Scholar 

  23. Cervera M, Chiumenti M, Agelet de Saracibar C (2004) Shear band localization via local J2 continuum damage mechanics. Comput Methods Appl Mech Eng 193:849–880. doi:10.1016/j.cma.2003.11.009

    Article  MATH  Google Scholar 

  24. Cervera M, Chiumenti M, Agelet de Saracibar C (2004) Softening, localization and stabilization: capture of discontinuous solutions in J2 plasticity. Int J Numer Anal Methods Geomech 28:373–393. doi:10.1002/nag.341

    Article  MATH  Google Scholar 

  25. Cervera M, Chiumenti M, Codina R (2010) Mixed stabilized finite element methods in nonlinear solid mechanics. Part I: formulation. Comput Methods Appl Mech Eng 199:2559–2570. doi:10.1016/j.cma.2010.04.006

    Article  MATH  MathSciNet  Google Scholar 

  26. Cervera M, Chiumenti M, Codina R (2010) Mixed stabilized finite element methods in nonlinear solid mechanics. Part II: strain localization. Comput Methods Appl Mech Eng 199:2571–2589. doi:10.1016/j.cma.2010.04.005

    Article  MATH  MathSciNet  Google Scholar 

  27. Cervera M, Chiumenti M, Codina R (2011) Mesh objective modeling of cracks using continuous linear strain and displacement interpolations. Int J Numer Methods Eng 87:962–987. doi:10.1002/nme.3148

    Article  MATH  MathSciNet  Google Scholar 

  28. Chen CM, Kovacevic R (2003) Finite element modeling of friction stir welding - thermal and thermomechanical analysis. Int J Mach Tools Manuf 43:1319–1326. doi:10.1016/S0890-6955(03)00158-5

    Article  Google Scholar 

  29. Chiumenti M, Valverde Q, Agelet de Saracibar C, Cervera M (2002) A stabilized formulation for incompressible elasticity using linear displacement and pressure interpolations. Comput Methods Appl Mech Eng 191:5253–5264. doi:10.1016/S0045-7825(02)00443-7

    Article  MATH  MathSciNet  Google Scholar 

  30. Chiumenti M, Valverde Q, Agelet de Saracibar C, Cervera M (2004) A stabilized formulation for incompressible plasticity using linear triangles and tetrahedra. Int J Plast 20:1487–1504. doi:10.1016/j.ijplas.2003.11.009

    Article  MATH  Google Scholar 

  31. Chiumenti M, Cervera M, Salmi A, Agelet de Saracibar C, Dialami N, Matsui K (2010) Finite element modeling of multi-pass welding and shaped metal deposition processes. Comput Methods Appl Mech Eng 199:2343–2359. doi:10.1016/j.cma.2010.02.018

    Article  MATH  Google Scholar 

  32. Chiumenti M, Cervera M, Agelet de Saracibar C (2010) A mixed stabilized finite element formulation for strain localization analysis. In: Proceedings of the 11th Pan-American Congress of Applied Mechanics—PACAM XI, January 4–8, Foz do Iguaçu, PR, Brazil

  33. Chiumenti M, Cervera M, Agelet de Saracibar C, Dialami N (2013) Numerical modelling of friction stir welding processes. Comput Methods Appl Mech Eng 254:353–369. doi:10.1016/j.cma.2012.09.013

    Article  MathSciNet  Google Scholar 

  34. Chiumenti M, Cervera M, Agelet de Saracibar C, Dialami N (2013) A novel stress-accurate FE technology for highly non-linear analysis with incompressibility constraint. Application to the numerical simulation of the FSW process, AIP conference proceedings. Proceedings of the international conference on numerical methods in forming processes, NUMIFORM 2013, Shenyang, China, 2013. NUMIFORM 2013, AIP Conference Proceedings, vol 1532, 2013, pp. 45–56

  35. Christ D, Cervera M, Chiumenti M, Agelet de Saracibar C (2003) A mixed finite element formulation for incompressibility using linear displacement and pressure interpolations, monograph no. 77, CIMNE, Barcelona, Spain

  36. Codina R, Blasco J (1997) A finite element formulation for the stokes problem allowing equal velocity-pressure interpolation. Comput Methods Appl Mech Eng 143:373–391. doi:10.1016/S0045-7825(96)01154-1

    Article  MATH  MathSciNet  Google Scholar 

  37. Codina R (1998) Comparison of some finite element methods for solving the diffusion-convection-reaction equations. Comput Methods Appl Mech Eng 156:185–210. doi:10.1016/S0045-7825(97)00206-5

    Article  MATH  MathSciNet  Google Scholar 

  38. Codina R, Blasco J (2000) Stabilized finite element method for transient Navier-Stokes equations based on pressure gradient projection. Comput Methods Appl Mech Eng 182:287–300. doi:10.1016/S0045-7825(99)00194-2

    Article  MathSciNet  Google Scholar 

  39. Codina R (2000) Stabilization of incompressibility and convection through orthogonal sub-scales in finite element methods. Comput Methods Appl Mech Eng 190:1579–1599. doi:10.1016/S0045-7825(00)00254-1

    Article  MATH  MathSciNet  Google Scholar 

  40. Codina R, Blasco J (2000) Analysis of a pressure-stabilized finite element approximation of the stationary Navier-Stokes equations. Numer Math 87:59–81. doi:10.1007/s002110000174

    Article  MATH  MathSciNet  Google Scholar 

  41. Codina R (2001) A stabilized finite element method for generalized stationary incompressible flows. Comput Methods Appl Mech Eng 190:2681–2706. doi:10.1016/S0045-7825(00)00260-7

    Article  MATH  MathSciNet  Google Scholar 

  42. Codina R (2002) Stabilized finite element approximation of transient incompressible flows using orthogonal subscales. Comput Methods Appl Mech Eng 191:4295–4321. doi:10.1016/S0045-7825(02)00337-7

    Article  MATH  MathSciNet  Google Scholar 

  43. Codina R, Principe J, Guasch O, Badia S (2007) Time dependent subscales in the stabilized finite element approximation of incompressible flow problems. Comput Methods Appl Mech Eng 196:2413–2430. doi:10.1016/j.cma.2007.01.002

    Article  MATH  MathSciNet  Google Scholar 

  44. Codina R, Principe J (2007) Dynamic subscales in the finite element approximation of thermally coupled incompressible flows. Int J Numer Methods Fluids 54:707–730. doi:10.1002/fld.1481

    Article  MATH  MathSciNet  Google Scholar 

  45. Codina R, Principe J, Avila M (2010) Finite element approximation of turbulent thermally coupled incompressible flows with numerical sub-grid scale modelling. Int J Numer Methods Heat Fluid Flow 20(5):492–516. doi:10.1108/09615531011048213

    Article  MATH  MathSciNet  Google Scholar 

  46. Colegrove P, Painter M, Graham D, Miller T (2000) Three dimensional flow and thermal modelling of the friction stir welding process. In: Proceedings of the 2nd International Symposium on Friction Stir Welding (2ISFSW), Gothenburg, Sweden, June 27–29

  47. Colegrove P, Shercliff H, Threadgill P (2004) Modelling the friction stir welding of aerospace alloys. Proceedings of the 5th International Symposium on Friction Stir Welding (5ISFSW), Metz, France, September 14–16

  48. De Vuyst T, D’Alvise L, Simar A, de Meester B, Pierret S (2005), Finite element modelling of friction stir welding aluminium alloys plates—inverse analysis using a genetic algorithm. Weld World 49(3/4):44–55

    Google Scholar 

  49. De Vuyst T, D’Alvise L, Simar A, de Meester B, Pierret S (2004) Inverse analysis using a genetic algorithm for the finite element modelling of friction stir welding. In: Proceedings of the 5th International Symposium on Friction Stir Welding (5ISFSW), Metz, France, September 14–16

  50. De Vuyst T, D’Alvise L, Robineau A, Goussain JC (2006) Material flow around a friction stir welding tool—experiment and simulation. In: Proceedings of the 8th international seminar on numerical analysis of weldability, Graz, Austria, September 25–27

  51. De Vuyst T, D’Alvise L, Robineau A, Goussain JC (2006) Simulation of the material flow around a friction stir welding tool. In: Proceedings of the 6th International Symposium on Friction Stir Welding (6ISFSW), Saint-Sauveur, Quebec, Canada, October 10–13

  52. Dialami N, Chiumenti M, Cervera M, Agelet de Saracibar C (2013) An apropos kinematic framework for the numerical modelling of friction stir welding. Comput Struct 117:48–57. doi:10.1016/j.compstruc.2012.12.006

    Article  Google Scholar 

  53. Dong P, Lu F, Hong JK, Cao Z (2001) Coupled thermomechanical analysis of friction stir welding process using simplified models. Sci Technol Weld Join 6(5):281–287. doi:10.1179/136217101101538884

    Article  Google Scholar 

  54. GiD: The Personal Pre and Post processor, CIMNE, 2011. http://www.gidhome.com

  55. Heurtier P, Desrayaud C, Montheillet F (2002) A thermomechanical analysis of the friction stir process. Mater Sci Forum 396:1537–1542. doi:10.4028/www.scientific.net/MSF.396-402.1537

    Google Scholar 

  56. Heurtier P, Jones MJ, Desrayaud C, Driver JH, Montheillet F, Allehaux D (2006) Mechanical and thermal modeling of friction stir welding. J Mater Process Technol 171:348–357. doi:10.1016/j.jmatprotec.2005.07.014

    Article  Google Scholar 

  57. Hughes TJR, Franca L, Balestra M (1986) A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuska-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal order interpolations. Comput Methods Appl Mech Eng 59:85–99. doi:10.1016/0045-7825(86)90025-3

    Article  MATH  MathSciNet  Google Scholar 

  58. Hughes TJR (1995) Multiscale phenomena: green’s function, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized formulations. Comput Methods Appl Mech Eng 127:387–401. doi:10.1016/0045-7825(95)00844-9

    Article  MATH  Google Scholar 

  59. Hughes TJR, Feijóo GR, Mazzei L, Quincy JB (1998) The variational multiscale method—a paradigm for computational mechanics. Comput Methods Appl Mech Eng 166:3–24. doi:10.1016/S0045-7825(98)00079-6

    Article  MATH  Google Scholar 

  60. Hughes TJR, Scovazzi G, Franca L (2004) Multiscale and stabilized methods. In: Stein E, de Borst R, Hughes TJR (eds), Encyclopedia of computational mechanics. Wiley, Chichester, 2004. doi:10.1002/0470091355

  61. Jorge AM Jr, Balancin O (2005) Prediction of steel flow stresses under hot working conditions. Mater Res 8(3):309–315. doi:10.1590/S1516-14392005000300015

    Google Scholar 

  62. Khandkar M, Khan J (2001) Thermal modeling of overlap friction stir welding for Al-alloys. J Mater Process Manuf Sci 10:91–105. doi:10.1177/1062065602010002613

    Google Scholar 

  63. Khandkar M, Khan J, Reynolds A (2003) Prediction of temperature distribution and thermal history during friction stir welding: input torque based model. Sci Technol Weld Joining 8(3):165–174. doi:10.1179/136217103225010943

    Article  Google Scholar 

  64. Langerman M, Kvalvik E (2003) Modeling plasticized aluminum flow and temperature fields during friction stir welding. In: Proceedings of the 6th ASME-JSME Thermal Engineering Joint Conference, Hapuna Beach Prince Hotel, Kohala Coast, Hawaii Island, Hawaii, USA, March 16–20

  65. López R, Ducoeur B, Chiumenti M, de Meester B, Agelet de Saracibar C (2008) Modeling precipitate dissolution in hardened aluminium alloys using neural networks. Int J Mater Form 1(1):1291–1294. doi:10.1007/s12289-008-0139-4

    Article  Google Scholar 

  66. McClure JC, Tang W, Murr LE, Guo X, Feng Z, Gould JE (1998) A thermal model of friction stir welding. In: Proceedings of the 5th international conference on trends in welding research, Pine Mountain, Georgia, USA, June 1–5, 1998, pp 590–595

  67. Nikiforakis N (2005) Towards a whole system simulation of FSW. In: Proceedings of the 2nd FSW modelling and flow visualisation seminar, GKSS Forschungszentrum, Geesthacht, Germany, January 31—February 1

  68. Principe J (2008) Subgrid scale stabilized finite elements for low speed flows, Ph.D. Thesis. Technical University of Catalonia, Barcelona, Spain

  69. Principe J, Codina R (2008) A stabilized finite element approximation of low speed thermally coupled flows. Int J Numer Methods Heat Fluid Flow 18(7/8):835–867. doi:10.1108/09615530810898980

    Article  MATH  MathSciNet  Google Scholar 

  70. Principe J, Codina R (2009) Mathematical models for thermally coupled low speed flows. Adv Theor Appl Mech 2:93–112 http://www.m-hikari.com/atam/atam2009/atam1-4-2009/principeATAM1-4-2009.pdf

  71. Santiago D, Lombera G, Urquiza S, Agelet de Saracibar C, Chiumenti M (2010) Modelado termo-mecánico del proceso de Friction Stir Welding utilizando la geometría real de la herramienta. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería 26:293–303. doi:10.1016/j.rimni.2012.02.003

    Google Scholar 

  72. Schmidt H, Hattel J (2004) Modelling thermo mechanical conditions at the tool/matrix interface in friction stir welding. In: Proceedings of the 5th International Symposium on Friction Stir Welding (5ISFSW), Metz, France, September 14–16

  73. Seidel TU, Reynolds AP (2003) Two-dimensional friction stir welding process model based on fluid mechanics. Sci Technol Weld Joining 8(3):175–183. doi:10.1179/136217103225010952

    Article  Google Scholar 

  74. Shercliff HR, Russell MJ, Taylor A, Dickerson TL (2000) Microstructural modeling in friction stir welding of 2000 series aluminium alloys. Mécanique & Industries 6(2005):25–35. doi:10.1051/meca:2005004

  75. Shi Q, Dickerson T, Shercliff H (2003) Thermo-mechanical FE modeling of friction stir welding of AL-2024 including tool loads. In: Proceedings of the 4th International Symposium on Friction Stir Welding (4ISFSW), Park City, Utah, USA, May 14–16

  76. Song M, Kovacevic R (2003) Numerical and experimental study of the heat transfer process in friction stir welding. J Eng Manuf 217(Part B):73–85

    Google Scholar 

  77. Thomas WM, Nicholas ED, Needham JC, Murch MG, Temple-Smith P, Dawes CJ (1991) Friction stir butt welding. GB Patent No. 9125978.8, International Patent No. PCT/GB92/02203

  78. Ulysse P (2002) Three-dimensional modeling of the friction stir-welding process. Int J Mach Tools Manuf 42:1549–1557. doi:10.1016/S0890-6955(02)00114-1

    Article  Google Scholar 

  79. Xu S, Deng X, Reynolds AP, Seidel TU (2001) Finite element simulation of material flow in friction stir welding. Sci. Technol. Weld. Joining 6(3):191–193. doi:10.1179/136217101101538640

    Article  Google Scholar 

  80. Xu S, Deng X (2003) Two and three-dimensional finite element models for the friction stir welding process. In: Proceedings of the 4th International Symposium on Friction Stir Welding (4ISFSW), Park City, Utah, USA, May 14–16

  81. Xu S, Deng X (2004) Two and three-dimensional finite element models for the friction stir welding process, University of South Carolina, Department of Mechanical Engineering, Columbia, South Carolina 29208, USA

  82. Zhao H (2005) Friction stir welding (FSW) simulation using an Arbitrary Lagrangian-Eulerian (ALE) moving mesh approach, Ph.D. Dissertation, West Virginia University, Morgantown, West Virginia, USA, 2005. http://hdl.handle.net/10450/4367

  83. Zhu XK, Chao YJ (2004) Numerical simulation of transient temperature and residual stresses in friction stir welding of 304L stainless steel. J Mater Process Technol. 146(2):263–272. doi:10.1016/j.jmatprotec.2003.10.025

    Article  Google Scholar 

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Acknowledgments

This work has been supported by the European Commission under the STREP project of the VI Framework Programme “Detailed Multi-Physics Modeling of Frictional Stir Welding” (DEEPWELD), the European Research Council under the Advanced Grant: ERC-2009-AdG “Real Time Computational Mechanics Techniques for Multi-Fluid Problems”, the Spanish Ministerio de Educación y Ciencia under the PROFIT project CIT-020400-2007-82: “Nuevas Herramientas para Optimizar el Proceso de Soldadura por Fricción” (FSWNET) and the project of the Plan Nacional de I + D + I (2004–2007) “Simulación Numérica del Proceso de Soldadura Mediante Batido por Fricción” (FSW)

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  1. ETS Ingenieros de Caminos, Canales y Puertos, Universidad Politécnica de Cataluña (UPC), Edificio C1, Campus Norte, UPC, Jordi Girona 1-3, 08034 , Barcelona, Spain

    C. Agelet de Saracibar, M. Chiumenti & M. Cervera

  2. International Center for Numerical Methods in Engineering (CIMNE), Gran Capitán s/n, 08034 , Barcelona, Spain

    C. Agelet de Saracibar, M. Chiumenti, M. Cervera, N. Dialami & A. Seret

  3. Ecole Nationale Supérieure des Mines de Saint-Étienne, 158 cours Fauriel, 42023 , St-Étienne Cedex 2, France

    A. Seret

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  1. C. Agelet de Saracibar
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de Saracibar, C.A., Chiumenti, M., Cervera, M. et al. Computational Modeling and Sub-Grid Scale Stabilization of Incompressibility and Convection in the Numerical Simulation of Friction Stir Welding Processes. Arch Computat Methods Eng 21, 3–37 (2014). https://doi.org/10.1007/s11831-014-9094-z

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