Eulerian elasto-visco-plastic formulations for residual stress prediction

International Journal for Numerical Methods in Engineering

Volumn 77, Issue 5, 2009, Pages 634-663

  Qin, Xiaoliang ^a   Michaleris, P ^a  

^a The Pennsylvania State University   (United States)

Author keywords

Anand's model; Elasto visco plastic; Eulerian; Mixed finite element analysis; Rate equilibrium equation; Residual stress

Indexed keywords

DEFORMATION; DIFFERENTIAL EQUATIONS; GALERKIN METHODS; LASER BEAM WELDING; PLASTICS; RESIDUAL STRESSES; STRENGTH OF MATERIALS; SYSTEMS ANALYSIS;

ANAND'S MODEL; ELASTO-VISCO-PLASTIC; EULERIAN; MIXED FINITE ELEMENT ANALYSIS; RATE EQUILIBRIUM EQUATION;

FINITE ELEMENT METHOD;

EID: 60949097997     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2429     Document Type: Article

References (34)

1. Tekriwal P, Mazumder J. Transient and residual thermal strain-stress analysis of GMAW. Journal of Engineering Materials and Technology 1991; 113:336-343.
2. Argyris JH, Szimmat J, Willam KJ. Computational aspects of welding stress analysis. Computer Methods in Applied Mechanics and Engineering 1982; 33:635-666.
3. Hibbitt H, Marcal PV. A numerical, thermo-mechanical model for the welding and subsequent loading of a fabricated structure. Computers and Structures 1973; 3(1145-1174):1145-1174
4. Braudel HJ, Abouaf M, Chenot JL. An implicit and incremental formulation for the solution of elastoplastic problems by the finite element method. Computers and Structures 1986; 22(5):801-814.
5. McDill JMJ, Oddy AS, Goldak JA. Consistent strain fields in 3d finite element analysis of welds. ASME Journal of Pressure Vessel Technology 1990; 112(3):309-311.
6. Oddy AS, Goldak JA, McDill JMJ. Numerical analysis of transformation plasticity in 3d finite element analysis of welds. European Journal of Mechanics, A: Solids 1990; 9:1-11.
7. Michaleris P, DeBiccari A. Prediction of welding distortion. Welding Journal 1997; 76(4):172-180.
8. Rybicki EF, Stonesifer RB. Computation of residual stresses due to multipass welds in piping systems. Journal of Pressure Vessel Technology 1979; 101:149-154.
9. Shim Y, Feng Z, Lee S, Kim DS, Jaeger H, Paparitan JC, Tsai CL. Determination of residual stress in thick-section weldments. Welding Journal 1992; 71:305s-312s.
10. Bertram LA, Ortega AR. Automated thermomechanical modeling of welds using interface elements for 3D metal deposition. Proceedings of ABAQUS User's Conference. Hibbit Karlsson and Sorensen Inc.: Oxford, 1991.
11. Michaleris P, Zhang L, Marugabandhu P. Evaluation of applied plastic strain methods for welding distortion prediction. Journal of Manufacturing Science and Engineering 2007; 129:1000-1010.
12. Simon G, Lionel F. Error estimation and accurate mapping based ale formulation for 3d simulation of friction stir welding. Proceedings of the 9th International Conference on Numerical Methods in Industrial Forming Process, Porto, Portugal, 2007.
13. Nguyen QS, Rahimian M. Mouvement permanent d'une fissure en milieu elastoplastique. Journal de Mecanique Appliquee 1981; 5:95-120.
14. Agrawal A, Dawson PR. A comparison of Galerkin and streamline techniques for integration strains from an Eulerian flow field. International Journal for Numerical Methods in Engineering 1985; 21:853-881.
15. Heinrich JC, Zienkiewicz OC. Quadratic finite element schemes for two dimensional convective-transport problems. International Journal for Numerical Methods in Engineering 1977; 11:1831-1844.
16. Brooks AN, Hughes TJR. Streamline upwind/Petrov-Galerkin formulation for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equation. Computer Methods in Applied Mechanics and Engineering 1982; 32:199-259.
17. Donea J, Belytschko T, Smolinski P. A generalized Galerkin method for steady state convection-diffusion problems with application to quadratic shape functions. Computer Methods in Applied Mechanics and Engineering 1985; 48:25-43.
18. Hughes TJR, Franca LP, Hulbert GM. A new finite element formulation for computational fluid dynamics: Viii. the Galerkin/least-squares methods for advective-diffusive equations. Computer Methods in Applied Mechanics and Engineering 1989; 73:173-189.
19. Maniatty AM, Dawson PR, Weber GG. An Eulerian elasto-viscoplastic formulation for steady-state forming processes. International Journal of Mechanical Sciences 1991; 33:361-377.
20. Shanghvi J, Michaleris P. Thermo-elasto-plastic finite element analysis of quasi-state processes in Eulerian reference frames. International Journal for Numerical Methods in Engineering 2002; 53:1533-1556.
21. Dawson PR. On modeling of mechanical property changes during flat rolling of aluminum. International Journal of Solids and Structures 1987; 23:947-968.
22. Kobayashi S, Oh S, Altan T. Metal Forming and the Finite Element Method. Oxford University Press: New York, 1989.
23. Maniatty AM, Chen M. Shape sensitivity analysis for steady metal forming processes. International Journal for Numerical Methods in Engineering 1996; 39:1199-1217.
24. Maniatty AM, Liu Y. Stabilized finite element method for viscoplastic flow: formulation with state variable evolution. International Journal for Numerical Methods in Engineering 2003; 56:185C-209C.
25. Thomson EG, Yu S-W. A flow formulation for rate equilibrium equations. International Journal for Numerical Methods in Engineering 1990; 30:1619-1632.
26. Brown SB, Kim KH, Anand L. An internal variable constitutive model for hot working of metals. International Journal of Plasticity 1989; 5:95-130.
27. Weber GG, Lush AM, Zavaliangos A, Anand L. An objective time-integration procedure for isotropic rate-independent and rate-dependent elastic-plastic constitutive equations. International Journal of Plasticity 1990; 6:701-744.
28. Weber G, Anand L. Finite deformation constitutive equations and a time integration procedure for isotropic hyperelastic-viscoplastic solids. Computer Methods in Applied Mechanics and Engineering 1990; 79:173-202.
29. Boyce MC, Weber GG, Parks DM. On the kinematics of finite strain plasticity. Journal of the Mechanics and Physics of Solids 1989; 37:647-665.
30. Belytschko T, Liu WK, Moran B. Nonlinear Finite Elements for Continua and Structures (4th edn). Wiley: New York, 2000.
31. Bathe K-J. Finite Element Procedures. Prentice-Hall: New Jersey, 1996.
32. Hughes TJR, Brooks A. A theoretical framework for Petrov-Galerkin methods with discontinuous weighting functions: application to the streamline-upwind procedure. Finite Elements in Fluids 1982; 4:47-65.
33. Nemat-Nasser S, Guo W-G. Thermomechanical response of hsla-65 steel plates: experiments and modeling. Mechanics of Materials 2003; 37:379-405.
34. Lush AM, Weber G, Anand L. An implicit time-integration procedure for a set of internal variable constitutive equations for isotropic elasto-viscoplasticity. International Journal of Plasticity 1989; 5:521-549.