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Eulerian elasto‐visco‐plastic formulations for residual stress prediction
Author(s) -
Qin Xiaoliang,
Michaleris P.
Publication year - 2008
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2429
Subject(s) - eulerian path , finite element method , petrov–galerkin method , spurious relationship , mechanics , deformation (meteorology) , galerkin method , mathematics , extrusion , state variable , convergence (economics) , stress (linguistics) , mathematical analysis , structural engineering , materials science , engineering , physics , lagrangian , statistics , economics , metallurgy , composite material , economic growth , linguistics , philosophy , thermodynamics
A stabilized, Galerkin finite element formulation for modeling the elasto‐visco‐plastic response of quasi‐steady‐state processes, such as welding, laser surfacing, rolling and extrusion, is presented in an Eulerian frame. The mixed formulation consists of four field variables, such as velocity, stress, deformation gradient and internal variable, which is used to describe the evolution of the material's resistance to plastic flow. The streamline upwind Petrov–Galerkin method is used to eliminate spurious oscillations, which may be caused by the convection‐type of stress, deformation gradient and internal variable evolution equations. A progressive solution strategy is introduced to improve the convergence of the Newton–Raphson solution procedure. Two two‐dimensional numerical examples are implemented to verify the accuracy of the Eulerian formulation. Copyright © 2008 John Wiley & Sons, Ltd.