Author | A. M. Maniatty, Y. Liu, O. Klaas, M.S. Shephard |
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Title | Stabilized finite element method for viscoplastic flow : formulation and a simple progressive solution strategy |

Year | 2000 |

Journal | Computer Methods in Applied Mechanics and engineering |

Volume | 190 (2001) |

Pages | 4609-4625 |

Abstract | This paper presents a stabilized finite element formulation for steady-state viscoplastic flow and a simple strategy for solving the resulting non-linear equations with a Newton-Raphson algorithm. An Eulerian stabilized finite element formulation is presented, where mesh depend terms are added element-wise to enhance the stability of the mixed finite element formulation. A local reconstruction method is used for computing derivatives of the stress field needed when higher order element are used. Linearization of the weak form is derived to enable a Newton-Raphson solution procedure of the resulting non-linear equations. In order to get convergence in the Newton-Raphson algorithm, a trial solution is needed which is within the radius convergence. An effective strategy for progressively moving inside the radius of convergence for highly non-linear and quadratic shape functions for the velocity and pressure fields in viscoplastc flow problems show that the stabilized method and the progressive convergence strategy are effective in non-linear steady forming problems. Finally, conclusions are inferred and extensions of this work are discussed. |