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An adaptive descent method for non‐linear viscoplasticity
Author(s) -
Eggert Geoffrey M.,
Dawson Paul R.,
Mathur Kapil K.
Publication year - 1991
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.1620310602
Subject(s) - viscoplasticity , robustness (evolution) , rate of convergence , mathematics , descent (aeronautics) , stiffness , convergence (economics) , mathematical optimization , mathematical analysis , computer science , materials science , finite element method , constitutive equation , physics , structural engineering , engineering , key (lock) , composite material , chemistry , computer security , economics , gene , economic growth , biochemistry , meteorology
A forming model based on a viscoplastic flow formulation is derived which includes the effects of small elastic strains. A significant feature of the formulation is its reliance on the dominant inelastic material characteristics in the formation of the stiffness matrix for large strain problems. The resultant non‐linear system of equations is solved by an adaptive descent method which combines the rapid convergence of Newton's method near the solution with the robustness of a method of successive approximations. The use of the adaptive descent method effectively extends the viscoplastic flow formulations into the nearly rate‐insensitive range of behaviours exhibited, for example, by metals at low temperature, where slow convergence of the non‐linear solution algorithm has traditionally hampered their use.