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Numerical technique in plasticity including solution advancement control
Author(s) -
Runesson Kenneth,
Samuelsson Alf,
Bernspång Lars
Publication year - 1986
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.1620220315
Subject(s) - discretization , von mises yield criterion , mathematics , finite element method , plasticity , numerical analysis , nonlinear system , hardening (computing) , mathematical analysis , optimal control , quadratic equation , stress field , mathematical optimization , geometry , structural engineering , materials science , engineering , physics , layer (electronics) , quantum mechanics , composite material
Abstract Numerical techniques applied to the consistent formulation of plasticity, which is based on convex analysis, are investigated. For each time step the stress is found as the projection in complementary energy of the elastic stress onto the set of plastically admissible stresses, while the velocity field is the extremal of a non‐quadratic functional. Explicit formulas for von Mises' yield criterion with mixed hardening are developed and the nonlinear equations arising from finite element discretization are solved, for comparison, by a number of Newton‐type iteration procedures with line search and are‐length control. A few numerical examples with proportional and non‐proportional loading are analyzed.