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A comparative study of stress update algorithms for rate‐independent and rate‐dependent crystal plasticity
Author(s) -
Miehe Christian,
Schröder Jörg
Publication year - 2000
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 - 10.1002/1097-0207(20010120)50:2<273::aid-nme17>3.0.co;2-q
Subject(s) - regularization (linguistics) , jacobian matrix and determinant , diagonal , algorithm , plasticity , mathematics , slip (aerodynamics) , mathematical optimization , computer science , geometry , artificial intelligence , physics , thermodynamics
The paper presents a comparative discussion of stress update algorithms for single‐crystal plasticity at small strains. The key result is a new unified fully implicit multisurface‐type return algorithm for both the rate‐independent and the rate‐dependent setting, endowed with three alternative approaches to the regularization of possible redundant slip activities. The fundamental problem of the rate‐independent theory is the possible ill condition due to linear‐dependent active slip systems. We discuss three possible algorithmic approaches to deal with this problem. This includes the use of alternative generalized inverses of the Jacobian of the currently active yield criterion functions as well as a new diagonal shift regularization technique, motivated by a limit of the rate‐dependent theory. Analytical investigations and numerical experiments show that all three approaches result in similar physically acceptable predictions of the active slip of rate‐independent single‐crystal plasticity, while the new proposed diagonal shift method is the most simple and efficient concept. Copyright © 2001 John Wiley & Sons, Ltd.