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A novel ‘optimal’ exponential‐based integration algorithm for von‐Mises plasticity with linear hardening: Theoretical analysis on yield consistency, accuracy, convergence and numerical investigations
Author(s) -
Artioli E.,
Auricchio F.,
Beirão da Veiga L.
Publication year - 2006
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.1637
Subject(s) - von mises yield criterion , mathematics , backward euler method , exponential function , numerical integration , pointwise , extrapolation , plasticity , numerical analysis , algorithm , mathematical optimization , mathematical analysis , finite element method , structural engineering , euler equations , physics , engineering , thermodynamics
In this communication we propose a new exponential‐based integration algorithm for associative von‐Mises plasticity with linear isotropic and kinematic hardening, which follows the ones presented by the authors in previous papers. In the first part of the work we develop a theoretical analysis on the numerical properties of the developed exponential‐based schemes and, in particular, we address the yield consistency, exactness under proportional loading, accuracy and stability of the methods. In the second part of the contribution, we show a detailed numerical comparison between the new exponential‐based method and two classical radial return map methods, based on backward Euler and midpoint integration rules, respectively. The developed tests include pointwise stress–strain loading histories, iso‐error maps and global boundary value problems. The theoretical and numerical results reveal the optimal properties of the proposed scheme. Copyright © 2006 John Wiley & Sons, Ltd.