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A new fixed‐point algorithm for hardening plasticity based on non‐linear mixed variational inequalities
Author(s) -
Venini P.,
Nascimbene R.
Publication year - 2003
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.672
Subject(s) - differentiable function , mathematics , fixed point , discretization , variational inequality , regularization (linguistics) , finite element method , algorithm , mathematical optimization , mathematical analysis , computer science , physics , artificial intelligence , thermodynamics
Moving from the seminal papers of Han and Reddy, we propose a fixed‐point algorithm for the solution of hardening plasticity two‐dimensional problems. The continuous problem may be classified as a mixed non‐linear non‐differentiable variational inequality of the second type and is discretized by means of a truly mixed finite‐element scheme. One of the main peculiarities of our approach is the use of the composite triangular element of Johnson and Mercier for the approximation of the stress field. The non‐differentiability is coped with via regularization whereas the non‐linearity is approached with a fixed‐point iterative strategy. Numerical results are proposed that investigate the sensitivity of the approach with respect to the mesh size and the regularization parameter ε. The simplicity of the proposed fixed‐point scheme with respect to more classical return mapping approaches seems to represent one of the key features of our algorithm. Copyright © 2003 John Wiley & Sons, Ltd.