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Adaptive finite element procedures for elastoplastic problems at finite strains
Author(s) -
Koch A.,
Miehe C.
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310243
Subject(s) - discretization , necking , finite element method , a priori and a posteriori , nonlinear system , context (archaeology) , computer science , stability (learning theory) , mathematical optimization , adaptive algorithm , mathematics , algorithm , mathematical analysis , structural engineering , engineering , machine learning , paleontology , philosophy , materials science , physics , epistemology , quantum mechanics , metallurgy , biology
A major difficulty in the context of adaptive analysis of geometrically nonlinear problems is to provide a robust remeshing procedure that accounts both for the error caused by the spatial discretization and for the error due to the time discretization. For stability problems, such as strain localization and necking, it is essential to provide a step–size control in order to get a robust algorithm for the solution of the boundary value problem. For this purpose we developed an easy to implement step–size control algorithm. In addition we will consider possible a posteriori error indicators for the spatial error distribution of elastoplastic problems at finite strains. This indicator is adopted for a density–function–based adaptive remeshing procedure. Both error indicators are combined for the adaptive analysis in time and space. The performance of the proposed method is documented by means of representative numerical examples.