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Three‐dimensional finite element implementation of the nonuniform transformation field analysis
Author(s) -
Fritzen Felix,
Böhlke T.
Publication year - 2010
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.2920
Subject(s) - finite element method , linearization , discretization , fast fourier transform , transformation (genetics) , field (mathematics) , mathematics , transformation matrix , matrix (chemical analysis) , computer science , algorithm , nonlinear system , mathematical analysis , structural engineering , engineering , physics , classical mechanics , materials science , biochemistry , chemistry , kinematics , quantum mechanics , pure mathematics , composite material , gene
In this paper aspects of the nonuniform transformation field analysis (NTFA) introduced by Michel and Suquet ( Int. J. Solids Struct . 2003; 40 :6937–6955) are investigated for materials with three‐dimensional microtopology. A novel implementation of the NTFA into the finite element method (FEM) is described in detail, whereas the NTFA was originally used in combination with the fast Fourier transformation (FFT). In particular, the discrete equivalents of the averaging operators required for the preprocessing steps and an algorithm for the implicit time integration and linearization of the constitutive equations of the homogenized material are provided. To the authors knowledge this is the first implementation of the method for three‐dimensional problems. Further, an alternative mode identification strategy is proposed with the aim of small computational cost in combination with good efficiency. The new identification strategy is applied to three‐dimensional metal matrix composites in order to investigate its effective non‐linear behaviour. The homogenized material model is implemented into ABAQUS/STANDARD. Numerical examples at integration point level and in terms of structural problems highlight the efficiency of the method for three‐dimensional problems. Copyright © 2010 John Wiley & Sons, Ltd.