The Convergence of a DFT-Algorithm for Solution of Stress-Strain Problems in Composite Mechanics

[+] Author and Article Information
C. M. Brown

Department of Mechanical and Chemical Engineering, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, UK

W. Dreyer

Weierstraß Institut für Angewandte Analysis und Stochastik, Mohrenstraße 39, 10117 Berlin, Germany

W. H. Müller

Technische Universität Berlin, Fakultät V, Institut für Mechanik, Einsteinufer 5, 10587 Berlin, Germany

J. Eng. Mater. Technol 125(1), 27-37 (Dec 31, 2002) (11 pages) doi:10.1115/1.1526859 History: Received November 05, 2001; Revised March 07, 2002; Online December 31, 2002
Copyright © 2003 by ASME
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RVE showing heterogeneities of different elastic stiffness than the surrounding matrix and external strains
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Discretization of the RVE
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ε11 for (first row) E+/E=10,ν+=0.3,vf=0.2; (second row): E+/E=0.1,ν+=0.3,vf=0.2.
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Some 2D kijkl’s for N=64,νaux=0.3
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Diagonal element k1111 at higher discretizations N=128 and N=256 for νaux=0.3
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The choice C͇aux=C͇+:q1(N) for three different volume fractions, vf=0.2, 0.4, 0.6 and ν+=0.3.
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The choice C͇aux=C͇:q1(N) for vf=0.6 and ν+=0.3
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The choice C͇aux=0.5(C͇++C͇):q1(N) for ν+=0.3
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The choice C͇aux=C͇+:q1(N) for vf=0.2 and different Poisson’s ratios
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The choice C͇aux=C͇+:q1 as a function of Poisson’s ratio for various volume fractions
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Relative error, q1m/(1−q1), as a function of number of iterations, m, for various choices of Poisson’s ratios and vf=0.2
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The choice C͇aux=C͇+:q1(m) in the case of a void for various volume fractions and different choices of Poisson’s ratio




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