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TECHNICAL PAPERS

Structure, Mechanics and Failure of Stochastic Fibrous Networks: Part I—Microscale Considerations

[+] Author and Article Information
C. W. Wang, L. Berhan, A. M. Sastry

Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, MI 48109-2125

J. Eng. Mater. Technol 122(4), 450-459 (May 30, 2000) (10 pages) doi:10.1115/1.1288769 History: Received May 26, 2000; Revised May 30, 2000
Copyright © 2000 by ASME
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References

Figures

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SEM image (50×) of an NiMH positive plate substrate, produced by National Standard (Fibrex), containing 50/50 fiber/powder by weight ratio, 97 percent pure nickel by mass; calculated porosity: 82 percent; fiber diameter: 30 mm; staple lengths: 0.64–1.27 cm; content
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Network generation approach, with a single fiber shown for simplicity. Fiber is placed in the unit cell (a) whereupon periodic boundary conditions are applied, effectively “wrapping” overlapping ends back into unit cell (b), and nondomain-spanning segments are removed, as they do not bear network loads (c). Notation for a two-element case, with fixed end. Location and numbering of nodes used in calculating maximum stress are shown below the two-beam schematic.
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Two-beam network analyses notation
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Two-beam structural moduli, with notation of Fig. 3, for α=30, 90 and 150 deg, plotted for varying beam lengths as log(l1/l2). Nodes between segments are rigid. Euler-Bernoulli and Timoshenko beam results are compared in each case; two-beam assemblies are comprised of segments of diameter d=0.2.
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Maximum loads in two-beam assemblies, with notation of Fig. 3, for α=30, 90 and 150 deg, plotted for varying beam lengths as log(l1/l2). Euler-Bernoulli and Timoshenko beam results are compared in each case; two-beam assemblies are comprised of segments of diameter d=0.2.
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Two-beam structural moduli, with notation of Fig. 3, for α=30, α=90 and α=150 deg, plotted for varying beam lengths as log(l1/l2). Segments are joined by torsion springs, (a) for normalized spring constants 1.0 and 0.1, and (b) for normalized spring constants 0.01, 0.001, and 0.0001. Euler-Bernoulli and Timoshenko beam results are compared in each case; two-beam assemblies are comprised of segments of diameter d=0.2.
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Maximum loads in two-beam assemblies, with notation of Fig. 3, for α=30, α=90 and α=150 deg, plotted for varying beam lengths as log(l1/l2). Segments are joined by torsion springs, (a) for normalized spring constant 1.0 and 0.1, and (b) for normalized spring constant 0.01, 0.001, and 0.0001. Euler-Bernoulli and Timoshenko beam results are compared in each case; two-beam assemblies are comprised of segments of diameter d=0.2.
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A reduction of a physically realistic bond between fibers in a fiber/particle network to a 2D beam assembly (a), and notation for the two-beam assembly of rigidly joined beams, with each beam having a “compliant zone” of lengths b2 (b)
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Two-beam assembly of beams joined by a torsion spring at B
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Results for the virtual displacement method. Plots of moduli in compliant zones 1 and 2 versus normalized torsion spring constant, for the specific case of b2=b1/10. The solution for E2 is singular as K→0 (load applied to segment 2).

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