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Research Papers

Parametric Finite-Volume Micromechanics of Uniaxial Continuously-Reinforced Periodic Materials With Elastic Phases

[+] Author and Article Information
Mahendra Gattu

 Gilsanz Murray Steficek LLP, New York City, NY 10001

Hamed Khatam, Anthony S. Drago

Civil Engineering Department, University of Virginia, Charlottesville, VA 22904-4742

Marek-Jerzy Pindera

Civil Engineering Department, University of Virginia, Charlottesville, VA 22904-4742mp3g@virginia.edu

J. Eng. Mater. Technol 130(3), 031015 (Jun 11, 2008) (15 pages) doi:10.1115/1.2931157 History: Received October 24, 2007; Revised February 19, 2008; Published June 11, 2008

The finite-volume direct averaging micromechanics (FVDAM) theory for periodic heterogeneous materials is extended by incorporating parametric mapping into the theory’s analytical framework. The parametric mapping enables modeling of heterogeneous microstructures using quadrilateral subvolume discretization, in contrast with the standard version based on rectangular subdomains. Thus arbitrarily shaped inclusions or porosities can be efficiently rendered without the artificially induced stress concentrations at fiber/matrix interfaces caused by staircase approximations of curved boundaries. Relatively coarse unit cell discretizations yield effective moduli with comparable accuracy of the finite-element method. The local stress fields require greater, but not exceedingly fine, unit cell refinement to generate results comparable with exact elasticity solutions. The FVDAM theory’s parametric formulation produces a paradigm shift in the continuing evolution of this approach, enabling high-resolution simulation of local fields with much greater efficiency and confidence than the standard theory.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 2

Unit cells with the same 24×24 subvolume discretization representative of a square array of infinitely long circular inclusions in a matrix phase: (a) rectangular discretization employed in the standard FVDAM theory; (b) quadrilateral discretization employed in the parametric FVDAM theory

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Figure 3

Mapping of the reference square subvolume onto a quadrilateral subvolume of the actual microstructure (after Cavalcante (16))

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Figure 4

Unit cells containing 0.05 fiber-volume fraction with increasing finer discretizations: (a) 24×24; (b) 48×48

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Figure 5

Effective moduli as a function of the fiber-volume fraction based on the two discretizations: (a) Ef∕Em=10; (b) Ef∕Em=0.01

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Figure 9

Effective moduli as a function of the fiber-volume fraction predicted by the standard and parametric FVDAM theories for unit cells with the modulus contrast Ef∕Em=0.01 based on the 24×24 subvolume discretizations shown in Fig. 2

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Figure 10

Local stress fields σ12 and σ13 generated by the applied macroscopic strain ε¯12=0.01 for unit cells shown in Fig. 2 containing 0.30 fiber-volume fraction with the modulus contrast Ef∕Em=10. Comparison of the parametric (left column) and standard (right column) FVDAM predictions: (a) σ12; (b) σ13.

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Figure 8

Local stress fields σ22, σ23, and σ33 generated by the applied macroscopic stress σ22o=σ¯22=1psi for a unit cell containing 0.05 fiber-volume fraction with the modulus contrast Ef∕Em=10. Comparison of the parametric FVDAM predictions (left column) with the Eshelby solution (right column): (a) σ22; (b) σ23; (c) σ33

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Figure 7

Comparison of the effective moduli as a function of the fiber-volume fraction predicted by the parametric FVDAM theory with the finite-element results: (a) Ef∕Em=10; (b) Ef∕Em=0.01

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Figure 6

Local σ12 (left column) and σ13 (right column) stress fields generated by the applied macroscopic strain ε12=0.01 for a unit cell containing 0.05 fiber-volume fraction with the modulus contrast Ef∕Em=10 as a function of increasingly finer discretizations: (a) 24×24; (b) 48×48; (c) 96×96

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Figure 1

(a) A uniaxial continuously reinforced heterogeneous material along the x1 axis with periodic microstructure in the x2-x3 plane constructed with RUCs (highlighted). (b) Discretization of the RUC into rectangular subvolumes employed in the standard version of the FVDAM theory.

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