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Article

A Second Look at the Higher-Order Theory for Periodic Multiphase Materials

[+] Author and Article Information
Yogesh Bansal, Marek-Jerzy Pindera

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

J. Appl. Mech 72(2), 177-195 (Mar 15, 2005) (19 pages) doi:10.1115/1.1831294 History: Received March 18, 2003; Revised July 26, 2004; Online March 15, 2005
Copyright © 2005 by ASME
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References

Aboudi,  J., Pindera,  M.-J., and Arnold,  S. M., 2001, “Linear Thermoelastic Higher-Order Theory for Periodic Multiphase Materials,” J. Appl. Mech., 68, No. 5, pp. 697–707.
Aboudi, J., Pindera, M.-J., and Arnold, S. M., 2002, High-Fidelity Generalized Method of Cells for Inelastic Periodic Multiphase Materials, NASA TM 2002-211469.
Aboudi,  J., Pindera,  M.-J., and Arnold,  S. M., 2003, “Higher-Order Theory for Periodic Multiphase Materials With Inelastic Phases,” Int. J. Plast., 19, No. 6, pp. 805–847.
Kalamkarov, A. L., and Kolpakov, A. G., 1997, Analysis, Design and Optimization of Composite Structures, John Wiley & Sons, New York.
Aboudi,  J., Pindera,  M.-J., and Arnold,  S. M., 1999, “Higher-Order Theory for Functionally Graded Materials,” Composites, Part B, 30, No. 8, pp. 777–832.
Paley,  M., and Aboudi,  J., 1992, “Micromechanical Analysis of Composites by the Generalized Method of Cells,” Mech. Mater., 14, pp. 127–139.
Pindera,  M.-J., Aboudi,  J., and Arnold,  S. M., 2003, “Analysis of Locally Irregular Composites Using High-Fidelity Generalized Method of Cells,” AIAA J., 41, No. 12, pp. 2331–2340.
Bufler,  H., 1971, “Theory of Elasticity of a Multilayered Medium,” J. Elast., 1, pp. 125–143.
Pindera,  M.-J., 1991, “Local/Global Stiffness Matrix Formulation for Composite Materials and Structures,” Composites Eng., 1, No. 2, pp. 69–83.
Bansal,  Y., and Pindera,  M.-J., 2003, “Efficient Reformulation of the Thermoelastic Higher-Order Theory for FGMs,” J. Therm. Stresses, 26, Nos. 11/12, pp. 1055–1092; see also: NASA CR 2002-211909.
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Bansal, Y., and Pindera, M.-J., 2004, “Testing the Predictive Capability of the High-Fidelity Generalized Method of Cells Using an Efficient Reformulation,” NASA CR 2004-213043.
Bednarcyk,  B. A., Arnold,  S. M., Aboudi,  J., and Pindera,  M.-J., 2004, “Local Field Effects in Titanium Matrix Composites Subject to Fiber-Matrix Debonding,” Int. J. Plast., 20, pp. 1707–1737.
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Arnold,  S. M., Pindera,  M. J., and Wilt,  T. E., 1996, “Influence of Fiber Architecture on the Inelastic Response of Metal Matrix Composites,” Int. J. Plast., 12, No. 4, pp. 507–545.
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Figures

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A generic cell (q,r) with four subcells (β,γ) employed in the two-level discretization of the unit cell in the original higher-order theory for multiphase periodic materials, presently known as HFGMC. Adapted from Fig. 2 in Aboudi et al. 1.
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〈Color〉 Comparison of σ23 and σ22 stress fields (MPa) within the unit cell of the glass/epoxy unidirectional composite rotated by 26.57 deg about the fiber axis and subjected to the average shear strain ε̄23=0.1%: HFGMC (left column) and GMC (right column) predictions
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Normalized engineering moduli of the aluminum matrix weakened by cylindrical porosities as a function of the rotation angle θ about the fiber axis. Comparison of HFGMC and GMC predictions with the transformation equations.
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〈Color〉 Comparison of σ2233, and σ23 stress fields (MPa) within the unit cell of aluminum matrix with cylindrical porosities rotated by 26.57 deg about the porosity axis and subjected to the average normal strain ε̄22=0.1%: HFGMC (left column) and GMC (right column) predictions
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〈Color〉 Comparison of σ23 and σ22 stress fields (MPa) within the unit cell of aluminum matrix with cylindrical porosities rotated by 26.57 deg about the porosity axis and subjected to the average shear strain ε̄23=0.1%: HFGMC (left column) and GMC (right column) predictions
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(a) A continuously reinforced multiphase composite with a periodic microstructure in the x2–x3 plane constructed with repeating unit cells. (b) Discretization of the repeating unit cell into subcells employed in the reformulation of HFGMC.
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A view of a subcell illustrating the convention employed in designating the surface-averaged displacement and traction components employed in the reformulation of HFGMC
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A representation of an infinite array of inclusions in square packing, showing five repeating unit cells which represent the same array in different coordinate systems rotated by the indicated angles about the fiber axis
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Detailed volume discretizations of the four repeating unit cells in the rotated coordinate systems employed to accurately capture the geometric details within each unit cell
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Normalized engineering moduli of the glass/epoxy unidirectional composite as a function of the rotation angle θ about the fiber axis. Comparison of GMC and HFGMC predictions with the transformation equations.
Grahic Jump Location
〈Color〉 Comparison of σ2233, and σ23 stress fields (MPa) within the unit cell of the glass/epoxy unidirectional composite rotated by 26.57 deg about the fiber axis and subjected to the average normal strain ε̄22=0.1%: HFGMC (left column) and GMC (right column) predictions

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