Technical Brief

Mechanical Properties of the Idealized Inverse-Opal Lattice

[+] Author and Article Information
Bijoy Pal

Department of Mechanical and Aerospace Engineering,
Indian Institute of Technology,
Hyderabad 502285, Kandi, India

S. N. Khaderi

Department of Mechanical and Aerospace Engineering,
Indian Institute of Technology,
Hyderabad 502285, Kandi, India
e-mail: snk@iith.ac.in

1Corresponding author.

Manuscript received August 26, 2017; final manuscript received January 9, 2018; published online February 5, 2018. Assoc. Editor: George Kardomateas.

J. Appl. Mech 85(4), 044501 (Feb 05, 2018) (6 pages) Paper No: JAM-17-1463; doi: 10.1115/1.4038965 History: Received August 26, 2017; Revised January 09, 2018

The idealized inverse-opal lattice is a network of slender struts that has cubic symmetry. We analytically investigate the elastoplastic properties of the idealized inverse-opal lattice. The analysis reveals that the inverse-opal lattice is bending-dominated under all loadings, except under pure hydrostatic compression or tension. Under hydrostatic loading, the lattice exhibits a stretching dominated behavior. Interestingly, for this lattice, Young's modulus and shear modulus are equal in magnitude. The analytical estimates for the elastic constants and yield behavior are validated by performing unit-cell finite element (FE) simulations. The hydrostatic buckling response of the idealized inverse-opal lattice is also investigated using the Floquet–Bloch wave method.

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Fig. 1

Schematic representation of the unit-cell of the inverse-opal lattice: (a) view through z-axis and (b) oblique view. The unit-cell and the lattice structure are shown using transparent cube and orange network, respectively (volume fraction 0.46).

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Fig. 2

An oblique view of the inverse-opal lattice

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Fig. 3

Yield surface under plane stress loading with σzz=0 for a relative density ρ¯=4.35×10−3

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Fig. 4

Yield surface under multi-axial shearing stress loading with for a relative density ρ¯=4.35×10−3

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Fig. 5

Plastic collapse mode due to multiaxial shearing in mode 5

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Fig. 6

Flow chart to calculate the buckling stress σ for a givenk

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Fig. 7

Eigenvalues as a function of the hydrostatic stress various choices of wave vectors (ρ¯=4.35×10−3). A vanishing eigenvalue implies bifurcation for the corresponding wave vector.



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