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Research Papers

Finite-Element Analysis of Rate-Dependent Buckling and Postbuckling of Viscoelastic-Layered Composites

[+] Author and Article Information
Kashyap Alur

Woodruff School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: kashalur@gatech.edu

Thomas Bowling

Woodruff School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: tbowling3@gatech.edu

Julien Meaud

Woodruff School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: julien.meaud@me.gatech.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received September 23, 2015; final manuscript received November 10, 2015; published online December 10, 2015. Assoc. Editor: Kyung-Suk Kim.

J. Appl. Mech 83(3), 031005 (Dec 10, 2015) (8 pages) Paper No: JAM-15-1510; doi: 10.1115/1.4032024 History: Received September 23, 2015; Revised November 10, 2015

The buckling and postbuckling responses of viscoelastic-layered composites are investigated using finite-element simulations. These composites consist of alternating layers of a stiff elastic constituent and of a soft viscoelastic constituent. In response to compressive loads in the layer direction, elastic instabilities significantly affect the finite deformation mechanics of these composites. The dependence of the critical strain and critical wavenumber on strain rate is analyzed. In the postbuckling regime, the wavenumber of the mode of deformation is found to be highly dependent on strain rate and time and can be used to identify three different regimes that depend on the volume fraction of the stiff constituent. Interestingly, a transition from a wrinkling mode to a longwave mode can be observed when the strain rate is varied for moderate volume fractions of the stiff material. Analytical formulae for the buckling and postbuckling of the elastic-layered composites are used to interpret numerical results obtained for viscoelastic-layered composites. Viscoelastic-layered composites exhibit a wide range of rate-dependent mechanical behavior and could have applications in vibration damping and acoustic metamaterials.

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Figures

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Fig. 1

(a) Layered composite with materials A (stiff constituent) and B (soft viscoelastic constituent). TA and TB are thelayer thicknesses. The volume fraction of material A is ϕA=TA/(TA+TB). The composite is loaded in the layer direction, Y. (b) Unit cell of height H and width W. (c) Mode of deformation of the unit cell with a buckling wavelength much larger than the unit cell height (longwave instability). (d) Mode of deformation of the unit cell with a finite wavelength (wrinkling instability).

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Fig. 2

Mechanical properties of material B: (a) ratio of Young's modulus of material A to relaxation modulus of material B versus normalized time and (b) shear stress versus shear strain for loading/unloading at a constant shear strain rate

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Fig. 3

Buckling of elastic-layered composites. Theory is shown in dashed lines and finite-element simulations are marked by a cross symbol. (a) Critical strain as a function of the stiffness ratio, EA/EB, for ϕA=1% (thick solid line), 5% (thin dashed line), and 25% (thin solid line). (b) Nondimensional wavenumber, K¯cr=KcrW, as a function of the stiffness ratio. (c) Volume fraction at which the buckling wavelength changes from finite (wrinkling mode) to infinite (longwave mode) as a function of the stiffness ratio.

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Fig. 4

Stress versus strain responses in the dilute (ϕA=1%), transition (ϕA=5%), and nondilute (ϕA=25%) cases at low(β = 1.5 × 10−6%), moderate (β = 0.15%), and high (β = 15%) strain rates. The vertical dashed line corresponds to the buckling strain (identified by a change in the slope of the response).

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Fig. 5

Modes of deformation for the dilute case (ϕA=1%). Nondimensional wavenumber spectrum versus normalized time for (a) low strain rate (β = 1.5 × 10−6%); (b) moderate strain rate (β = 0.15%); and (c) high strain rate (β = 15%). Dark black line refers to the wavenumber of maximum amplitude at any given time. Nondimensional wavenumber spectrum at the time of buckling, tcr, the time of maximum applied strain, t(ϵmax), and the final time, t(ϵ = 0) for (d) low strain rate; (e) moderate strain rate; and (f) high strain rate.

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Fig. 6

Modes of deformation for the transition case (ϕA=5%). Nondimensional wavenumber spectrum versus normalized time for (a) low strain rate (β = 1.5 × 10–6%); (b) moderate strain rate (β = 0.15%); and (c) high strain rate (β = 15%). Dark black line refers to the wavenumber of maximum amplitude at any given time. Nondimensional wavenumber spectrum at the time of buckling, tcr, the time of maximum applied strain, t(ϵmax), and the final time, t(ϵ = 0) for (d) low strain rate; (e) moderate strain rate; and (f) high strain rate.

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Fig. 7

Critical buckling strain, ϵcr, as a function of the normalized strain rate, β, for (a) dilute case (ϕA=1%) and (b) transition case (ϕA=5%). Results are shown for R = 10−9 and R = 10−5.

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Fig. 8

Critical wavenumber, kcr, as a function of the normalized strain rate, β, the (a) dilute case (ϕA=1%) and (b) transition case (ϕA=5%)

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Fig. 9

(a) and (b) RMS value of the amplitude of the buckling mode, θRMS, as a function of strain in the dilute (a) and transition cases (b). (c) and (d) Length of the interface between the layers normalized by the length of the interface at the onset of buckling in the dilute (c) and transition cases (d).

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Fig. 10

Stress relaxation simulations in the dilute (ϕA=1% (a) and (c)) and transition (ϕA=5% (b) and (d)) cases. (a) and (b) Wavenumber spectrum versus time. Dark black line refers to the maximum wavenumber at any given time. (c) and (d) Vertical position as a function of the normalized displacement (that has been shifted horizontally to facilitate visualization of the results) for a small segment of the interface around the midpoint of the height of the unit cell. The displacement is plotted at t¯h, t¯=300 and t¯end.

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