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Research Papers

A Floquet-Based Bar-Spring Model for the Dynamic Modulus of Bioinspired Composites With Arbitrary Staggered Architectures

[+] Author and Article Information
Wen Xie

Department of Engineering Mechanics,
School of Civil Engineering,
Wuhan University,
Wuhan 430072, China
e-mail: benxwen@whu.edu.cn

Yanan Yuan

Department of Engineering Mechanics,
School of Civil Engineering,
Wuhan University,
Wuhan 430072, China
e-mail: yuanyn@whu.edu.cn

Zuoqi Zhang

Department of Engineering Mechanics,
School of Civil Engineering,
Wuhan University,
Wuhan 430072, China;
Suzhou Institute of Wuhan University,
Suzhou 215123, China
e-mail: zhang_zuoqi@whu.edu.cn

1Corresponding authors.

Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received April 24, 2019; final manuscript received May 24, 2019; published online June 27, 2019. Assoc. Editor: Caglar Oskay.

J. Appl. Mech 86(9), 091007 (Jun 27, 2019) (8 pages) Paper No: JAM-19-1200; doi: 10.1115/1.4043888 History: Received April 24, 2019; Accepted May 29, 2019

Staggered architectures widely seen in load-bearing biological materials provide not only excellent supporting functions resisting static loading but also brilliant protecting functions attenuating the dynamic impact. However, there are very few efforts to unveil the relationship between staggered architectures and damping properties within load-bearing biological and bioinspired materials, while its static counterpart has been intensively studied over the past decades. Here, based on the Floquet theory, we developed a new generic method to evaluate the dynamic modulus of the composites with various staggered architectures. Comparisons with the finite element method results showed that the new method can give more accurate predictions than previous methods based on the tension-shear chain model. Moreover, the new method is more generic and applicable for two- and three-dimensional arbitrarily staggered architectures. This method provides a useful tool to understand the relationship between micro-architecture and damping property in natural load-bearing biological materials and to facilitate the architectural design of high-damping bioinspired composites.

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Figures

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Fig. 1

Diverse staggered microarchitectures found in the load-bearing biological composites in nature: (a) the regular staggered microstructure in nacre [7,9,12], (b) the stairwise staggered pattern in the mineralized collagen of bone [1315], and (c) randomly staggered alignment of enamel rods in tooth [16,17]

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Fig. 2

(a) A two-dimensional schematic of composites with unidirectional reinforcements, (b) a representative unit cell with nonuniform reinforcements nonuniformly aligned in matrices in a staggered fashion, (c) a bar-spring model converted from the representative unit cell, and (d) the axial forces and shear stress on an infinitesimal bar segment

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Fig. 3

A schematic of the regular staggered composites, also well known as “brick-and-mortar” structure

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Fig. 4

The Floquet-based bar-spring (FBBS) model predicted (a) storage modulus and (b) loss modulus varying against the reinforcement aspect ratio, with comparison to the results of FEM simulations, the tension-shear chain (TSC) model, and its refined version

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Fig. 5

The Floquet-based bar-spring model predicted (a) storage modulus and (b) loss modulus varying against the angular frequency for different reinforcement aspect ratio, and (c) and (d) for different modulus ratio, with comparison to the corresponding FEM results for verification purposes

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Fig. 6

Staggered structure with hybrid long and short fibers

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Fig. 7

Variation of (a) storage modulus and (b) loss modulus with frequency

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Fig. 8

(a) Representative elementary volume, (b) longitudinal section view, and (c) cross-sectional view of the 3D model

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Fig. 9

(a) Storage modulus and (b) loss modulus of the 3D model

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