Research Papers

Optimization of Damping Properties of Staggered Composites Through Microstructure Design

[+] Author and Article Information
Junjie Liu

College of Engineering,
Peking University,
Beijing 100871, China
e-mail: liujunjie625@pku.edu.cn

Xusheng Hai

College of Engineering,
Peking University,
Beijing 100871, China
e-mail: 1400011011@pku.edu.cn

Wenqing Zhu

College of Engineering,
Peking University,
Beijing 100871, China
e-mail: zhu_wq@pku.edu.cn

Xiaoding Wei

College of Engineering,
Peking University,
Beijing 100871, China;
Beijing Innovation Center for Engineering
Science and Advanced Technology,
Peking University,
Beijing 100871, China
e-mail: xdwei@pku.edu.cn

1Corresponding authors.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received March 28, 2018; final manuscript received June 6, 2018; published online June 27, 2018. Assoc. Editor: Pedro Reis.

J. Appl. Mech 85(10), 101002 (Jun 27, 2018) (9 pages) Paper No: JAM-18-1177; doi: 10.1115/1.4040538 History: Received March 28, 2018; Revised June 06, 2018

Many natural materials, such as shell and bone, exhibit extraordinary damping properties under dynamic outside excitations. To explore the underlying mechanism of these excellent performances, we carry out the shear-lag analysis on the unit cell in staggered composites. Accordingly, the viscoelastic properties of the composites, including the loss modulus, storage modulus, and loss factor, are derived. The damping properties (particularly, the loss modulus and loss factor) show an optimization with respect to the constituents' properties and morphology. The optimal scheme demands a proper selection of four key factors: the modulus ratio, the characteristic frequency of matrix, aspect ratios of tablets, and matrix. The optimal loss modulus is pointed out to saturate to an upper bound that is proportional to the elastic modulus of tablets when the viscosity of matrix increases. Furthermore, a loss factor even greater than one is achievable through microstructure design. Without the assumption of a uniform shear stress distribution in the matrix, the analysis and formulae reported herein are applicable for a wide range of reinforcement aspect ratios. Further, for low-frequency loading, we give practical formulae of the three indexes of damping properties. The model is verified by finite element analysis (FEA) and gives novel ideas for manufacturing high damping composites.

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Grahic Jump Location
Fig. 1

Schematic of the unit cell for the shear-lag analysis

Grahic Jump Location
Fig. 2

(a) Two-dimensional finite element model used for the validation of the shear-lag analysis. (b) Comparison between the theoretical model and FEA. All the parameters are treated to be dimensionless. In this case, the dimensionless frequency ω¯=1. (c) Contour plot shows the variation of E¯″ with dimensionless frequency ω¯ and dimensionless overlap length L¯, suggesting an optimal design for high damping composites. The optimal design guidelines are highlighted for the cases when L¯ (the solid line) is given and ω¯ is given (the dashed line), respectively. (d) Plot shows how E¯″ depends on ω¯ for L¯=1. (e) Comparison between the loss modulus from the approximate expression, Eq. (13) and the full expression, Eq. (15) at ω¯ = 0.1, 0.3, and 0.5.

Grahic Jump Location
Fig. 3

(a) Contour plot shows how the storage modulus E¯′ relies on ω¯ and L¯. (b) Contour plot with a log scale color bar depicts the relation between loss factor tan δ with ω¯ and L¯. The dashed line highlights the optimal match for ω¯ and L¯ when L¯ is given. (c) Plot shows how tan δ varies with ω¯ for L¯=1, suggesting an optimal design. (d) Plot shows that the loss factor tan δ is able to be highly improved even greater than 1.

Grahic Jump Location
Fig. 4

Determination of the unit cell for the mechanical analysis: (a) schematic of the whole staggered composite containing the brick-and-mortar microstructure, (b) crystallographic unit cell that replicates of the complete composite, and (c) mechanical unit cell that reflects the symmetry of the stress and strain distributions in this problem

Grahic Jump Location
Fig. 5

Validation of model assumptions through FEA simulations: (a) schematic of the large FEA model containing 11 × 7 unit cells, (b) comparison between dimensionless loss moduli obtained from the large FEA model, unit cell FEA model, and the theoretical prediction, (c) comparison between dimensionless loss moduli of unit cells with different tablet densities obtained by abaqus/Explicit, abaqus/Standard, and the analytical model, and (d) influence of Poisson's ratio on the dimensionless loss moduli of unit cell




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