Research Papers

Highly Enhanced Damping Figure of Merit in Biomimetic Hierarchical Staggered Composites

[+] Author and Article Information
Pu Zhang

Department of Mechanical Engineering and Materials Science,
University of Pittsburgh,
Pittsburgh, PA 15261
e-mail: puz1@pitt.edu

Albert C. To

Department of Mechanical Engineering and Materials Science,
University of Pittsburgh,
Pittsburgh, PA 15261
e-mail: albertto@pitt.edu

1Corresponding author.

Manuscript received October 22, 2013; final manuscript received December 10, 2013; accepted manuscript posted December 13, 2013; published online January 15, 2014. Editor: Yonggang Huang.

J. Appl. Mech 81(5), 051015 (Jan 15, 2014) (5 pages) Paper No: JAM-13-1440; doi: 10.1115/1.4026239 History: Received October 22, 2013; Revised December 10, 2013; Accepted December 13, 2013

Most composites exhibit a damping figure of merit, a crucial index of a material's dynamic behavior, lower than the value predicted by the Hashin–Shtrikman bound. This work found that the biomimetic hierarchical staggered composites inspired by bone structure can have a damping figure of merit tens of times higher than the Hashin–Shtrikman composite. The optimum state is achieved when the hard and soft phases contribute equally to the overall stiffness of the composite in the direction parallel to the platelets. At this optimal point, the model predicts that the overall stiffness is half the Voigt bound while the damping loss factor is half that of the soft phase. This behavior stems from a deformation mechanism transition from soft-phase-dominant to hard-phase-dominant as the platelet's aspect ratio increases. The findings from this study may have important implications in the future design of composites to mitigate vibration and absorb shock in load-bearing structures.

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Grahic Jump Location
Fig. 1

Schematic illustration of the mechanistic model for hierarchical staggered structures. (a) Self-similar hierarchical model established for bone-like structures. The hard platelets disperse in a soft matrix and assemble in a self-similar way. (b) The loading transfer path in the staggered structure, which is indicated by arrows. The external force is eventually sustained by large shear deformation in the soft matrix, which results in an enhancement of stiffness. This tension-shear transition also gives rise to comparably high damping in this structure. (c) Tension region between the ends of two adjacent hard platelets. The position of hard platelets before deformation is indicated by dash lines. The effect of this region can be simply incorporated by introducing a factor α in Eqs. (1) and (A1). (d) Force equilibrium on one hard platelet and the tensile stress distribution in it. The maximum tensile stress σm occurs at the center of a hard platelet.

Grahic Jump Location
Fig. 2

Storage modulus (E'1) and loss modulus (E"1) enhancement in staggered structure with only one hierarchy (N = 1, Φ = 0.45). Solid lines indicate results derived from Eq. (3) for the loss modulus and Eq. (A1) for the storage modulus while dash lines are results when omitting the tension region factorα. In addition, triangular markers indicate the finite element results. It is clear that the model predicts more accurate results after introducing the tension region factor, especially when the aspect ratio is not that large. The storage modulus will always increase with larger aspect ratio ρ of the hard phase. In contrast, the loss modulus has an optimum value due to the stiffness competition between the tension in the hard phase and shear in the soft matrix. The whole composite loses its damping once ρ is large as a result of reduced shear deformation in the soft matrix.

Grahic Jump Location
Fig. 3

Loss modulus enhancement of staggered structures with different number of hierarchies (Φ = 0.45). It can be seen that the loss modulus would not change so much if N is large enough. However, the optimal platelet aspect ratio ρ∧ can be reduced, which may be beneficial for the purpose of strength enhancement.

Grahic Jump Location
Fig. 4

Contour plot on the loss modulus enhancement of hierarchical staggered materials with respect to the hard phase volume fraction and aspect ratio (N = 5). The dashed lines indicate the optimal platelet aspect ratio for staggered structure containing certain hard phase content (N = 1 and N = 2 cases are shown for comparison).

Grahic Jump Location
Fig. 5

Comparison of loss modulus enhancement among Voigt, Reuss, H–S (Hashin–Shtrikman), and staggered composites. It can be seen that the staggered structure can be optimized to achieve a loss modulus, or damping figure of merit, being much higher than other three composites over a broad range of hard phase content Φ. In addition, the strength of the staggered structure should be much better than the Reuss and H–S composites.



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