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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Currey, J. , 1977, “ Mechanical Properties of Mother of Pearl in Tension,” Proc. R. Soc. London B, 196(1125), pp. 443–463. [CrossRef]
Landis, W. , 1995, “ The Strength of a Calcified Tissue Depends in Part on the Molecular Structure and Organization of Its Constituent Mineral Crystals in Their Organic Matrix,” Bone, 16(5), pp. 533–544. [CrossRef] [PubMed]
Meyers, M. A. , Chen, P.-Y. , Lin, A. Y.-M. , and Seki, Y. , 2008, “ Biological Materials: Structure and Mechanical Properties,” Prog. Mater. Sci., 53(3), pp. 1–206. [CrossRef]
Munch, E. , Launey, M. E. , Alsem, D. H. , Saiz, E. , Tomsia, A. P. , and Ritchie, R. O. , 2008, “ Tough, Bio-Inspired Hybrid Materials,” Science, 322(5907), pp. 1516–1520. [CrossRef] [PubMed]
Wegst, U. G. , Bai, H. , Saiz, E. , Tomsia, A. P. , and Ritchie, R. O. , 2015, “ Bioinspired Structural Materials,” Nat. Mater., 14(1), pp. 23–36. [CrossRef] [PubMed]
Silver, F. H. , Freeman, J. W. , and DeVore, D. , 2001, “ Viscoelastic Properties of Human Skin and Processed Dermis,” Skin Res. Technol., 7(1), pp. 18–23. [CrossRef] [PubMed]
Robinson, P. S. , Lin, T. W. , Reynolds, P. R. , Derwin, K. A. , Iozzo, R. V. , and Soslowsky, L. J. , 2004, “ Strain-Rate Sensitive Mechanical Properties of Tendon Fascicles From Mice With Genetically Engineered Alterations in Collagen and Decorin,” ASME J. Biomech. Eng., 126(2), pp. 252–257. [CrossRef]
Fessel, G. , and Snedeker, J. G. , 2009, “ Evidence Against Proteoglycan Mediated Collagen Fibril Load Transmission and Dynamic Viscoelasticity in Tendon,” Matrix Biol., 28(8), pp. 503–510. [CrossRef] [PubMed]
Lujan, T. J. , Underwood, C. J. , Jacobs, N. T. , and Weiss, J. A. , 2009, “ Contribution of Glycosaminoglycans to Viscoelastic Tensile Behavior of Human Ligament,” J. Appl. Physiol., 106(2), pp. 423–431. [CrossRef] [PubMed]
Zhang, P. , and To, A. C. , 2013, “ Broadband Wave Filtering of Bioinspired Hierarchical Phononic Crystal,” Appl. Phys. Lett., 102(12), p. 121910. [CrossRef]
Chen, Y. , and Wang, L. , 2014, “ Tunable Band Gaps in Bio-Inspired Periodic Composites With Nacre-Like Microstructure,” J. Appl. Phys., 116(6), p. 063506. [CrossRef]
Chen, Y. , and Wang, L. , 2015, “ Bio-Inspired Heterogeneous Composites for Broadband Vibration Mitigation,” Sci. Rep., 5, p. 17865. [CrossRef] [PubMed]
Qwamizadeh, M. , Zhang, Z. , Zhou, K. , and Zhang, Y. W. , 2015, “ On the Relationship Between the Dynamic Behavior and Nanoscale Staggered Structure of the Bone,” J. Mech. Phys. Solids, 78, pp. 17–31. [CrossRef]
Qwamizadeh, M. , Zhang, Z. , Zhou, K. , and Zhang, Y. W. , 2016, “ Protein Viscosity, Mineral Fraction and Staggered Architecture Cooperatively Enable the Fastest Stress Wave Decay in Load-Bearing Biological Materials,” J. Mech. Behav. Biomed. Mater., 60, pp. 339–355. [CrossRef] [PubMed]
Yin, J. , Huang, J. , Zhang, S. , Zhang, H. , and Chen, B. , 2014, “ Ultrawide Low Frequency Band Gap of Phononic Crystal in Nacreous Composite Material,” Phys. Lett. A, 378(32–33), pp. 2436–2442. [CrossRef]
Yin, J. , Zhang, S. , Zhang, H. , and Chen, B. , 2016, “ Band Structure Characteristics of Nacreous Composite Materials With Various Defects,” Z. Naturforsch. A, 71(6), pp. 493–499. [CrossRef]
Jäger, I. , and Fratzl, P. , 2000, “ Mineralized Collagen Fibrils: A Mechanical Model With a Staggered Arrangement of Mineral Particles,” Biophys. J., 79(4), pp. 1737–1746. [CrossRef] [PubMed]
Gao, H. , Ji, B. , Jäger, I. L. , Arzt, E. , and Fratzl, P. , 2003, “ Materials Become Insensitive to Flaws at Nanoscale: Lessons From Nature,” Proc. Natl. Acad. Sci., 100(10), pp. 5597–5600. [CrossRef]
Zhang, P. , and To, A. C. , 2014, “ Highly Enhanced Damping Figure of Merit in Biomimetic Hierarchical Staggered Composites,” ASME J. Appl. Mech., 81(5), p. 051015. [CrossRef]
Zhang, P. , Heyne, M. A. , and To, A. C. , 2015, “ Biomimetic Staggered Composites With Highly Enhanced Energy Dissipation: Modeling, 3D Printing, and Testing,” J. Mech. Phys. Solids, 83, pp. 285–300. [CrossRef]
Qwamizadeh, M. , Liu, P. , Zhang, Z. , Zhou, K. , and Zhang, Y. W. , 2016, “ Hierarchical Structure Enhances and Tunes the Damping Behavior of Load-Bearing Biological Materials,” ASME J. Appl. Mech., 83(5), p. 051009. [CrossRef]
Qwamizadeh, M. , Zhou, K. , and Zhang, Y. W. , 2017, “ Damping Behavior Investigation and Optimization of the Structural Layout of Load-Bearing Biological Materials,” Int. J. Mech. Sci., 120, pp. 263–275. [CrossRef]
Qwamizadeh, M. , Lin, M. , Zhang, Z. , Zhou, K. , and Zhang, Y. W. , 2017, “ Bounds for the Dynamic Modulus of Unidirectional Composites With Bioinspired Staggered Distributions of Platelets,” Compos. Struct., 167, pp. 152–165. [CrossRef]
Liu, G. , Ji, B. , Hwang, K.-C. , and Khoo, B. C. , 2011, “ Analytical Solutions of the Displacement and Stress Fields of the Nanocomposite Structure of Biological Materials,” Compos. Sci. Technol., 71(9), pp. 1190–1195. [CrossRef]
Wu, J. , Yuan, H. , Li, L. , Fan, K. , Qian, S. , and Li, B. , 2018, “ Viscoelastic Shear Lag Model to Predict the Micromechanical Behavior of Tendon Under Dynamic Tensile Loading,” J. Theor. Biol., 437, pp. 202–213. [CrossRef] [PubMed]
Cox, H. , 1952, “ The Elasticity and Strength of Paper and Other Fibrous Materials,” Br. J. Appl. Phys., 3(3), p. 72. [CrossRef]
Wei, X. , Naraghi, M. , and Espinosa, H. D. , 2012, “ Optimal Length Scales Emerging From Shear Load Transfer in Natural Materials: Application to Carbon-Based Nanocomposite Design,” ACS Nano, 6(3), pp. 2333–2344. [CrossRef] [PubMed]
Obaid, N. , Kortschot, M. T. , and Sain, M. , 2017, “ Understanding the Stress Relaxation Behavior of Polymers Reinforced With Short Elastic Fibers,” Materials, 10(5), p. 472. [CrossRef]
Dutta, A. , Tekalur, S. A. , and Miklavcic, M. , 2013, “ Optimal Overlap Length in Staggered Architecture Composites Under Dynamic Loading Conditions,” J. Mech. Phys. Solids, 61(1), pp. 145–160. [CrossRef]
Barry, P. , 1978, “ The Longitudinal Tensile Strength of Unidirectional Fibrous Composites,” J. Mater. Sci., 13(10), pp. 2177–2187. [CrossRef]
Ji, X. , Liu, X.-R. , and Chou, T.-W. , 1985, “ Dynamic Stress Concentration Factors in Unidirectional Composites,” J. Compos. Mater., 19(3), pp. 269–275. [CrossRef]
Achenbach, J. , 2012, Wave Propagation in Elastic Solids, Elsevier, North Holland, The Netherlands.
Ghoreishi, R. , and Suppes, G. , 2015, “ Chain Growth Polymerization Mechanism in Polyurethane-Forming Reactions,” RSC Adv., 5(84), pp. 68361–68368. [CrossRef]
Lakes, R. S. , 2009, Viscoelastic Materials, Cambridge University Press, Cambridge, UK. [CrossRef]
Koratkar, N. A. , Suhr, J. , Joshi, A. , Kane, R. S. , Schadler, L. S. , Ajayan, P. M. , and Bartolucci, S. , 2005, “ Characterizing Energy Dissipation in Single-Walled Carbon Nanotube Polycarbonate Composites,” Appl. Phys. Lett., 87(6), p. 063102. [CrossRef]
Ogasawara, T. , Tsuda, T. , and Takeda, N. , 2011, “ Stress–Strain Behavior of Multi-Walled Carbon Nanotube/PEEK Composites,” Compos. Sci. Technol., 71(2), pp. 73–78. [CrossRef]
Dai, R. , and Liao, W. , 2009, “ Fabrication, Testing, and Modeling of Carbon Nanotube Composites for Vibration Damping,” ASME J. Vib. Acoust., 131(5), p. 051004. [CrossRef]
Suhr, J. , Koratkar, N. , Keblinski, P. , and Ajayan, P. , 2005, “ Viscoelasticity in Carbon Nanotube Composites,” Nat. Mater., 4(2), pp. 134–137. [CrossRef] [PubMed]
Wang, T.-Y. , Liu, S.-C. , and Tsai, J.-L. , 2016, “ Micromechanical Stick-Slip Model for Characterizing Damping Responses of Single-Walled Carbon Nanotube Nanocomposites,” J. Compos. Mater., 50(1), pp. 57–73. [CrossRef]
Zhou, X. , Shin, E. , Wang, K. , and Bakis, C. , 2004, “ Interfacial Damping Characteristics of Carbon Nanotube-Based Composites,” Compos. Sci. Technol., 64(15), pp. 2425–2437. [CrossRef]
Lin, R. , and Lu, C. , 2010, “ Modeling of Interfacial Friction Damping of Carbon Nanotube-Based Nanocomposites,” Mech. Syst. Signal Process., 24(8), pp. 2996–3012. [CrossRef]
Dwaikat, M. , Spitas, C. , and Spitas, V. , 2011, “ A Model for Elastic Hysteresis of Unidirectional Fibrous Nano Composites Incorporating Stick-Slip,” Mater. Sci. Eng.: A, 530, pp. 349–356. [CrossRef]
Savvas, D. , Papadopoulos, V. , and Papadrakakis, M. , 2012, “ The Effect of Interfacial Shear Strength on Damping Behavior of Carbon Nanotube Reinforced Composites,” Int. J. Solids Struct., 49(26), pp. 3823–3837. [CrossRef]


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. 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

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. 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.



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