Inscrição na biblioteca: Guest
Portal Digital Begell Biblioteca digital da Begell eBooks Diários Referências e Anais Coleções de pesquisa
International Journal for Multiscale Computational Engineering
Fator do impacto: 1.016 FI de cinco anos: 1.194 SJR: 0.554 SNIP: 0.82 CiteScore™: 2

ISSN Imprimir: 1543-1649
ISSN On-line: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2020032669
pages 141-157


Giovanni Formica
Dipartimento di Architettura, University of Roma Tre, Rome, 00181, Italy
Franco Milicchio
Dipartimento di Ingegneria, University of Roma Tre, Rome, 00146, Italy
Walter Lacarbonara
Dipartimento di Ingegneria Strutturale e Geotecnica, Sapienza University of Rome, Rome, 00184, Italy


Optimization of the storage modulus and the hysteretic damping capacity of multilayer carbon nanotube (CNT) nanocomposites is carried out via a differential evolution algorithm coupled with a nonlinear finite element implementation of a 3D mesoscale theory of nanocomposites exhibiting CNT/polymer stick-slip behavior. Such constitutive theory describes the hysteresis due to the shear stick-slip between the carbon nanotubes and the long molecular chains of the hosting matrix wrapped around them. The storage modulus and the amount of energy dissipated through the CNT-matrix stick-slip depend on the nanocomposite microstructural parameters, such as the elastic mismatch, the nanofiller content, its distribution, and the CNT-matrix interfacial shear strength. The optimization problem seeks to determine the set of material parameters of a multilayer stacking sequence that can give rise to the largest storage modulus and damping capacity of the ensuing nanocomposite. The results confirm that the genetic-type multilayer nanocomposite damping optimization resorting on a sound mechanical model of the nonlinear hysteretic material response can be an effective and affordable design method.


  1. Awad, Z., Aravinthan, T., Zhuge, Y., and Gonzalez, F., A Review of Optimization Techniques Used in the Design of Fibre Composite Structures for Civil Engineering Applications, Mater. Des., vol. 33, pp. 534-544, 2018.

  2. Bessa, M., Bostanabad, R., Liu, Z., Hu, A., Apley, D., Brinson, C., Chen, W., and Liu, W., A Framework for Data-Driven Analysis of Materials under Uncertainty: Countering the Curse of Dimensionality, Comput. Methods Appl. Mech. Eng., vol. 320, pp. 633-667, 2017.

  3. Casciaro, R., Time Evolutional Analysis of Nonlinear Structures, Meccanica, vol. 10, no. 3, pp. 156-167, 1975.

  4. Crowe, M.J., A History of Vector Analysis: The Evolution of the Idea of a Vectorial System, Dover Books on Mathematics, New York: Dover Publications, 2011.

  5. Das, S.,Mullick, S.S., and Suganthan, P., Recent Advances in Differential Evolution-An Updated Survey, Swarm Evol. Comput:., vol. 27, pp. 1-30,2016.

  6. Formica, G. and Lacarbonara, W., Three-Dimensional Modeling of Interfacial Stick-Slip in Carbon Nanotube Nanocomposites, Int. J. Plasticity, vol. 88, pp. 204-217,2017.

  7. Formica, G., Lacarbonara, W., and Alessi, R., Vibrations of Carbon Nanotube-Reinforced Composites, J. Sound Vibr., vol. 329, no. 10, pp. 1875-1889,2010.

  8. Formica, G., Milicchio, F., and Lacarbonara, W., Computational Efficiency and Accuracy of Sequential Nonlinear Cyclic Analysis of Carbon Nanotube Nanocomposites, Adv. Eng. Software, vol. 125, pp. 126-135, 2018a.

  9. Formica, G., Milicchio, F., and Lacarbonara, W., Hysteretic Damping Optimization in Carbon Nanotube Nanocomposites, Compos. Struct., vol. 194, pp. 633-642, 2018b.

  10. Formica, G., Talc), M., and Lacarbonara, W., Nonlinear Modeling of Carbon Nanotube Composites Dissipation due to Interfacial Stick-Slip, Int. J. Plasticity, vol. 53, pp. 148-163, 2014.

  11. Formica, G., Talo, M., Lanzara, G., and Lacarbonara, W., Parametric Identification of Carbon Nanotube Nanocomposites Constitutive Response, J. Appl. Mech., vol. 86, no. 4, p. 041007, 2019.

  12. Ghasemi, H., Brighenti, R., Zhuang, X., Muthu, J., and Rabczuk, T., Optimization of Fiber Distribution in Fiber Reinforced Composite by Using NURBS Functions, Comput. Mater. Sci., vol. 83, pp. 463-473, 2014.

  13. Ghosh, S., Das, S., Vasilakos, A.V., and Suresh, K., On Convergence of Differential Evolution over a Class of Continuous Functions with Unique Global Optimum, IEEE Trans. Syst., Man, and Cybernet., Part B, vol. 42, no. 1, pp. 107-124, 2012.

  14. Imani Yengejeh, S., Kazemi, S., and Ochsner, A., Carbon Nanotubes as Reinforcement in Composites: A Review of the Analytical, Numerical and Experimental Approaches, Comput. Mater. Sci., vol. 136, pp. 85-101,2017.

  15. Lacarbonara, W. and Lanzara, G., Bridging High Strength and Dissipation in Carbon Nanotube Composites, Tech. Rep. Grant N. FA9550-141-0082 DEF, EOARD/AFOSR Proposal, 2014.

  16. Liu, Q., Lomov, S., and Gorbatikh, L., Spatial Distribution and Orientation ofNanotubes for Suppression of Stress Concentrations Optimized Using Genetic Algorithm and Finite Element Analysis, Mater. Des., vol. 158, pp. 136-146, 2018.

  17. Liu, Q., Lomov, S.V., and Gorbatikh, L., The Interplay between Multiple Toughening Mechanisms in Nanocomposites with Spatially Distributed and Oriented Carbon Nanotubes as Revealed by Dual-Scale Simulations, Carbon, vol. 142, pp. 141-149, 2019.

  18. Maghsoudlou, M.A., Barbaz Isfahani, R., Saber-Samandari, S., and Sadighi, M., Effect of Interphase, Curvature and Agglomeration of SWCNTs on Mechanical Properties of Polymer-Based Nanocomposites: Experimental and Numerical Investigations, Composites Part B, vol. 175, p. 107119,2019.

  19. Malekimoghadam, R. and Icardi, U., Prediction of Mechanical Properties of Carbon Nanotube-Carbon Fiber Reinforced Hybrid Composites Using Multi-Scale Finite Element Modelling, Composites PartB, vol. 177, p. 107405, 2019.

  20. Mura, T., Micromechanics of Defects in Solids, New York: Springer Science & Business Media, 2013.

  21. Odegard, G., Gates, T., Wise, K., Park, C., and Siochi, E., Constitutive Modeling of Nanotube-Reinforced Polymer Composites, Compos. Sci. Technol, vol. 63, no. 11, pp. 1671-1687,2003.

  22. Reddy, J.N., Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, Boca Raton, FL: CRC Press, 2003.

  23. Safdari, M. and Al-Haik, M.S., Optimization of Stress Wave Propagation in a Multilayered Elastic/Viscoelastic Hybrid Composite based on Carbon Fibers/Carbon Nanotubes, Polymer Composites, vol. 33, no. 2, pp. 196-206, 2011.

  24. Schiebold, M., Schmidt, H., and Mehner, J., A Finite Element Approach for Modeling and Simulation of CNT/Polymer Composites, Physica Status Solidi (A), vol. 216, no. 19, p. 1800952, 2019.

  25. Seifert, R., Patil, M., Seidel, G., and Reich, G., Multi-Functional Topology Optimization of Piezoresistive Nanocomposite Beams, ASME 2015 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, vol. 1, ASME Paper No. SMASIS2015-8958, 6 pages, 2015.

  26. Storn, R. and Price, K., Differential Evolution-A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces, J. Global Optim., vol. 11, no. 4, pp. 341-359, 1997.

  27. Stricklin, J.A. and Haisler, W.E., Formulations and Solution Procedures for Nonlinear Structural Analysis, Comput. Struct., vol. 7, no. 1,pp. 125-136, 1977.

  28. Tac, V. and Gtirses, E., Micromechanical Modelling of Carbon Nanotube Reinforced Composite Materials with a Functionally Graded Interphase, J. Compos. Mater, vol. 53, nos. 28-30, pp. 4337-4348, 2019.

  29. Talo, M., Krause, B., Pionteck, J., Lanzara, G., and Lacarbonara, W., An Updated Micromechanical Model based on Morphological Characterization ofCarbon Nanotube Nanocomposites, Composites Part B, vol. 115, pp. 70-78, 2017.

  30. Talo, M., Lanzara, G., Karimzadeh, M., and Lacarbonara, W., Interface Engineering of CNT/Polymer Nanocomposites with Tunable Damping Properties, ASME 2018 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, vol. 1, ASME Paper No. SMASIS2018-8066, p. V001T01A015; 6 pages, 2018.

  31. Talo, M., Lanzara, G., Krause, B., Janke, A., and Lacarbonara, W., Sliding Crystals on Low-Dimensional Carbonaceous Nanofillers as Distributed Nanopistons for Highly Damping Materials, ACS Appl. Mater. Interf., no. 18, pp. 9725-9735, 2019.

  32. Wang, G. and Pindera, M.J., Elasticity-Based Microstructural Optimization: An Integrated Multiscale Framework, Mater. Des., vol. 132, pp. 337-348,2017.

  33. Wang, Y., Xie, K., Fu, T., and Shi, C., Bending and Elastic Vibration of a Novel Functionally Graded Polymer Nanocomposite Beam Reinforced by Graphene Nanoplatelets, Nanomaterials, vol. 9, no. 12, pp. 1690-1711, 2019.

Articles with similar content:

Composites: Mechanics, Computations, Applications: An International Journal, Vol.4, 2013, issue 2
Yu. A. Basistov, Yuri G. Yanovsky
Nanoscience and Technology: An International Journal, Vol.9, 2018, issue 2
G. I. Kriven, Sergey A. Lurie, Dmitriy B. Volkov-Bogorodsky
International Journal for Multiscale Computational Engineering, Vol.16, 2018, issue 5
M. Jahanshahi, N. Jafarian, N. Heidarzadeh, Amir R. Khoei
Nanoscience and Technology: An International Journal, Vol.5, 2014, issue 3
Yury Solyaev, D. Q. Nguen, A. V. Afanasiev, A. A. Dudchenko
Effects of Shape and Size of Crystal Grains on the Strengths of Polycrystalline Metals
International Journal for Multiscale Computational Engineering, Vol.4, 2006, issue 4
Kenjiro Terada, Masayoshi Akiyama, Ikumu Watanabe