The aim of this work was to develop a method for optimizing both the design parameters and the mechanical properties of polymer-based nanocomposites using multi-objective optimization (MOO) methods. The objective was to maximize both the elastic modulus and the tensile strength of nanocomposites simultaneously by varying the design parameters. The Ji and Zare models were selected as the objective functions for the elastic modulus and tensile strength of polymer nanocomposites, respectively. For this purpose, the NSGA-II approach implemented in MATLAB was used to obtain optimal solutions of the design variables. The optimization model was able to successfully find optimum solutions of the design variables and the overall optimization results were found to be in good agreement with the available published data. In addition, the proposed optimization model was found to be sufficiently accurate in finding the optimum values of the design variables for improving the mechanical properties of nanocomposites.
BhattacharyaM.Polymer nanocomposites – a comparison between carbon nanotubes, graphene, and clay as nanofillers. Materials2016;
9: 262–297.
2.
SubramanianNRaiAChattopadhyayA.Atomistically informed stochastic multiscale model to predict the behavior of carbon nanotube-enhanced nanocomposites. Carbon2015;
94: 661–672.
3.
Stein IY, Vincent HM, Steiner SA, et al. Processing and Mechanical Property Characterization of Aligned Carbon Nanotube Carbon Matrix Nanocomposites. In: 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. American Institute of Aeronautics and Astronautics, 5 April 2013. DOI: 10.2514/6.2013-1583.
4.
ZareY.Assumption of interphase properties in classical Christense-Lo model for young’s modulus of polymer nanocomposites reinforced with spherical nanoparticles. RSC Adv2015;
5: 95532–95533.
5.
HuaYGuLPremarajS, et al.
Role of interphase in the mechanical behaviour of silica/epoxy resin nanocomposites. Materials2015;
8: 3519–3531.
6.
MsekhMACuongNHZiG, et al.
Fracture properties prediction of clay/epoxy nanocomposites with interphase zones using a phase field model. Eng Fract Mech2018;
188: 287–299.
7.
KhareHBurrisD.A quantitative method for measuring nanocomposite dispersion. Polymer2010;
51: 719–729.
8.
NjugunaJPielichowskiK.Polymer nanocomposites for aerospace applications. Adv Eng Mater2004;
6: 193–203.
9.
ThostensonELiCChouTW.Nanocomposites in context. Compos Sci Technol2005;
65: 491–516.
DengFItoMNoguchiT, et al.
Elucidation of the reinforcing mechanism in carbon nanotube/rubber nanocomposites. ACS Nano2011;
5: 3858–3866.
12.
ChengQBaoJParkJ, et al.
High mechanical performance composite conductor: Multi-walled carbon nanotube sheet/bismaleimide nanocomposites. Adv Funct Mater2009;
19: 3219–3225.
13.
ShankarKR.Preparation and characterization of magnetically aligned carbon nanotube buckypaper and composite. Master of Science Dissertation, Florida State University, 2003.
14.
HandlinDSteinIYGuzman de VilloriaR, et al.
Three-dimensional elastic constitutive relations of aligned carbon nanotube architecture. J Appl Phys2013;
114: 224310–224318.
15.
AxinteABejanLTaranuN, et al.
Modern approaches on the optimization of composite structures. Buletinul Institutului Politehnic Din Lasi, Sectia Constructii, Arhitectura2013;
59: 43–55.
16.
GilletAFrancescatoPSaffreP.Single- and multi-objective optimization of composite structures: the influence of design variables. Journal of Composite Materials2010;
44: 457–448.
17.
Bandyopadhyay S and Saha S. Some single - and multiobjective optimization techniques. In: Unsupervised Classification, Heidelberg: Springer, 2013, pp. 17–58.
18.
ErtasA.Optimization of fiber reinforced laminates for maximum fatigue life using particle swarm optimization. Proc Eng2012;
38: 473–478.
19.
RostamiyanYFereidoonB.Preparation, modeling, and optimization of mechanical properties of epoxy/hips/silica hybrid nanocomposite using combination of Central composite design and genetic algorithm. Part 1. Study of damping and tensile strengths. Strength Mater2013;
45: 619–634.
20.
MoghriMShamaeeHShahrajabianH, et al.
The effect of different parameters on mechanical propertied of PA-6/clay nanocomposite through genetic algorithm and response surface methods. Int Nano Lett2015;
5: 133–140.
21.
KhandanRNorooziSSewellP, et al.
Optimum design of fibre orientation in composite laminate plates for out-plane stresses. Adv Mater Sci Eng2012;
2012: 1–11.
22.
ErtasASonmezF.Application of stochastic global optimization algorithms to practical problems. Finite Elem Anal Des2011;
47: 413–423.
23.
Awad Z, Aravinthan T, Zhuge Y et al. Multi-objective design optimization of an innovative fiber composite sandwich panel for civil engineering applications. In: 21st Australasian Conference on the Mechanics of Structures and Materials (ACMSM 21): Incorporating Sustainable Practice in Mechanics of Structures and Materials, Melbourne, Australia, 7–10 December 2010.
24.
Vo-DuyTDuong-GiaDHo-HuuV, et al.
Multi-objective optimization of laminated composite beam structures using NSGA-II algorithm. Compos Struct2017;
168: 498–509.
25.
GhasemiHBrighentiRXiaoyingZ, et al.
Optimal fiber content and distribution in fiber-reinforced solids using a reliability and NURBS based sequential optimization approach. Struct Multidisc Optim2015;
51: 99–112.
26.
GhasemiHKerfridenPBordasSPA, et al.
Interfacial shear stress optimization in sandwich beams with polymeric core using non-uniform distribution of reinforcing ingredients. Compos Struct2015;
120: 221–230.
27.
BloomfieldMHerenciaJWeaverP.Analysis and benchmarking of meta-heuristic techniques for lay-up optimization. Compos Struct2010;
88: 272–282.
28.
GhiasiHPasiniDLessardL.Optimum stacking sequence design of composite materials part I: constant stiffness design. Compos Struct2009;
90: 1–11.
29.
ErghottM.Vilfredo Pareto and multi-objective optimization. Documenta Mathematica2012; 447–453.
30.
GhiasiM.Multi-objective optimization of composite structures made by resin transfer moulding. Doctoral Thesis, McGill University, 2009.
31.
KonakACoitDWSmithAE.Multi-objective optimization using genetic algorithms: a tutorial. Reliab Eng Syst Saf2006;
91: 992–1007.
32.
Coello-CoelloC.Introduction to evolutionary multiobjective optimization.
Berlin, Heidelberg:
Springer, 2002.
33.
JafariMSoroushianSKhayatiG.Hardness optimization for Al6061-MWCNT nanocomposite prepared by mechanical alloying using artificial neural networks and genetic algorithm. J Ultrafine Grained Nanostruct Mater2017;
50: 23–32.
34.
SrinivasNDebK.Multiobjective optimization using nondominated sorting in genetic algorithms. Evol Comput1994;
2: 221–248.
35.
DebKAgrawalSPratapA, et al.
A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II, Int3 parallel problem solving from.Nature PPSN VI2000;
6: 849–858.
36.
StanislavIAjayK.Multiobjective optimization of industrial petroleum processing units using genetic algorithms. Proc Chem2014;
10: 7–14.
37.
DvorakG.Micromechanics of composite materials.
Netherlands:
Springer, 2013.
38.
ZareYGarmabiH.Thickness, modulus and strength of interphase in clay/polymer nanocomposites. Appl Clay Sci2015;
105-106: 66–70.
39.
JiXJingJJiangW, et al.
Tensile modulus of polymer nanocomposites. Polym Eng Sci2002;
42: 983–993.
40.
SamandariSKhatibiA.The effect of interphase on the elastic modulus of polymer based nanocomposites. Key Eng Mater2006;
312: 199–204.
41.
TakayanagiMUemuraSMinamiS.Application of equivalent model method to dynamic rheo-optical properties of crystalline polymer. J Polym Sci, C Polym Symp2007;
5: 113–122.
42.
ZareY.Effects of interphase on tensile strength of polymer/CNT nanocomposites by Kelly-Tyson theory. Mech Mater2015;
85: 1–6.
43.
RazaviSDehghanpourNAhmadiS, et al.
Thermal, mechanical, and corrosion resistance properties of vinyl ester/clay nanocomposites for the matrix of carbon fiber-reinforced composites exposed to electron beam. Appl Polym Sci2015;
132: 42393–42401.
44.
LuoJDanielI.Characterization and modeling of mechanical behaviour of polymer/clay nanocomposites. Compos Sci Technol2003;
63: 1607–1616.
45.
ZareYRheeKParkS.Modeling of tensile of strength in polymer particulate nanocomposites based on material and interphase properties. Appl Polym Sci2017;
34: 29–35.
46.
ZareYGarmabiH.A developed model to assume the interphase properties in a ternary polymer nanocomposite reinforced with two nanofillers. Compos Part: B2015;
75: 29–35.
47.
StojsicJRaosPKalendovaA.A study of structure and tensile properties of polyamide12/clay nanocomposites. Polym Compos2016;
37: 684–691.
48.
KrenchelH.Fibre reinforcement: theoretical and practical investigations of the elasticity and strength of fibre-reinforced materials.
Copenhagen:
Akademisk Forlag, 1964.
49.
BligheFMYoungKVilatelaJJ, et al.
The effect of nanotube content and orientation on the mechanical properties of polymer nanotube composite fibers: separating intrinsic reinforcement from orientational effects. Adv Funct Mater2011;
21: 364–371.
50.
ChopraSDeshmukhKPeshweD.Theoretical prediction of interfacial properties of PBT/CNT nanocomposites and its experimental evaluation. Mech Mater2017;
109: 11–17.
51.
SalvetatJBonardJThomsonN, et al.
Mechanical properties of carbon nanotubes. Appl Physics A1999;
69: 255–260.
52.
SharifEGhasemiIKarrabiM, et al.
A new approach in modeling of mechanical properties of nanocomposites: effect of interface and random orientation. Iran Polym J2014;
23: 835–845.
53.
LaiDLiDYangJ.Improved mechanical properties of montmorillonite/nylon 6 nanocomposites by the modification of novolac. J Macromol Science Part A2015;
52: 1009–1016.
54.
ZareY.Estimation of material and interfacial/interphase properties in clay/polymer nanocomposites by yield strength data. Appl Clay Sci2015;
115: 61–66.
55.
GhadamAGJ.Investigation of mechanical properties prediction of synthesized nylon-66/nano-calcium carbonate composites. J Part Sci Technol2015;
1: 241–251.
56.
HuangFShangguanL.Morphology and mechanical properties of low density polyethylen/multi-walled carbon nanotubes nanocomposites. MS2017;
23: 129–132.
57.
BikiarisD.Microstructure and properties of polypropylene/carbon nanotube nanocomposites. Materials2010;
3: 2884–2946.
