### FRACTAL APPROACH TO MECHANICAL AND ELECTRICAL PROPERTIES OF GRAPHENE/SIC COMPOSITES

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#### Abstract

Graphene and carbon nanotubes have a Steiner minimum tree structure, which endows them with extremely good mechanical and electronic properties. A modified Hall-Petch effect is proposed to reveal the enhanced mechanical strength of the SiC/graphene composites, and a fractal approach to its mechanical analysis is given. Fractal laws for the electrical conductivity of graphene, carbon nanotubes and graphene/SiC composites are suggested using the two-scale fractal theory. The Steiner structure is considered as a cascade of a fractal pattern. The theoretical results show that the two-scale fractal dimensions and the graphene concentration play an important role in enhancing the mechanical and electrical properties of graphene/SiC composites. This paper sheds a bright light on a new era of the graphene-based materials.

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Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Zhang, Y., Dubonos, S.V., Grigorieva, I.V., Firsov, A.A., 2004, Electric field effect in atomically thin carbon films, Science, 306(5696), pp. 666-669.

Geim, A.K., Novoselov, K.S., 2007, The rise of graphene, Nature Materials, 6(2007), pp. 183-191.

Li, X.-X., Xu, L.-Y., He, J.-H., 2020, Nanofibers membrane for detecting heavy metal ions, Thermal Science, 24(4), pp. 2463-2468.

Yao, X., He, J.-H.,2020, On fabrication of nanoscale non-smooth fibers with high geometric potential and nanoparticle’s non-linear vibration, Thermal Science, 24(4), pp. 2491-249.

Yin, J., Wang, Y., Xu, L., 2020, Numerical approach to high-throughput of nanofibers by a modified bubble-electrospinning, Thermal Science, 2020 24(4), pp. 2367-2375.

You, X., Yang, J.S., Huang, K., Wang M.M., Zhang, X.Y., Dong, S.M., 2019, Multifunctional silicon carbide matrix composites optimized by three-dimensional graphene scaffolds, Carbon, 155, pp. 215-222.

Zuo, Y.T., Liu, H.J., 2021, A fractal rheological model for sic paste using a fractal derivative, Journal of Applied and Computational Mechanics, 7, pp. 13-18.

Wang, Y.C., Zhu, Y.B., He, Z.Z., Wu, H.A., 2020, Multiscale investigations into the fracture toughness of SiC/graphene composites: Atomistic simulations and crack-bridging model, Ceramics International , 46(18A), pp. 29101-29110.

Gnatowski, A., Kijo-Kleczkowska, A., Otwinowski, H., Sikora, P., 2019, The research of the thermal and mechanical properties of materials produced by 3D printing method, Thermal science, 23(Suppl. 4), pp. 1211-1216.

Kuilla, T., Bhadra, S., Yao, D., Kim, N.H., Bose, S., Lee, J.H., 2010, Recent advances in graphene based polymer composites, Progress in Polymer Science, 35(11), pp. 1350-1375.

Tian, D., Zhou, C.J., He, J.H., 2018, Hall-Petch effect and inverse Hall-Petch effect: A fractal unification, Fractals, 6(26), 1850083.

Tian, D., Zhou, C.J., He, J.H., 2019, Strength of bubble walls and the Hall–Petch effect in bubble-spinning, Textile Research Journal, 89(7), pp. 1340-1344.

He, J.H., 2008, A new resistance formulation for carbon nanotubes, Journal of Nanomaterials, doi: 10.1155/2008/954874.

Yao, X., He, J.H., 2020, On fabrication of nanoscale non-smooth fibers with high geometric potential and nanoparticle’s non-linear vibration, Thermal Science, 24(4), pp. 2491-2497.

Xu, L.Y., Li, Y., Li, X.X., He, J.H., 2020, Detection of cigarette smoke using a fiber membrane filmed with carbon nanoparticles and a fractal current law, Thermal Science, 24(4), pp. 2469-2474.

Yang, Z.P., Li, Z., Feng, D., Li, J., Feng, X.M., 2020, A fractal model for pressure drop through a cigarette filter, Thermal Science, 24(4), pp. 2653-2659.

Wu, Y.K., Liu, Y.,2020, Fractal-like multiple jets in electrospinning process, Thermal Science, 24(4), pp. 2499-2505.

Deng, S.X., Ge, X.X., 2020, Fractional Fokker-Planck equation in a fractal medium, Thermal Science, 24(4), pp. 2589-2595.

He, J.H., El-Dib, Y.O., 2020, Periodic property of the time-fractional Kundu-Mukherjee-Naskar equation, Results in Physics, 19, 103345.

He, J.H., 2020, On the fractal variational principle for the telegraph equation, Fractals, doi: 10.1142/S0218348X21500225.

He, J.H., 2020, A simple approach to Volterra-Fredholm integral equations, Journal of Applied and Computational Mechanics, 6(SI), pp. 1184-1186.

He, J.H., 2019, The simpler, the better: Analytical methods for nonlinear oscillators and fractional oscillators, Journal of Low Frequency Noise Vibration and Active Control, 38(3-4), pp. 1252-1260.

Ji, F.Y., He, C.H., Zhang, J.J., He, J.H., 2020, A fractal Boussinesq equation for nonlinear transverse vibration of a nanofiber-reinforced concrete pillar, Applied Mathematical Modelling, 82, pp. 437-448.

He, J.H., 2020, A fractal variational theory for one-dimensional compressible flow in a microgravity space, Fractals, 28(02), 2050024.

He, C.H., Shen, Y., Ji, F.Y., He, J.H., 2020, Taylor series solution for fractal Bratu-type equation arising in electrospinning process, Fractals, 28(01), 2050011.

Lin, L., Yao, S.W., 2019, Fractal diffusion of silver ions in hollow cylinders with unsmooth inner surface, Journal of Engineered Fibers and Fabrics, 14(1), 1558925019895643.

Li, X., Liu, Z., He, J.H., 2020, A fractal two-phase flow model for the fiber motion in a polymer filling process, Fractals, 28(5), 2050093.

He, J.H., 2020, A short review on analytical methods for a fully fourth-order nonlinear integral boundary value problem with fractal derivatives, International Journal of Numerical Methods for Heat and Fluid Flow, doi: 10.1108/HFF-01-2020-0060.

He, J.H., 2019, A simple approach to one-dimensional convection-diffusion equation and its fractional modification for E reaction arising in rotating disk electrodes, Journal of Electroanalytical Chemistry, 854, 113565.

Randjbaran, E., Majid, D.L., Zahari, R., Sultan, M.T.B.H., Mazlan, N., 2020, Effects of volume of carbon nanotubes on the angled ballistic impact for carbon kevlar hybrid fabrics, Facta Universitatis-Series Mechanical Engineering, 18(2), pp. 1-16.

Rysaeva, L.K., Korznikova, E.A., Murzaev, R.T., Abdullina, D.U., Kudreyko, A., Baimova, Y.A., Lisovenko, D., Dmitriev, Sergey V., 2020, Elastic damper based on the carbon nanotube bundle, Facta Universitatis-Series Mechanical Engineering, 18(1), pp. 1-12.

He, J.H., Ain, Q.T., 2020, New promises and future challenges of fractal calculus: from two-scale thermodynamics to fractal variational principle, Thermal Science, 24(2A), pp. 659-681.

Ain, Q.T., He, J.H, 2019, On two-scale dimension and its applications, Thermal Science, 23(3), pp. 1707-1712.

He, J.H., 2018, Fractal calculus and its geometrical explanation, Results in Physics, 10, pp. 272-276.

He, J.H., 2020, Thermal science for the real world: Reality and challenge, Thermal Science, 24(4), pp.2289-2294.

Anjum, N., Ain, Q.T., 2020, Application of he's fractional derivative and fractional complex transform for time fractional camassa-holm equation, Thermal Science, 24(5), pp. 3023-3030.

Liu, F.J., Zhang, X.J., Li, X., 2019, Silkworm (bombyx mori) cocoon vs. wild cocoon multi-layer structure and performance characterization, Thermal Science, 23(4), pp. 2135-2142.

Wang, Y., Yao, S.W., Yang, H.W., 2019, A fractal derivative model for snow's thermal insulation property, Thermal Science, 23(4), pp. 2351-2354.

Fan, J., Yang, X., Liu, Y., 2019, Fractal calculus for analysis of wool fiber: Mathematical insight of its biomechanism, Journal of Engineered Fibers and Fabrics, 14, doi: 10.1177/1558925019872200.

Wang, Q.L., Shi, X.Y., He, J.H., Li, Z.B., 2018, Fractal calculus and its application to explanation of biomechanism of polar bear’s hairs, Fractals, 26(6), 1850086.

Wang, Q.L., Shi, X.Y., He, J.H., Li, Z.B., 2018, Fractal calculus and its application to explanation of biomechanism of polar bear’s hairs, Fractals, 27(5), 1992001.

Sundqvist, P., Garcia-Vidal, F.J., Flores, F., Moreno-Moreno, M., Julio Gómez-Herrero, 2007, Voltage and length-dependent phase diagram of the electronic transport in carbon nanotubes, Nano Letters, 7(9), pp. 2568-2573.

Le, N.Y., Nguyen, T.P., Vu, H.N., Nguyen, T.T., Vu, M.D., 2020, An analytical approach of nonlinear thermo-mechanical buckling of functionally graded graphene-reinforced composite laminated cylindrical shells under compressive axial load surrounded by elastic foundation, Journal of Applied and Computational Mechanics, 6(2), pp. 357-372.

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