### FRACTAL DIMENSIONS OF A POROUS CONCRETE AND ITS EFFECT ON THE CONCRETE’S STRENGTH

**DOI Number**

**First page**

**Last page**

#### Abstract

#### Keywords

#### Full Text:

PDF#### References

Xue, R.J., Liu, F.J., 2022, A fractional model and its application to heat prevention coating with cocoon-like hierarchy, Thermal Science, 26(3), pp. 2493-2498.

Mo, X.X., Lu, Y.H., Liu, F.J., 2022, Research on the design and performance of multilayer textiles with a cocoon-like hierarchy, Journal of the Textile Institute, 113(12), pp. 2722-2731.

Xue, R.J., Mo, X.X., Liu, F.J., 2021, Tussah cocoon's biomechanism: Fractal insight and experimental verification, International Journal of Thermal Sciences, 169, 107089.

Wang, D.W., Li, F., Liu, M., Lu, G.Q., Cheng, H.M., 2008, 3D aperiodic hierarchical porous graphitic carbon material for high-rate electrochemical capacitive energy storage, Angewandte Chemie-International Edition, 47(2), pp. 373-376.

Hou, J.H., Cao, C.B., Idrees, F., Ma, X.L., 2015, Hierarchical Porous Nitrogen-Doped Carbon Nanosheets Derived from Silk for Ultrahigh-Capacity Battery Anodes and Supercapacitors, ACS Nano, 9(3), pp. 2556-2564.

He, C.H., Amer, T.S., Tian, D., Abolila, A.F., Galal, A.A.,2022, Controlling the kinematics of a spring-pendulum system using an energy harvesting device, Journal of Low Frequency Noise Vibration and Active Control, 41(3), pp. 1234-1257.

Wang, Q.L., He, J.H., Liu, Z., 2022, Intelligent Nanomaterials for Solar Energy Harvesting: From Polar Bear Hairs to Unsmooth Nanofiber Fabrication, Frontiers in Bioengineering and Biotechnology, 10, 926253.

Yin, N., Liu, F.J., 2021, Nanofibrous Filters for PM2.5 Filtration: Conception, Mechanism and Progress, Nano, 16(4), 2130004.

Meng, D.P., Zhang, Y.H., Wu, J.T., 2022, Graphene/polyimide nanofibrous mat for high-efficiency filtration, AATCC Journal of Research, 9 (4), pp. 176-181.

Robert, B., Nallathambi, G., 2022, Tailoring mechanically robust nanofibrous membrane for PM2.5-0.3 filtration and evaluating their behaviour using response surface Box-Behnken design, Separation Science and Technology, 57 (16), pp. 2583-2595.

Cheng, X., Zhao, L., Zhang, Z.W., et al., 2022, Highly efficient, low-resistant, well-ordered PAN nanofiber membranes for air filtration, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 655, 130302.

He, J.H., Qian, M.Y., 2022, A fractal approach to the diffusion process of red ink in a saline water, Thermal Science, 26(3B), pp. 2447-2451.

Gao, J., Xiao, B.Q., Tu, B.L., et al., 2022, A fractal model for gas diffusion in dry and wet fibrous media with tortuous converging-diverging capillary bundle, Fractals, 30(9), 2250176.

Li, Z.Y., Chen, Q.T., Wang, Y.L., Li, X.Y., 2022, Solving two-sided fractional super-diffusive partial differential equations with variable coefficients in a class of new reproducing kernel spaces, Fractal and Fractional, 6(9), 492.

Wang, K.J., 2022, Variational principle and approximate solution for the fractal vibration equation in a microgravity space, Iranian Journal of Science and Technology-Transactions of Mechanical Engineering, 46(1), pp. 161–165.

Feng, G.Q., 2021, He’s frequency formula to fractal undamped Duffing equation, Journal of Low Frequency Noise Vibration and Active Control, 40 (4), pp. 1671-1676.

Feng, G.Q., Niu, J.Y., 2021, He's frequency formulation for nonlinear vibration of a porous foundation with fractal derivative, GEM-International Journal on Geomathematics, 12(1), 14.

Babič, M., Fragassa, C., Lesiuk, G., Marinković, D., 2020, A new method for complexity determination by using fractals and its applications in material surface characteristics, International Journal for Quality Research, 14(3), pp. 705-716.

Babič, M., Marinkovic, D., Bonfanti, M., Calì M., 2022, Complexity Modeling of Steel-Laser-Hardened Surface Microstructures, Applied Sciences, 12(5), 2458.

Babic M., Lesiuk G., Marinkovic D., Calì M., 2021, Evaluation of microstructural complex geometry of robot laser hardened materials through a genetic programming model, Procedia Manufacturing, 55(C), pp. 253-259.

Varzaneh, A.S., Naderi, M., 2022, Experimental and Finite Element Study to Determine the Mechanical Properties and Bond Between Repair Mortars and Concrete Substrates, Journal of Applied Computational Mechanics, 8 (2), pp. 493-509.

Mander; J. B., Priestley, M. J. N., Park, R., 1988, Theoretical Stress-Strain Model for Confined Concrete, Journal of Structural Engineering-ASCE, 114 (8), pp. 1804-1826.

Lee, J.H., Fenves, G.L., 1998, Plastic-damage model for cyclic loading of concrete structures, Journal of Engineering Mechanics-ASCE, 124 (8), pp. 892-900.

Mandelbrot, B. B., 1967, How long is the coast of Britain? Statistical self-similarity and fractional dimension, Science, 156(3775), pp. 636–638.

Zuo, Y.-T., Liu, H.-J., 2021, Fractal approach to mechanical and electrical properties of graphene/sic composites, Facta Universitatis-Series Mechanical Engineering, 19(2), pp. 271-284.

Mandelbrot, B.B., Passojat, D.E., Paullay, A.J., 1984, Fractal character of fracture surfaces of metals, Nature, 308 (5961) , pp. 721-722.

Feng, Y.J., Yu, B.M., Zou, M.Q., Zhang, D.M., 2004, A generalized model for the effective thermal conductivity of porous media based on self-similarity, Journal of Physics D, 37(21), pp. 3030-3040.

Kong, H.Y., 2015, Research on Principle of Bubble Electrospinning and Morphologies Controlling and Applications of Bubble Electrospun Nanofibers, PhD Thesis, Soochow University; DOI: 10.7666/d.D658152

Gao, J., Pan, N., Yu, W.D., 2007, Golden mean and fractal dimension of goose down, International Journal of Nonlinear Sciences and Numerical Simulation, 8 (1), pp. 113-116.

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

Rieu, M., Sposito, G., 1991, Fractal Fragmentation, Soil Porosity, and Soil Water Properties: I. Theory, Soil Science Society of America Journal, 55(5), pp. 1231-1238.

Yu, B.M., 2007, Comments on “Fractal Fragmentation, Soil Porosity, and Soil Water Properties: I. Theory”, Soil Science Society of America Journal, 71 (2), pp. 632-632.

He, J.H., 2021, Seeing with a single scale is always unbelieving: From magic to two-scale fractal, Thermal Science, 25 (2), pp. 1217-1219.

Nadeem, M., He, J.-H.,2022, The homotopy perturbation method for fractional differential equations: part 2, two-scale transform, International Journal of Numerical Methods for Heat & Fluid Flow, 32(2), pp. 559-567.

Ain, Q. T., Sathiyaraj, T., Karim, S., et al., 2022, ABC Fractional Derivative for the Alcohol Drinking Model using Two-Scale Fractal Dimension, Complexity, 2022, 8531858.

Elias-Zuniga, A ., 2022, On the two-scale dimension and its application for deriving a new analytical solution for the fractal Duffing’s equation, Fractals, 30(3), 2250061.

Elias-Zuniga, A., Palacios-Pineda, L.M., Olvera-Trejo, D., Martinez-Romero, O., 2022, Recent strategy to study fractal-order viscoelastic polymer materials using an ancient Chinese algorithm and He's formulation, Journal of Low Frequency Noise Vibration and Active Control, 41(3), pp. 842-851 .

He, J.H., El-Dib, Y.O.,2021, A tutorial introduction to the two-scale fractal calculus and its application to the fractal Zhiber-Shabat Oscillator, Fractals, 29(08), 2150268.

Yang, J.R., Afzal, F., Appiah, P., 2022, Fractional Derivative for Varicella-Zoster Virus Using Two-Scale Fractal Dimension Approach with Vaccination, Advances in Mathematical Physics, 2022, 1725110

Yao, S.W., 2021, A rigid pendulum in a microgravity: some special properties and a two-scale fractal model, Fractals, 29(6), 2150127 .

Balshin, M.Y., 1949, Relation of mechanical properties of powder metals and their porosity and the ultimate properties of porous metal-ceramic materials, Dokl. Acad. Nauk SSSR, 67, pp. 831- 834.

Tang, L. P., 1986, A study of the quantitative relationship between strength and pore-size distribution of porous materials, Cement and Concrete Research, 16, pp. 87-96.

Kumar, R., Bhattacharjee, B., 2003, Porosity, pore size distribution and in situ strength of concrete, Cement and Concrete Research, 33, pp. 155–164.

Estrada-Diaz, J.A., Olvera-Trejo, D., Elias-Zuniga, A., Martinez-Romero, O., 2021, A mathematical dimensionless model for electrohydrodynamics, Results in Physics, 25, 104256.

He, C.H., Liu, S.H., Liu, C., Mohammad-Sedighi, H., 2022, A novel bond stress-slip model for 3-D printed concretes, Discrete and Continuous dynamical Systems, 15(7) , pp. 1669-1683.

He, J.H., Wan, Y.Q., Xu, L., 2007, Nano-effects, quantum-like properties in electrospun nanofibers, Chaos Solitons & Fractals, 33(1), pp. 26-37.

Tian, D., Li, X.X., He, J.H., 2019, Geometrical potential and nanofiber’s highly selective adsorption property, Adsorption Science & Technology, 37 (5-6), pp. 367-388.

Wu, P.X., Ling, W.W., Li, X.M., He, X.C., Xie, L.J., 2022, Dynamics research of Fangzhu's nanoscale surface, Journal of Low Frequency Noise Vibration and Active Control, 41 (2), pp. 479-487.

Elías-Zúñiga, A., Palacios-Pineda, L.M., Jiménez-Cedeño, I.H., Martínez-Romero, O., Trejo, D.O.,2020, He’s frequency–amplitude formulation for nonlinear oscillators using Jacobi elliptic functions, Journal of Low Frequency Noise, Vibration and Active Control. 39(4), pp. 1216-1223.

Fan, J., Zhang, Y.R., Liu, Y., et al., 2019, Explanation of the cell orientation in a nanofiber membrane by the geometric potential theory, Results in Physics, 15, 102537 .

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

West, G.B., Brown, J.H., Enquist, B.J., 1999, The fourth dimension of life: Fractal geometry and allometric scaling of organisms, Science, 284 (5420), pp. 1677-1679.

Atangana, A., 2017, Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system, Chaos, Solitons & Fractals, 102, pp. 396-406.

Li, Z.Y., Wang, M.C., Wang, Y.L., 2022, Solving a class of variable order nonlinear fractional integral differential equations by using reproducing kernel function, AIMS Mathematics, 7(7), pp. 12935-12951.

DOI: https://doi.org/10.22190/FUME221215005H

### Refbacks

- There are currently no refbacks.

ISSN: 0354-2025 (Print)

ISSN: 2335-0164 (Online)

COBISS.SR-ID 98732551

ZDB-ID: 2766459-4