Research on one-dimensional ubiquitiformal constitutive relations for a bimaterial bar

• Autorzy: Yang Min , Ou Zhuo-Cheng , Duan Zhuo-Ping , Huang Feng-Lei

Identyfikatory

DOI

10.15632/jtam-pl/104510

• Języki publikacji: EN

Abstrakty

EN

A one-dimensional ubiquitiformal constitutive model for a bimaterial bar is proposed in this paper. An explicit analytical expression for the effective Young modulus is then obtained, which, unlike the fractal one, leads to a continuous displacement distribution along the bar. Moreover, numerical results for concretes are calculated and found to be in agreement with previous experimental data. In addition, some previous empirical and semi-empirical constitutive models are also examined, which shows that each of these models can correspond well to a ubiquitiformal one under a certain complexity.

Słowa kluczowe

EN

ubiquitiform; fractal; composite; displacement distribution; elasticity modulus

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2019
• Tom: Vol. 57 nr 2
• Strony: 291--301
• Opis fizyczny: Bibliogr. 22 poz., rys., tab.

Twórcy

autor

Yang Min

• State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing, China

autor

Ou Zhuo-Cheng

• State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing, China

autor

Duan Zhuo-Ping

• State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing, China

autor

Huang Feng-Lei

• State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing, China

Bibliografia

• 1. Bazant Z.P., Yavari A., 2005, Is the cause of size effect on structural strength fractal or energetic- -statistical? Engineering Fracture Mechanics, 72, 1-31
• 2. Carpinteri A., Chiaia B., Cornetti P., 2003, On the mechanics of quasi-brittle materials with a fractal microstructure, Engineering Fracture Mechanics, 70, 2321-2349
• 3. Carpinteri A., Cornetti P., 2002, A fractional calculus approach to the description of stress and strain localization in fractal media, Chaos, Solitons and Fractals, 13, 85-94
• 4. Counto U.J., 1964, The effect of the elastic modulus of the aggregate on the elastic modulus, creep and creep recovery of concrete, Magazine of Concrete Research, 16, 129-138
• 5. Davey K., Alonso Rasgado M.T., 2011, Analytical solutions for vibrating fractal composite rods and beams, Applied Mathematical Modelling, 35, 1194-1209
• 6. Hashin Z., 1962, The elastic moduli of heterogeneous materials, Journal of Applied Mechanics, 29, 1, 143-150
• 7. Hafner S., Eckardt S., Luther T., 2006, Mesoscale modeling of concrete: Geometry and numerics, Computers and Structures, 84, 450-461
• 8. Hirsch T.J., 1962, Modulus of elasticity of concrete affected by elastic moduli of cement paste matrix and aggregate, Journal of the American Concrete Institute, 59, 427-452
• 9. Li C.Q., Zheng J.J., Zhou X.Z., McCarthy M.J., 2003, A numerical method for the prediction of elastic modulus of concrete, Magazine of Concrete Research, 55, 6, 497-506
• 10. Li G.Y., Ou Z.C., Xie R., Duan Z.P., Huang F.L., 2016, A ubiquitiformal one-dimensional steady-state conduction model for a cellular material rod, International Journal of Thermophysics, 37, 47, 1-13
• 11. Li J.Y., Ou Z.C., Tong Y., Duan Z.P., Huang F.L., 2017, A statistical model for ubiquitiformal crack extension in quasi-brittle materials, Acta Mechanica, 228, 2725-2732
• 12. Mandelbrot B.B., 1967, How long is the coast of Britain? Statistical self-similarity and fractional dimension, Science, 156, 636-638
• 13. Mandelbrot B.B., 1977, Fractals: Form, Chance, and Dimension, Freeman, San Francisco
• 14. Mandelbrot B.B., 1982, The Fractal Geometry of Nature, Freeman, New York
• 15. Mandelbrot B.B., Passoja D.E., Paullay A.J., 1984, Fractal character of fracture surfaces of metals, Nature, 308, 721-722
• 16. Ou Z.C., Li G.Y., Duan Z.P., Huang F.L., 2014, Ubiquitiform in applied mechanics, Journal of Theoretical and Applied Mechanics, 52, 1, 37-46
• 17. Ou Z.C., Li G.Y., Duan Z.P., Huang F.L., 2019, A stereological ubiquitiformal softening model for concrete, Journal of Theoretical and Applied Mechanics, 57, 1, 27-35
• 18. Ou Z.C., Yang M., Li G.Y., Duan Z.P., Huang F.L., 2017, Ubiquitiformal fracture energy, Journal of Theoretical and Applied Mechanics, 55, 3, 1101-1108
• 19. Road Research Laboratory, 1950, Design of Concrete Mixes, 2nd ed. London, H.M. Stationery Office, pp. 16, Road Note No. 4
• 20. Stock A.F., Hannantt D.J., Williams R.I.T., 1979, The effect of aggregate concentration upon the strength and modulus of elasticity of concrete, Magazine of Concrete Research, 31, 109, 225-234
• 21. Vilardell J., Aguado A., Agullo L., Gettu R., 1998, Estimation of the modulus of elasticity for dam concrete, Cement and Concrete Research, 28, 1, 93-101
• 22. Zheng J.J., Li C.Q., Zhou X.Z., 2006, An analytical method for prediction of the elastic modulus of concrete, Magazine of Concrete Research, 58, 10, 6

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).