A stereological ubiquitiformal softening model for concrete
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State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing, China
Publish date: 2019-01-20
Submission date: 2017-08-01
Acceptance date: 2018-06-12
Journal of Theoretical and Applied Mechanics 2019;57(1):27–35
A stereological ubiquitiformal softening model for describing the softening behavior of con- crete under quasi-static uniaxial tensile loadings is presented in this paper. In the model, both the damage evaluation process of fracture cross-sections and their distribution along the specimens axis are taken into account. The numerical results of a certain kind of full grade concrete made of crushed coarse aggregate are found to be in good agreement with the experimental data. Moreover, an experiental relation between the lower bound to the scale invariance of concrete and its tensile strength is also obtained by data fitting of the experimental data, which provides an effective approach to determine the lower bound to scale invariance of concrete.
1. Barenblatt G.I., 1959, The formation of equilibrium cracks during brittle fracture: General ideas and hypotheses, axially symmetric cracks, Journal of Applied Mathematics and Mechanics, 23, 622-636.
2. Barenblatt G.I., 1962, The mathematical theory of equilibrium cracks in brittle fracture, Advances in Applied Mechanics, 7, 55-129.
3. Bažant Z.P., Oh B.H., 1983, Crack band theory for fracture of concrete, Mat´eriaux et Construction, 16, 155-177.
4. Borodich F.M., 1997, Some fractal models of fracture, Journal of the Mechanics and Physics of Solids, 45, 239-259.
5. Carpinteri A., Chiaia B., Cornetti P., 2002, A scale-invariant cohesive crack model for quasibrittle materials, Engineering Fracture Mechanics, 69, 207-217.
6. Charkaluk E., Bigerelle M., Iost A., 1998, Fractals and fracture, Engineering Fracture Mechanics, 61, 119-139.
7. Deng Z.C., Li Q.B., Fu H., 2005, Mechanical properties of tension and compression about artificial full-graded aggregate concrete dam (in Chinese), Journal of Hydraulic Engineering, 36, 214-218.
8. Gopalaratnam V.S., Shah S.P., 1985, Softening response of plain concrete in direct tension, Journal Proceedings (American Concrete Institute), 82, 310-323.
9. Hillerborg A., Modeer M., Petersson P.E., 1976, Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, Cement and Concrete Research, 6, 773-782.
10. Karihaloo B.L., 1995, Fracture Mechanics and Structural Concrete, Longman Scientific & Technical, Harlow.
11. Khezrzadeh H., Mofid M., 2006, Tensile fracture behavior of heterogeneous materials based on fractal geometry, Theoretical and Applied Fracture Mechanics, 46, 46-56.
12. Mandelbrot B.B., 1982, The Fractal Geometry of Nature, Freeman, New York.
13. Mandelbrot B.B., Passoja D.E., Paullay A.J., 1984, Fractal character of fracture surfaces of metals, Nature, 308, 721-722.
14. Ou Z.C., Li G.Y., Duan Z.P., Huang F.L., 2014, Ubiquitiform in applied mechanics, Journal of Theoretical and Applied Mechanics, 52, 37-46.
15. Petersson P.E., 1981, Crack growth and development of fracture zone in plain concrete and similar materials, Division of Building Materials, Lund Institute of Technology.
16. Reinhardt H.W., Cornelissen H.A.W., Hordijk D.A., 1986, Tensile tests and failure analysis of concrete, Journal of Structural Engineering, 112, 2462-2477.
17. Saouma V.E., Barton C.C., 1994, Fractals, fractures, and size effects in concrete, Journal of Engineering Mechanics, 120, 835-854.
18. Stroeven P., 1973, Some aspects of the micro-mechanics of concrete, Ph.D. Thesis, Delft University of Technology, Delft.
19. Stroeven P., 2000, A stereological approach to roughness of fracture surfaces and tortuosity of transport paths in concrete, Cement and Concrete Composites, 22, 331-341.