|
[1]
|
B. B. “Mandelbrot, Fractals: Form, Chance, and Dimen-sion,” W. H. Freeman and Company, San Francisco, 1977.
|
|
[2]
|
B. B. Mandelbrot, “The Fractal Geometry of Nature,” W. H. Freeman and Company, San Francisco, 1983.
|
|
[3]
|
H. P. Xie and F. Gao, “The Mechanics of Cracks and a Statistical Strength Theory for Rocks,” International Journal of Rock Mechanics and Mining Sciences, Vol. 37, 2000, pp. 477-488.
|
|
[4]
|
A. Yavari, “Generalization of Barenblatt’s Cohesive Fracture Theory for Fractal Cracks,” Fractals, Vol. 10, No. 2, 2002, pp. 189-198.
|
|
[5]
|
A. Carpinteri, B. Chiaia and P. Cornetti, “On the Me-chanics of Quasi-Brittle Materials with a Fractal Micro-structure,” Engineering Fracture Mechanics, Vol. 70, 2003, pp. 2321-2349.
|
|
[6]
|
V. E. Saouma, J. J. Broz, E. Bruhwiler, et al., “Effect of Aggragate and Speciman Size on Fracture Properties of Dam Concrete,” Journal of Materials in Civil Engineer-ing, Vol. 3, No. 3, 1991, pp. 204-218.
|
|
[7]
|
M. A. Issa, A. M. Hammad and A. Chudnovsky, “Corre-lation between Crack Tortuosity and Fracture Toughness in Cementitious Materials,” International Journal of Fra- cture, Vol. 60, 1993, pp. 97-105.
|
|
[8]
|
Y. H. Zhao, “Crack Pattern Evolution and a Fractal Damage Constitutive Model for Rock,” International Journal of Rock Mechanics and Mining Sciences, Vol. 35, No. 3, 1996, pp. 349-366.
|
|
[9]
|
L. Guarracino, “A Fractal Constitutive Model for Un-saturated Flow in Fractured Hard Rocks,” Journal of Hy-drology, Vol. 324, 2006, pp. 154-162.
|
|
[10]
|
T. Yokobori, “Scientific Foundations for Strength and Fracture of Materials,” Naukova Dumka, Kiev, 1978.
|
|
[11]
|
M. P. Wnuk and A. Yavari, “On Estimating Stress Inten-sity Factors and Modulus of Cohesion for Fractal Cracks,” Engineering Fracture Mechanics, Vol. 70, 2003, pp. 1659-1674.
|
|
[12]
|
A. Carpinteri, B. Chiaia and K. M. Nemati, “Complex Fracture Energy Dissipation in Concrete under Different Loading Conditions,” Mechanics of Materials, Vol. 26, 1997, pp. 93-108.
|
|
[13]
|
Z. M. Ye, Fracture Mechanics of Anisotropic and Con-crete Materials, China Railway Publishing House, Bei-jing, in Chinese, 2000.
|
|
[14]
|
T. H. Antoun, Constitutive/Failure Model for the Static and Dynamic Behaviors of Concrete Incorporating Ef-fects of Damage and Anisotropy, Ph. D. Thesis, The University of Dayton, Dayton, Ohio, 1991.
|
|
[15]
|
H. P. Xie and Y. Ju, “A Study of Damage Mechanics Theory in Fractional Dimensional Space,” Acta Mecha-nica Sinica, in Chinese, Vol. 31, No. 3, 1999, pp. 300-310.
|
|
[16]
|
U. Cicekli, G. Z. Voyiadjis and R. K. A. Al-Rub, “A Plasticity and Anisotropic Damage Model for Plain Con-crete,” International Journal of Plasticity, Vol. 23, 2007, pp. 1874-1900.
|
|
[17]
|
M. Ortiz, “A Constitutive Theory for Inelastic Behavior of Concrete,” Mechanics of Materials, Vol. 4, 1985, pp. 67-93.
|
|
[18]
|
R. Faria, J. Oliver and M. Cervera, “A Strain-Based Plas-tic Viscous-Damage Model for Massive Concrete Struc-tures,” International Journal of Solids and Structures, Vol. 35, No. 14, 1998, pp. 1533-1558.
|
|
[19]
|
R. Faria, J. Oliver and M. Cervera, “On Isotropic Scalar Damage Models for the Numerical Analysis of Concrete Structures,” In: CIMNE Monograph, Barcelona, Spain, Vol. 198, 2000, pp. 422-426.
|
|
[20]
|
J. Lee and G. L. Fenves, “Plastic-Damage Model for Cyclic Loading of Concrete Structures,” Journal of En-gineering Mechanics, ASCE, Vol. 124, 1998, pp. 892- 900.
|
|
[21]
|
J. Y. Wu, J. Li and R. Faria, “An Energy Release Rate-Based Plastic-Damage Model for Concrete,” Inter-national Journal of Solids and Structures, Vol. 43, 2006, pp. 583-612.
|
|
[22]
|
J. C. Simo and T. J. R. Hughes, “Computational Inelas-ticity,” Springer-Verlag, New York, 1998.
|
|
[23]
|
A. I. Karsan and J. O. Jirsa, “Behavior of Concrete under Compressive Loadings,” Journal of the Structural Divi-sion, ASCE, Vol. 95, 1969, pp. 2535-2563.
|
|
[24]
|
H. Kupfer, H. K. Hilsdorf and H. Rusch, “Behavior of Concrete under Biaxial Stresses,” ACI Materials Journal, Vol. 66, 1969, pp. 656-666.
|
|
[25]
|
P. E. Petersson, “Crack Growth and Development of Fracture Zones in Plain Concrete and Similar Materials,” In: Report TVBM 1006, Division of Building Materials, University of Lund, Sweden, 1981.
|
|
[26]
|
R. Meyer, H. Ahrens and H. Duddeck, “Material Model for Concrete in Cracked and Uncracked States,” Journal of the Engineering Mechanics Division, ASCE, Vol. 120, No. 9, 1994, pp. 1877-1895.
|