Grufman C, Ellyin F. Determining a representative volume element capturing the morphology of fibre reinforced polymer composites [J]. Composites Science and Technology, 2007, 67(3/4): 766―775.
[2]
Man H, van Mier J G M. Influence of particle density on 3D size effects in the fracture of (numerical) concrete [J]. Mechanics of Materials, 2008, 40(6): 470―486.
[3]
Lilliu G, Van J G M. 3D lattice type fracture model for concrete [J]. Engineering Fracture Mechanics, 2003, 70: 927―941.
[4]
Pez C M L, Carol I, Aguado A. Meso-structural study of concrete fracture using interface elements. I: Numerical model and tensile behavior [J]. Materials and Structures, 2008, 41(3): 583―599.
Dang Faning, Han Wentao, Tian Wei. Three-dimensional numerical simulation on meso-level of uniaxial failure process in concrete [J]. Journal of Xi’an University of Technology, 2006, 22(2): 113―118. (in Chinese)
[7]
Lawler J S, Keane D T, Shah S P. Measuring three-dimensional damage in concrete under compression [J]. ACI Materials Journal, 2001, 98(6): 465―475.
[8]
Guo L, Carpinteri A, Sun W, et al. Measurement and analysis of defects in high-performance concrete with three-dimensional micro-computer tomography [J]. Journal of Southeast University (English Edition), 2009, 25(1): 83―88.
[9]
Xu X F, Chen X. Stochastic homogenization of random elastic multi-phase composites and size quantification of representative volume element [J]. Mechanics of Materials, 2009, 41(2): 174―186.
[10]
Gitman M I, Askes H, Sluys L J. Representative volume: Existence and size determination [J]. Engineering Fracture Mechanics, 2007, 74(16): 2518―2534.
Liu Guangting, Wang Zongmin. Numerical simulation study of fracture of concrete materials using random aggregate model [J]. Journal of Tsinghua University (Science and Technology), 1996, 36(1): 84―89. (in Chinese)
Du Chengbin, Sun Liguo. Numerical simulation of concrete aggregates with arbitrary shapes and its application [J]. Journal of Hydraulic Engineering, 2006, 37(6): 662―667. (in Chinese)
Graham S, Yang N. Representative volumes of materials based on microstructural statistics [J]. Scripta Materialia, 2003, 48: 269―274.
[17]
Al-Raoush R, Papadopoulos A. Representative elementary volume analysis of porous media using X-ray computed tomography [J]. Powder Technology, 2010, 200(1/2): 69―77.
[18]
Grassl P, Wong H S, Buenfeld N R. Influence of aggregate size and volume fraction on shrinkage induced micro-cracking of concrete and mortar [J]. Cement and Concrete Research, 2010, 40(1): 85―93.
[19]
Ma Huaifa, Chen Houqun, Wu Jianping, et al. Study on numerical algorithm of 3D meso-mechanics model of dam concrete [J]. Chinese Journal of Computational Mechanics, 2008, 25(2): 241―247. (in Chinese)
[20]
Zhu W C, Tang C A, Wang S Y. Numerical study on the influence of mesomechanical properties on macroscopic fracture of concrete [J]. Structural Engineering and Mechanics, 2005, 19(5): 519―533.