Prediction of Equivalent Elastic Modulus for Concrete Based on Homogenization Theory

Abstract

Abstract: From mesoscale aspect, concrete was considered as a three-phase composite material consisting of aggregate, cement mortar and the interfacial transition zone between aggregate and cement mortar. Based on Python language, a unite-cell model with periodicity was established by using Monte Carlo method. The prediction method of equivalent elastic modulus of concrete was proposed by combining homogenization theory and periodic boundary conditions. The predicted values of the model were compared with the results in existing literature to verify the validity of the present model. On this basis, the influences of unite-cell size, interfacial transition zone thickness, aggregate volume rate and maximum aggregate size on the equivalent elastic modulus of concrete were investigated. The results show that the unite-cell model can effectively predict the elastic properties of concrete composite materials. The error locates in the range of 1.87% to 4.97%, compared with the existing results. The size of concrete unite-cell model is recommended to be 150 mm. In the range of 20% to 40%, the aggregate volume rate has significant effect on the equivalent elastic modulus of concrete. Moreover, the interfacial transition zone thickness and maximum size of aggregate exhibit slight effect on the equivalent elastic modulus of concrete, showing a monotonically decreasing or monotonically increasing effect pattern.

Key words: concrete, unite-cell model, homogenization theory, periodic boundary condition, equivalent elastic modulus, aggregate volume rate

CLC Number:

TU528

CHEN Sihan, LYU Fangtao, HUANG Wei, WANG Lingling, KONG Dewen. Prediction of Equivalent Elastic Modulus for Concrete Based on Homogenization Theory[J]. BULLETIN OF THE CHINESE CERAMIC SOCIETY, 2022, 41(5): 1609-1616.

References

[1] 张楚汉.论岩石、混凝土离散-接触-断裂分析[J].岩石力学与工程学报,2008,27(2):217-235.
ZHANG C H. Discrete-contact-fracture analysis of rock and concrete[J]. Chinese Journal of Rock Mechanics and Engineering, 2008, 27(2): 217-235 (in Chinese).
[2] ROELFSTRA P E, SADOUKI H, WITTMANN F H. Le béton numérique[J]. Materials and Structures, 1985, 18(5): 327-335.
[3] 刘光廷,王宗敏.用随机骨料模型数值模拟混凝土材料的断裂[J].清华大学学报(自然科学版),1996,36(1):84-89.
LIU G T, WANG Z M. 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).
[4] CHRISTENSEN R M, LO K H. Solutions for effective shear properties in three phase sphere and cylinder models[J]. Journal of the Mechanics and Physics of Solids, 1979, 27(4): 315-330.
[5] NILSEN A U, MONTEIRO P J M. Concrete: a three phase material[J]. Cement and Concrete Research, 1993, 23(1): 147-151.
[6] NEUBAUER C M, JENNINGS H M, GARBOCZI E J. A three-phase model of the elastic and shrinkage properties of mortar[J]. Advanced Cement Based Materials, 1996, 4(1): 6-20.
[7] 姜雪光.基于渐进均匀化理论的复合材料性能预测与分析[D].哈尔滨:东北林业大学,2018:24-26.
JIANG X G. The property prediction and analyzation of composites based on asymptotic homogenization theory[D]. Harbin: Northeast Forestry University, 2018: 24-26 (in Chinese).
[8] BENSOUSSAN A, LIONS J L, PAPANICOLAOU G. Asymtopic structures[M]. Amsterdam: North Holland, 1978.
[9] 唐欣薇,张楚汉.基于均匀化理论的混凝土宏细观力学特性研究[J].计算力学学报,2009,26(6):876-881.
TANG X W, ZHANG C H. Study on concrete in macro-and meso-scale mechanical properties based on homogenization theory[J]. Chinese Journal of Computational Mechanics, 2009, 26(6): 876-881 (in Chinese).
[10] 邓方茜,徐礼华,池寅,等.基于均匀化理论的混杂纤维混凝土有效弹性模量计算[J].硅酸盐学报,2019,47(2):161-170.
DENG F Q, XU L H, CHI Y, et al. Calculation of effective elastic modulus for hybrid fiber reinforced concrete based on homogenization theory[J]. Journal of the Chinese Ceramic Society, 2019, 47(2): 161-170 (in Chinese).
[11] OUYANG X, SHI C J, WU Z M, et al. Experimental investigation and prediction of elastic modulus of ultra-high performance concrete (UHPC) based on its composition[J]. Cement and Concrete Research, 2020, 138: 106241.
[12] WALRAVEN J C, REINHARDT H W. Theory and experiments on the mechanical behaviour of cracks in plain and reinforced concrete subjected to shear loading[J]. Heron, 1991, 26(1A): 26-35.
[13] TANG X W, ZHANG C H, SHI J J. A multiphase mesostructure mechanics approach to the study of the fracture-damage behavior of concrete[J]. Science in China Series E: Technological Sciences, 2008, 51(2): 8-24.
[14] SUN X J, GAO Z, CAO P, et al. Mechanical properties tests and multiscale numerical simulations for basalt fiber reinforced concrete[J]. Construction and Building Materials, 2019, 202: 58-72.
[15] XU W X, MA H F, JI S Y, et al. Analytical effective elastic properties of particulate composites with soft interfaces around anisotropic particles[J]. Composites Science and Technology, 2016, 129: 10-18.
[16] ZOUAOUI R, MILED K, LIMAM O, et al. Analytical prediction of aggregates’ effects on the ITZ volume fraction and Young’s modulus of concrete[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2017, 41(7): 976-993.
[17] ZHANG N L, GUO X M, ZHU B B, et al. A mesoscale model based on Monte-Carlo method for concrete fracture behavior study[J]. Science China Technological Sciences, 2012, 55(12): 3278-3284.
[18] ZHENG J J, LI C Q, ZHOU X Z. An analytical method for prediction of the elastic modulus of concrete[J]. Magazine of Concrete Research, 2006, 58(10): 665-673.