Keywords: elastic modulus, interfacial transition zone, numerical concrete model, finite element method, random unit cell, composite materials.

Concrete should be considered as a three-phase composite instead of a two-phase one. The phase in which the presence of the aggregates affects the properties of cement paste is taken as the interfacial transition zone (ITZ). The mechanical properties of concrete are controlled by the presence of the ITZ [1]. Therefore, a three-phase concrete is a composite material with aggregates as a dispersed phase, ITZ as an interphase, and cement paste as a continuous phase or matrix. Numerical concrete models have been introduced using the conventional finite element method. The difficulty to model concrete in three dimensions arises from the mesh generation [2]. The conventional finite element method allows only one material property to be assigned to each element. This makes mesh generation difficult because finite elements of the ITZ are much smaller compared with the rest of the finite elements corresponding to aggregates and mortar matrix. A complicated interface between materials may cause the shape of elements to lose its convexity and lead to ill-conditioned stiffness matrix. In this work, in order to avoid meshing difficulties, we propose to use a random unit cell finite element method [3]. The random unit cells generated allows us to investigate the effects of the ITZ in the unit cell model. A study is conducted with a random unit cell method [4] in order to evaluate the effect of the ITZ phase and the bounds of the method for the prediction of elastic modulus in concrete composites. Results will be compared with other approaches. In spite of the fact that the proposed approach does not consider the ITZ as a thin layer of matrix material surrounding each aggregate, the estimations of elastic modulus of concrete are in good agreement with results given in the literature. The bounds of the model enable the method to be used for elastic modulus estimation of a large number of possible cement-based composites. For the determination of concrete elastic modulus, the method provides a powerful tool for fast calculation of a three-dimensional numerical concrete model, avoids meshing problems and allows the description of concrete with a very thin thickness of the ITZ.

1

G. Ramesh, E.D. Sotelino, W.F. Chen, "Effect of transition zone on elastic moduli of concrete materials", Cem Concr Res, 26, 611-622, 1996. doi:10.1016/0008-8846(96)00016-6

2

K.M. Lee, J.H. Park, "A numerical model for elastic modulus of concrete considering interfacial transition zone", Cem Concr Res, 38, 396-402, 2008. doi:10.1016/j.cemconres.2007.09.019

3

S. Kari, H. Berger, R. Rodriguez-Ramos, U. Gabbert, "Computational evaluation of effective material properties of composites reinforced by randomly distributed spherical particles", Compos Struct, 77, 223-231, 2007. doi:10.1016/j.compstruct.2005.07.003

4

S. Abdelmoumen, E. Bellenger and M. Quéneudec-t'Kint, "Finite Element analysis of elastic properties of rubberized concrete composites by a random unit cell method", in Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing, B.H.V. Topping, (Editor), Civil-Comp Press, Stirling, United Kingdom, paper 122, 2007. doi:10.4203/ccp.86.122

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