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PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Micromechanical Multiscale Simulation of Elastic Properties of Hydrating Concrete
V. Šmilauer and Z. Bittnar
Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Czech Republic
, "Micromechanical Multiscale Simulation of Elastic Properties of Hydrating Concrete", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 70, 2006. doi:10.4203/ccp.83.70
Keywords: FFT, homogenization, cement paste, concrete, elastic properties, hydration.
This paper shows how the simulation of elastic properties of hydrating concrete may be accomplished via the combination of a hydration model and various homogenization techniques. Under certain assumptions of length separation, the framework of homogenization allows independent analysis of the composite levels found in the concrete. Therefore, it is convenient to disassemble concrete into simpler components, where independent analysis on mutually different scales may be performed:
The most important level is that of cement paste, where the hydration and accompanying reactions change the disconnected, heterogeneous material to a solid one. This situation is complicated for an analysis since the material changes its porosity, connectedness and chemical phases during hydration.
The microstructure of the cement paste will be reconstructed in the periodic discrete form, using the hydration model CEMHYD3D . The resolution of the model is 1 μm and the basic chemical reactions of Portland cement are implemented. The reasonable size of representative volume element (RVE) is 50x50x50 μm for the simulation of elastic properties.
Moulinec and Suquet  introduced a new method of homogenization, based on a fast Fourier transformation (FFT). The strain field is decomposed into the behaviour of the reference medium and the polarization strain within a heterogeneous composite. The system of equations leads to the convolution that might be treated efficiently via FFT. The time of one iteration grows as , where is the number of elements. Another advantage of this method is no improvement of results under sampling refinement, as opposed to finite element mesh refinement.
To validate the multiscale approach, cement paste is homogenized via a FFT at discrete time points. When air is considered as entrained, i.e. remains on the level of cement paste, the Mori-Tanaka scheme  homogenizes the cement paste with the air, followed by a Hervé-Zaoui scheme  on the mortar level. This level contains fine aggregates, associated ITZ and cement paste with entrained air. The concrete level is homogenized via the same scheme and contains coarse aggregates, associated ITZ, and homogenized mortar level. The elastic properties of ITZ on fine or coarse aggregates were derived from the cement paste by a reduction of E-modulus by 50 %. Poisson's ratio remained unchanged.
Validation on the concrete with the water-to-cement ratios of 0.27 and 0.5 shows good agreement with experimental results on a macroscale. Moreover, elastic properties at early ages of concrete may be treated as well. The multiscale approach brings a new insight into behaviour of characteristic levels found in ordinary concrete, with a minimum of unknown variables needed for homogenization.
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