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PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping
Construction of a Statistically Equivalent Periodic Unit Cell for an Asphalt Mixture
R. Valenta, J. Šejnoha and M. Šejnoha
Centre for Integrated Design of Advanced Structures, Czech Technical University in Prague, Czech Republic
R. Valenta, J. ÂŠejnoha, M. ÂŠejnoha, "Construction of a Statistically Equivalent Periodic Unit Cell for an Asphalt Mixture", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 112, 2007. doi:10.4203/ccp.86.112
Keywords: micromechanical approach, asphalt mixture, statistically equivalent periodic unit cell, homogenization.
The paper offers a novel approach to the modelling of asphalt mixtures. Clearly, a computational analysis taking into account all geometrical details of a two-phase microstructure (stone aggregates bonded to a bitumen matrix) would be prohibitively expensive. The search for an efficient computational scheme is therefore required.
The present contribution introduces the concept of a so called statistically equivalent periodic unit cell (SECUP) known from the analysis of random composites. Such a unit cell allows us to take into account a microstructure of the asphalt mixture while keeping the computational cost of the underlying nonlinear analysis relatively low. Two scale uncoupled homogenization procedure is developed for the derivation of effective mechanical properties of asphalt mixtures. The computational efficiency is further enhanced by employing the Fast Fourier Transform method  for the solution of the governing equations of elasticity.
To arrive at the desired effective properties requires completing the following steps:
Although constructed by matching material statistics up to two-point probability function the unit cell is capable of providing almost identical results as derived for the original microstructure but at a fraction of computational time. This result supports the use of the statistically equivalent periodic unit cell in considerably more intensive nonlinear analysis. This is the subject of the present research.
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