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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 86
Edited by: B.H.V. Topping
Paper 112

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

Full Bibliographic Reference for this paper
R. Valenta, J. Šejnoha, M. Šejnoha, "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 [1] for the solution of the governing equations of elasticity.

To arrive at the desired effective properties requires completing the following steps:

  • Preparing a binary image of a real microstructure. This step leads to a set of representatives of the real microstructure with variable volume fraction of stone aggregates generated by gradually removing stones up to a given size from the original microstructure. While removing small stones simplifies the microstructure complexity on the one hand, it reduces the overall stiffness on the other hand. Substituting the actual matrix with a homogenized equivalent medium based on the volume of removed stones appears therefore inevitable leading to a two-scale uncoupled homogenization.
  • Formulation of a statistically equivalent periodic unit cell by comparing the material statistics [2], e.g. the two point probability function, of the most appropriate representative of the real microstructure and the periodic unit cell as suggested in [2,3].
  • Evaluation of the effective properties for the periodic unit cell to check the credibility of the proposed approach.

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.

J.C. Michel, H. Moulinec, P. Suquet, "Effective properties of composite materials with periodic microstructure: A computational approach", Computer Methods in Applied Mechanics and Engineering, 172, 109-143, 1999. doi:10.1016/S0045-7825(98)00227-8
J. Zeman, M. Šejnoha, "Numerical evaluation of effective properties of graphite fiber tow impregnated by polymer matrix", Journal of the Mechanics and Physics of Solids, 49 (1), 69-90, 2001. doi:10.1016/S0022-5096(00)00027-2
J. Zeman, M. Šejnoha, "From random microstructures to representative volume elements", Modelling and Simulation in Materials Science and Engineering, 15 (4), 325-335, 2007. doi:10.1088/0965-0393/15/4/S01

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