Effective Behavior of Lightweight Concrete Tested by Yang and Huang: Application of Several Mixing Laws

Abstract

The evaluation of the effective behavior of a composite using analytical method requires a deep knowledge of different approaches existing in the extensive literature in this field. As explained Gilormini and Bréchet, the choice of a model is governed by several parameters including the geometry of the heterogeneous medium, the mechanical contrast between the phases and the volume fraction of reinforcements. The prediction of effective mechanical properties of composites using the mixing rules properly validated is of great practical interest in all circumstances where the tests are impossible, difficult or costly. The approaches are different but not many, being confined to only part of the elasticity, and by exploiting the combined rheological models: Voigt-Reuss, Reuss-Voigt, Hirsch-Dougill, Halpin-Tsai, Popovics and estimation of Mori-Tanaka; our work focuses on determining the effective Young modulus of lightweight concrete (biphasic presentation) tested by Yang and Huang. Our results clearly show that the results obtained by the rheological model of Hirsch- Dougill and Halpin-Tsai are confused with the lower bound of Reuss-Voigt, the maximum deviation is 2.54%. The Mori-Tanaka estimate of Young's modulus gives the most accurate numbers; the results obtained by this model are in very good agreement with experimental results of Yang and Huang with a maximum deviation of about 0.94% for a volume fraction of reinforcements ranging from 18% to 36%.
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