Summary
A general method is proposed to account for the geometrical distribution of material inhomogeneity. It consists in a two-step micro-macro transition. The randomly inhomogeneous material is envisaged as made of cells, each one with a definite distribution of material inhomogeneity, i.e. with a definite “state”. Only a finite number of different states is considered for the cells. In other words, many identical cells exist, though at random places in the material. In the first step, the behavior of each set of identical cells, i.e., the constitutive relation that relates the average stress in that set of cells to the average strain-rate in the same set, is obtained by periodic homogenization. In the second step, a variational model is used to get the macroscopic behavior of the material, i.e. to appropriately average over the different sets of cells. The method is theoretically justified. It is then applied to a fibre-reinforced mortar. It is efficient in predicting the mechanically measured reinforcement. The influences of the fibres arrangement and the friction coefficient are investigated: an arrangement is found to reinforce more effectively than does another one.
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Arminjon, M., Guessab, B. A model with two micro-scales for the effects of geometrical distribution of material inhomogeneity. Acta Mechanica 134, 61–79 (1999). https://doi.org/10.1007/BF01170304
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DOI: https://doi.org/10.1007/BF01170304