VARIATIONAL MICRO-MACRO TRANSITION, WITH APPLICATION TO REINFORCED MORTARS

A variational approach is developed for the micro-macro transition in non-linear and randomly inhomogeneous materials, assuming a convex potential and a no-correlation condition. To establish the latter in the context of operational micro-macro models, an asymptotic definition of statistically homogeneous (S.H.) materials and S.H. micro-fields was given; also, a variational model was proposed for S.H. materials with convex local potential, taking into account the volume fractions of the ''states'' and the average inhomogeneity r of the local stimulus. This statistical theory and this variational model are summarized here. A principle of minimal inhomogeneity is found to underly the success of the model. The ''state'' contains the information considered relevant on the local behavior and micro-geometry. The approach is illustrated by its application to the failure criterion of a fibre-reinforced mortar. Two successive definitions of the state lead to (i) a volume-fraction model of the composite and (ii) a model accounting for the interaction between neighboring constituents. Model (ii) makes use of the homogenization theory for periodic media and restrains strongly the distance between the upper and lower bounds. For the studied composite, model (i) is yet found to give as good agreement as model (ii), due to the oversimplified micro-structural information entered in model (ii).