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 pot ential 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 th e ''states'' and the average inhomogeneity r of the local stimulus. Th is statistical theory and this variational model are summarized here. A principle of minimal inhomogeneity is found to underly the success o f the model. The ''state'' contains the information considered relevan t on the local behavior and micro-geometry. The approach is illustrate d by its application to the failure criterion of a fibre-reinforced mo rtar. Two successive definitions of the state lead to (i) a volume-fra ction model of the composite and (ii) a model accounting for the inter action between neighboring constituents. Model (ii) makes use of the h omogenization theory for periodic media and restrains strongly the dis tance between the upper and lower bounds. For the studied composite, m odel (i) is yet found to give as good agreement as model (ii), due to the oversimplified micro-structural information entered in model (ii).