This paper has two main objectives: first, to present a new statistical theory and a variational model for micro-macro transition in nonlinear and randomly inhomogeneous materials. assuming a convex potential and no- correlation condition. Here two important results are presented: the first one is the theoretical recognition of the principle of minimal inhomogeneity underlying the developed variational model. The second result is an effective procedure for taking into account the micro- geometry of material based on the homogenization theory of periodic media.
The other aim of this paper is to illustrate the application of the method in the case of mortars reinforced with steel hooks. The proposed model has been used to derive the failure criterion for fiber-reinforced mortar from the failure criteria for its components (mortar and steel) and from a simplified description of the geometrical structure of the composite.