Elasticity based approach to the buckling of reinforced solids

I consider the problem of surface buckling of reinforced solids by application of a simple model for composite materials. The model is based on an analytical solution to the problem of surface instabilities of orthotropic solids subjected to uniaxial compression (deBotton and Schulgasser [1]). A two phase model, in which a single layer of the reinforcement is bonded on top of a homogeneous orthotropic substrate whose properties are identical to the composite properties, is investigated. It is found that in the dilute limit, when the layers are far apart, the dominant failure mode is the microbuckling mode. In this limit the predictions for the buckling load are substantially lower than the corresponding predictions for the buckling load of the homogenized medium. As the volume fraction of the fibers increases, the predictions for the buckling loads converge to the corresponding predictions for the homogenized medium, implying that the edominant failure is the macrobuckling mode.