Buckling of a sheared cholesteric liquid crystal

We present qualitative and quantitative observations on structural instabilities in a cholesteric liquid crystal subjected to static shear. Using a model of a cholesteric that is tilted under shear, we find that, in a Landau--de Gennes coarse-grained picture, buckling instabilities can be created when the strain is larger than a critical value. The analogy with buckling obtained under dilations is sketched, and a comparison is made with the critical wave vector of the undulations. A good agreement is found between the theoretical values, both of the critical wave vector and of the threshold shear values and the experimental ones. New insight can be gained on the mechanism for the formation of hydrodynamical instabilities under shear.