Semi-inverse method à la Saint-Venant for two-dimensional linear isotropic homogeneous second gradient elasticity

Semi-inverse method is used to nd special analytical solutions of squared two-dimensional second gradient linear homogeneous and isotropic materials. Such semi-inverse method is similar to that used by Saint-Venant to solve the omonimus problem for cylindrical three-dimensional rst gradient linear homogeneous and isotropic materials. Two examples are also presented. It is found that the wedge forces are necessary to maintain the body in equilibrium and that they are not an artifact of the double application of the divergence theorem in the second gradient material derivations.