Analytical solutions of 2-dimensional second gradient linear elasticity for continua with cubic-D4 microstructure

We consider in this paper analytical solutions for some remarkable cases and for a linear anisotropic D4 second gradient elastic model. The purpose is that of constitutive parameter identification. In general, analytical solutions are considered less important than in the past due to fast numerical tools and to the fact that they are generally very difficult to achieve. However, they still play very important roles such as for numerical comparison and for dealing with pathological mechanical systems.