An inverse method to get further analytical solutions for a class of metamaterials aimed to validate numerical integrations

We consider an isotropic second gradient elastic two-dimensional solid. Besides, we relax the isotropic hypothesis and consider a D4 orthotropic material. The reason for this last choice is that such anisotropy is the most general for pantographic structures, which exhibit attracting mechanical properties. In this paper we analyze the role of the external body double force mextmext on the partial differential equations and we subsequently revisit some analytical solutions that have been considered in the literature for identification purposes. The revisited analytical solutions will be employed as well for identification purposes in a further contribution.