Continuum models for pantographic blocks with second gradient energies which are incomplete

We postulate a deformation energy for describing the mechanical behavior of so called pantographic blocks, that is bodies constituted by stacking of layers of pantographic sheets. We remark that the pantographic effect is limited in the plane of pantographic sheets and therefore only the second derivatives of transverse displacements along the pantographic fibers appear in the chosen deformation energy. We use this novel energy to predict the behavior of pantographic blocks when subjected to : (i) compression and traction test, (ii) torsion, (iii) shear and (iv) bending. A linearization of the energy shows one floppy mode in addition to the rigid body motions, assuming perfect pivots, similar to pantographic sheets