Continuum models for pantographic blocks with second gradient energies which are incomplete. (October 2022)

• Record Type: Journal Article
• Authors: Stilz, Maximilian; dell'Isola, Francesco; Giorgio, Ivan; Eremeyev, Victor A.; Ganzenmüller, Georg; Hiermaier, Stefan
• Is Part Of: Mechanics research communications. Volume 125(2022)
• Publication Date: 2022-10
• Subjects: Generalized continuum mechanics -- Second gradient materials -- Metamaterials; Mechanics, Applied -- Periodicals; Mécanique appliquée -- Périodiques; Mechanics, Applied; Periodicals; 530
• DOI: 10.1016/j.mechrescom.2022.103988
• Languages: English
• ISSNs: 0093-6413

Abstract

Abstract: We postulate a deformation energy for describing the mechanical behavior of so called pantographic blocks, that is bodies constituted by stacking of N 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.