On the effect of shear stiffness on the plane deformation of linear second gradient pantographic sheets. Issue 11 (29th April 2016)

• Record Type: Journal Article
• Authors: Scerrato, Daria; Zhurba Eremeeva, Inna A.; Lekszycki, Tomasz; Rizzi, Nicola L.
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 96:Issue 11(2016)
• Page Start: 1268
• Page End: 1279
• Publication Date: 2016-04-29
• Subjects: Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.201600066
• Languages: English
• ISSNs: 0044-2267

Abstract

Abstract : The bidimensional continua are the generalization of the continua introduced from Pipkin et al. as the authors take simultaneously into account the elastic energy in the extensional deformation and geodesic bending of constituting fibers. In the present paper the authors consider in the deformation energy a term accounting for the effect of shear deformation. The phenomena which they highlight can be of relevance to model the mechanical behavior of composite fiber reinforcements and of some lattices of beams constrained by internal pivots… Abstract : Recently it has been proposed the study of a new class of bidimensional metamaterials, 33 34 which have been called extensible pantographic sheets. Such bidimensional continua are the generalization of the continua introduced in68 69 80 as they take simultaneously into account the elastic energy in the extensional deformation and geodesic bending of constituting fibers. In the present paper we consider in the deformation energy a term accounting for the effect of shear deformation. The phenomena which we highlight can be of relevance to model the mechanical behavior of composite fiber reinforcements and of some lattices of beams constrained by internal pivots. We compare the effect of different linear or cubic shear stiffnesses i) on the deformation of pairs of pantographic sheets suitably interconnected and ii) on the deformation of pantographic sheets deformed under the action of forces concentrated on points.