The Mechanical Diode: On the Tracks of James Maxwell Employing Mechanical–Electrical Analogies in the Design of Metamaterials

Following the pioneering idea of James Clerk Maxwell, who first introduced mechanical-electrical analogies in the 19th century, we want to exploit his innovative vision in the design of new metamaterials. Indeed, metamaterials can be defined as engineered materials designed to implement one or more specific functionalities. In particular, we have in mind to realize a mechanical system whose behavior is characterized by a useful response, which is typical of an electrical system. In other words, we want to design a mechanical system whose constitutive behavior is the same as an electrical system, namely a diode. To this end, a pantographic material with perfect pivots can be seen as a mechanical diode. Indeed, it is constituted by two families of straight fibers, with remarkable deformation due to the presence of the hinges and a threshold behavior when the fibers tend to be aligned

Biaxial bias extension test for pantographic sheets

Pantographic fabrics are emerging in the literature as promising metamaterials. They are made up of two orthogonal families of fibers connected at their intersection points by pivots. Fibers are supposed to be straight in the reference configuration and to store energy while undergoing extension and bending deformations only. Pivots, which oppose to relative rotations of fibers, are supposed to store energy when undergoing torsion, thus to confer shear stiffness at macro level. In the paper we present some new numerical simulations in which a 2D planar non linear second gradient continuum model is employed, derived by a heuristic homogenization procedure (dell’Isola et al. 2016) and aimed at describing the mechanical behaviour inherited by its micro-structure. A bi-axial extension test has been studied. We show that, similarly to the uni-axial bias extension test, the internal stored energy is localized at the corners of the clamping areas, whereas in the central area the internal stored energy distributes almost uniformly. Unlike to the uni-axial test, due to symmetry reasons, shear deformation in the central area of the domain vanishes

The Loss and Recovery of the Works by Piola and the Italian Tradition of Mechanics

In this chapter, we look in detail at the aspects concerning the transmission of scientific knowledge of the Italian school of Continuum Mechanics, mainly headed by Gabrio Piola, which strongly supported the point of view of Archytas of Tarentum as rediscovered by D’Alembert and Lagrange. The process of systematically removing references to the name of Gabrio Piola in Continuum Mechanics (and part of his results) is just one of many examples of how some social groups have, over the centuries and in different cultural fields, rewritten more or less relevant parts of the cultural knowledge of a society. Specifically, Gabrio Piola’s contribution to mechanical sciences has been greatly underestimated in both the more theoretical mathematical-physics literature and in the more applied and engineering oriented one. We remark, in the discussion presented in this Chapter, that at the basis of this phenomenon one can always find common features as a sectarian vision of cultural progress or the conviction that the point of view of the own social group is clearly superior to that of all the others

Combined polarization field gradient and strain field gradient effects in elastic flexoelectric materials

We consider a constitutive model for the behavior of elastic flexoelectric materials including strain gradient fields and polarization gradient fields. This model is based on a stored elastic energy density function which depends on four independent variables: the polarization field and the polarization field gradient as well as the strain field and the strain field gradient. A generalized Toupin variational approach is utilized to find the governing equations (constitutive relations, equilibrium equations and boundary conditions) of the material. The present model is then applied to the problem of a thick walled cylindrical tube of elastic isotropic flexoelectric material, subjected to axisymmetric loading. The resulting radial displacement field noticeably differs from the elastic and strain gradient elastic cases