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

A review of recent developments in mathematical modeling of bone remodeling

In this article, we summarize the developments in the mathematical modeling of the mechanics of bone and related biological phenomena. We will devote special attention to the results of the last 10–15 years, although we will cover some relevant classical work to better frame the more recent researches. We will propose a division of the literature based on the main aim of the model (mechanical/biomathematical) and the type of biological phenomena considered (stimulus, growth, cell population dynamics). Finally, we will suggest some possible directions for future investigations

Modeling and designing micro- and nano-structured metamaterials: Towards the application of exotic behaviors

The lack of suitable computational methods has significantly restricted the creativity of engineers in designing the materials to be used in technological applications. When one wants exact analytical solutions for a given physical system, then usually drastic and restrictive simplifying assumptions are needed. In particular, homogeneity of physical and geometrical properties at lower length-scale is the standard assumption in continuum mechanics. On the other hand, it is well-known since the pioneering work of Gabrio Piola, and then re-established in the works by Mindlin, Toupin, Green, Adkins and Germain, that it is possible to synthetically describe microscopic inhomogeneity by means of field theories incorporating additional kinematical fields. The characteristic length-scale affecting macro-behavior can even be of the order of nanometers, in which case the intuition due to Richard Feynman about the importance of quantum effects at macro-scale could open the path to technological advancements. In the present paper we review some of the literature in the field and try to indicate some research perspectives that seem to us potentially ground-breaking. In particular, following the suggestion of Professor dell’Isola, we briefly describe his concept of pantographic lattices and sheets whose importance in nano-technology could be relevant

Euromech 563 Cisterna di Latina 17-21 March 2014 Generalized continua and their applications to the design of composites and metamaterials: A review of presentations and discussions

In the present paper, a rational report on Euromech 563, Generalized continua and their applications to the design of composites and metamaterials (Cisterna di Latina 17-21 March 2014), is provided. The frank and constructive spirit which animated the workshop by Dell'Isola et al. (ZAMM 2014; 94(5): 367-372) also characterized Euromech Colloquium 563. All presentations were video-recorded and are freely available online at the address http://www.memocsevents.eu/euromech563/?page-id=1013. The topics treated were selected by the organizers in order to allow a comparison of the available experimental evidence with the predictive capability of current theoretical models. The numerical investigations selected and presented aimed to make more effective the aforementioned comparison. The interested reader will find more details about the colloquium at the dedicated webpage http://www.memocsevents.eu/euromech563. The design and use of advanced materials and structural elements requires an extensive and rigorous process of mathematical modeling. The organizers of Euromech 563, being aware of this need, have chosen as participants renowned and reputed scientists (and some promising young researchers) who all agree on recognizing to mathematical sciences their role of unifying and coordinating tool in the effort for the advance of technology. The Colloquium has indeed surely contributed to the development of more advanced technological possibilities and to the theoretical conception of completely new ones