Equilibrium of Two-Dimensional Cycloidal Pantographic Metamaterials in Three-Dimensional Deformations

Abstract

A particular pantographic sheet, modeled as a two-dimensional elastic continuum consisting of an orthogonal lattice of continuously distributed fibers with a cycloidal texture, is introduced and investigated. These fibers conceived as embedded beams on the surface are allowed to be deformed in a three-dimensional space and are endowed with resistance to stretching, shearing, bending, and twisting. A finite element analysis directly derived from a variational formulation was performed for some explanatory tests to illustrate the behavior of the newly introduced material. Specifically, we considered tests on: (1) bias extension; (2) compressive; (3) shear; and (4) torsion. The numerical results are discussed to some extent. Finally, attention is drawn to a comparison with other kinds of orthogonal lattices, namely straight, parabolic, and oscillatory, to show the differences in the behavior of the samples due to the diverse arrangements of the fibers.

Are higher-gradient models also capable of predicting mechanical behavior in the case of wide-knit pantographic structures?

“…This study focuses on the mechanical behavior of wide-knit pantographic structures. Pantographic structures have been extensively investigated (for instance, see [20][21][22][23][24][25][26][27]). A pantographic structure is referred to as wideknit if the number of the fibers composing the grid is low.…”

Research perspective on multiphysics and multiscale materials: a paradigmatic case

“…6), as well as negative buckling effect (see Fig. 7), i.e., buckling due to critical extension (and not compression, as it is usual) load [55,83,84]. Pantographic structures proved to exhibit very interesting features.…”

The Study of the Genesis of Novel Mathematical and Mechanical Theories Provides an Inspiration for Future Original Research

“…In this context, the most difficult problem to face from a mathematical point of view is to connect micro-structures and macrobehaviors. So, given a macroscopic theory (appropriate action functionals and consequent stationary conditions) one wants to find an algorithm to calculate the microstructure that, once homogenized, at the macroscopic level is described by the chosen macroscopic model [28,[113][114][115][116][117][118]. In this context it is important to remark that a major change in the research tools has been induced by the use of powerful computers to find suitable motions for minimizing postulated action functionals: in fact, especially in non-linear regimes, it is simply inconceivable to find closed form solutions and therefore only by means of suitably conceived algorithms it is possible to design and to predict the behavior of novel metamaterials [80,[119][120][121][122][123][124].…”