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.
Highlights
Metamaterials has attracted the attention of the scientific community considerably
One may conceive many possible metamaterials depending on the particular properties to be obtained
We investigate a particular type of mechanical metamaterial [5,6,7]: a pantographic sheet [8,9,10,11,12,13,14,15]
Summary
Metamaterials has attracted the attention of the scientific community considerably. We investigate a particular type of mechanical metamaterial [5,6,7]: a pantographic sheet [8,9,10,11,12,13,14,15] This particular material has been introduced as the first synthetic example of material exhibiting a strain–energy function involving second gradient contributions relevant at a macroscopic scale of observation [16,17,18]. Symmetry 2019, 11, 1523 structure is identified with a surface composed of two families of continuously distributed fibers in the framework of continuum theory.
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