Homogenization of periodic hexa- and tetrachiral cellular solids

By Andrea Bacigalupo, Luigi Gambarotta. 2014

174 citations recorded by the source corpus.

Abstract The homogenization of periodic hexachiral and tetrachiral honeycombs is dealt with two different techniques. The first is based on a micropolar homogenization. The second approach, developed to analyse two-dimensional periodic cells consisting of deformable portions such as the ring, the ligaments and possibly a filling material, is based on a second gradient homogenization developed by the authors. The obtained elastic moduli depend on the parameter of chirality, namely the angle of inclination of the ligaments with respect to the grid of lines connecting the centers of the rings. For hexachiral cells the auxetic property of the lattice together with the elastic coupling modulus between the normal and the asymmetric strains is obtained; a property that has been confirmed here for the tetrachiral lattice. Unlike the hexagonal lattice, the classical constitutive equations of the tetragonal lattice turns out to be characterized by the coupling between the normal and shear strains through an elastic modulus that is an odd function of the parameter of chirality. Moreover, this lattice is found to exhibit a remarkable variability of the Young’s modulus and of the Poisson’s ratio with the direction of the applied uniaxial stress. Finally, a simulation of experimental results is carried out.

Subfields: Mechanical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/9604f21b50afbae0816b30d6a356c133afad9a46

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In Mechanical Engineering

In Mechanics of Materials

Citations in the corpus

Computational second-order homogenization of materials with effective anisotropic strain-gradient behavior (2020, methodology): “In [8], the same authors applied micropolar and strain-gradient homogenization schemes to auxetic materials (hexachiral and tetrachiral honeycombs) and obtained analytical expressions for effective higher-order coefficients, as well as numerical values based on FEM calculations.”
A novel two-dimensional mechanical metamaterial with negative Poisson’s ratio (2020, background): “However, the current re-entrant and chiral metamaterials [9,10] with negative Poisson’s ratio are generally designed to have beamdominated microstructures with bending dominated topologies.”