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2022
Journal Article
Titel
A 3D extension of pantographic geometries to obtain metamaterial with semi-auxetic properties
Abstract
In this work we present a three-dimensional extension of pantographic structures and describe its properties after homogenization of the unit cell. Here we rely on a description involving only the first gradient of displacement, as the semi-auxetic property is effectively described by first-order stiffness terms. For a homogenization technique, discrete asymptotic expansion is used. The material shows two positive (0≤νyx,νyz≤1) and one negative Poisson's ratios (−1≥νxz≥0). If, on the other hand, we assume inextensible Bernoulli beams and perfect pivots, we find a vanishing stiffness matrix, suggesting a purely higher gradient material.
Author(s)