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A 3D extension of pantographic geometries to obtain metamaterial with semi-auxetic properties. (English) Zbl 07601669

Summary: 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 \((0\leq\nu_{\mathrm{yx}},\nu_{\mathrm{yz}}\leq 1)\) and one negative Poisson’s ratios \((-1\geq\nu_{\mathrm{xz}}\geq 0)\). 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.

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74-XX Mechanics of deformable solids

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