A 3D extension of pantographic geometries to obtain metamaterial with semi-auxetic properties. (April 2022)

• Record Type: Journal Article
• Authors: Stilz, Maximilian; Plappert, David; Gutmann, Florian; Hiermaier, Stefan
• Is Part Of: Mathematics and mechanics of solids. Volume 27:Number 4(2022)
• Page Start: 673
• Page End: 686
• Publication Date: 2022-04
• Subjects: auxetic -- homogenization -- metamaterial -- pantographic structure; Materials -- Mechanical properties -- Periodicals; Solids -- Periodicals; Materials science -- Mathematics -- Periodicals; 620.11205
• DOI: 10.1177/10812865211033322
• Languages: English
• ISSNs: 1081-2865

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 ≤ ν yx, ν yz ≤ 1 ) and one negative Poisson's ratios (− 1 ≥ ν xz ≥ 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.