A 3D extension of pantographic geometries to obtain metamaterial with semi-auxetic properties
Maximilian Stilz, David Plappert, Florian Gutmann, Stefan Hiermaier
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 ([Formula: see text]) and one negative Poisson’s ratios ([Formula: see text]). 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.
Topics & Concepts
AuxeticsHomogenization (climate)MathematicsStiffnessMathematical analysisStiffness matrixMetamaterialBernoulli's principleAsymptotic homogenizationGeometryPhysicsMaterials scienceComposite materialEcologyBiologyComposite numberOptoelectronicsBiodiversityThermodynamicsAlgorithmNonlocal and gradient elasticity in micro/nano structuresComposite Structure Analysis and OptimizationAdvanced Materials and Mechanics