Material nonlinearities yield doubly negative holey metamaterials

Abstract

Mechanical metamaterials with negative stiffness and negative Poisson’s ratio are exciting prospects for advanced material design. A plastic column with a series of periodically-spaced holes exhibits both of these properties when buckled under compression. In this paper, the behaviour of such a column under compression is measured experimentally and described with a simple mathematical model. This model predicts the compression, buckling and post-buckling behaviour of the entire column from the mechanical response of the thin ligaments of material that form the column’s microarchitecture to compression, rotation and shear forces, which are characterised experimentally, The softening behaviour in holey columns beyond the critical level of compression for pattern transformation is shown to be due to material constitutive nonlinearities in the rotation and shear response of the microarchitecture. Geometric perturbations to the columns can cause the observed pattern to change, but result in approximately the same force–displacement measurements as for the column with perfect geometry. This approach provides a useful framework to study systems where both geometric and material nonlinearities underpin observed phenomena.