Indentation resistance of brittle auxetic structures: Combining discrete representation and continuum model

Abstract

This work investigates the indentation resistance of the auxetic/non-auxetic honeycomb ceramics layer by combining a discrete numerical representation and a continuum analytical model. The indentation depth of honeycombs with varying cell-wall angle and cell-wall thickness are measured. The indentation depth of auxetic honeycombs with negative Poisson’s ratio (NPR) is smaller than that of conventional ones in the premise of the same cell-wall thickness. But on the condition that the honeycombs possess the same relative density, there exists an inverse tendency. The corresponding mechanisms responsible for those trends are revealed. The stress intensity factor (SIF) is defined to characterize the stress singularity at the corner of the punch. The influence of NPR on the magnitudes of SIF is evaluated. A punch toughness concept is defined by a novel multi-scale method as the failure criterion of brittle honeycomb ceramics in indentation tests. The effects of NPR on the punch toughness of honeycombs are discussed. And the empirical formulas of punch toughness varying with the cell-wall thickness and the relative density are summarized. Finally, the NPR effects on the collinear punches problem are detected; the results show that the auxetic performance can significantly weaken the interaction between the punches.