Predicting the post-bifurcated patterns of architectured materials using group-theoretic tools

Abstract

Extensive studies on hexagonal honeycombs under in-plane compression have demonstrated that the structure's symmetry plays a decisive part in the emergence of deformation patterns in post-bifurcated configurations. In this work, the aim is to take advantage of this property by presenting a new group-theoretic approach to list the various attainable post-bifurcated patterns of periodic architectured materials. As of today, some group-theoretic approaches have been elaborated for determining the post-bifurcated paths and thus patterns of a symmetric system submitted to specific loading conditions. However, the application of these approaches requires knowledge of the system's governing equations. By making use of another group-theoretic tool, this work predicts the various possible post-bifurcated configurations of a periodic architectured material a priori of any non-linear computation by simply assessing the symmetry group of its undeformed configuration. This approach is applied, as an example, to the buckling of regular hexagonal honeycombs but can be easily transferred to any periodic architectured material. This work is a first step towards the elaboration of a more general process for the design of architectured materials when harnessing post-bifurcated behaviour is essential.