The long and winding road that leads to homogenisation of Kresling origami

What are the geometrical and mechanical properties ruling bistability of Kresling origami metamaterials? How can we tune the magnitude of their axial-torsional coupling? Complete answers to these compelling questions cannot be found in the scientific literature, as the intertwining between bistability, axial-torsional coupling and an other significant behaviour, namely transverse dilation/contraction, remains mostly uninvestigated. This contribution aims at shedding light on this intertwining, through the use of a discrete model of Kresling origami that takes into account folding resistance. The present study is mostly computational and involves both pre- and post-critical analyses. It is based on displacement controlled tests - shearing and axial shortening/lengthening. Single-storey Kresling origami's are first considered, preliminarly to multiple-storey tubes, where buckling is observed. Several parameters are taken into account such as the number of storeys, stretching and folding stiffnesses, and - for shearing tests - the prescribed displacement direction in the transversal plane. The ultimate goal of the paper is to provide evidence that can be useful in the construction of homogenised continuum models of Kresling origami metamaterials.