Graded origami honeycomb for energy absorption
Keywords: dynamic impact
graded stiffness
functional gradients
energy absorption structures
origami honeycomb

This thesis is concerned with the design of new cellular structures whose properties can be easily tuned to optimise the management of both quasi-static and dynamic external loads. This was achieved through the application of origami techniques, which allowed the mechanical performance to be functionally graded through the adjustment of the underlying crease pattern. The body of work is segmented into four areas of focus:
Firstly, a kinematic analysis was undertaken to identify the geometric possibilities for an origami honeycomb with both crease-to-crease and face-to-face connection methods. Techniques to introduce self-locking, through the restriction of the kinematic range, in the in- plane and out-of-plane direction were then highlighted. When grading in the out-of-plane direction, the Miura-ori facet width, a, was found to be dependent on the Miura-ori angle, α, for the crease-to-cease connection method. The face-to-face connection method therefore provided greater freedom in the design of grading in the out-of-plane direction. Through this analysis a family of cellular solids, that exhibit varying kinematics and the ability to self-lock, were identified.
Secondly, the effect of the underlying crease pattern variables and out-of-plane locking on the quasi-static behaviour of the regular origami honeycomb were assessed through an experimental, numerical, and analytical study. The peak force was shown to be strongly dependant on the initial eccentricity of the horizontal creases. Additionally, with all other variables equal, α could be varied to tune the peak force and the SEA. The face-to-face connection method resulted in an increased SEA when compared to the crease-to-crease connection method. Grading α along the height of the core was shown to provide a graded stiffness. For cores with the crease-to-crease connection method, the increase in stiffness was related to the alternative deformation mode that results from the restraint provided by adjacent units within the core. In contrast, for the face-to-face connection method, the stiffness increase was strongly related to the eccentricity of the units, where similar eccentricities resulted in minimal increases in stiffness. An analytical model was then developed for the face-to-face connection method, providing an expression that can facilitate the functional grading of such a core for a given application, subject to quasi-static loading.
Thirdly, the ability to imbue honeycombs with a graded mechanical behaviour using origami techniques is investigated for dynamic loading. 2×1 representative origami honeycomb cores were manufactured using a sequential stamping technique from aluminium sheets and experimentally tested using the Direct Impact Hopkinson bar and Taylor type test setup. These results validated a numerical approach that was then extrapolated to a numerical model of a 6×6 ungraded and graded core. Similar advantages, as those found for typical grading methods, were observed for the graded origami honeycomb when subjected to dynamic loading for both connection methods. However, the graded behaviour was enhanced for the face-to-face connection method due to the ability to arbitrarily select a. These results show that origami techniques can successfully be applied to introduce a gradient in the mechanical behaviour under dynamic loading, providing an attractive alternative to standard grading methods.
Lastly, the dynamic behaviour of an ungraded core is numerically investigated to assess the applicability of certain analytical models. It was shown that the force transferred to the distal end is influenced greatly by lateral inertia effects, in some cases resulting in significantly larger force when compared to the quasi-static predictions. This increase resulted from the deformation deviating from the crease pattern. For the geometry simulated a super folding element was defined to predict this force increase. Through this analysis it was illustrated that the force increase from the quasi-static prediction could be reduced through the appropriate selection of a. Alternatively, the number of units along the height and/or minimising the lateral inertia through the adjustment of the crease pattern variables could also reduce the force increase at the distal end. The force at the proximal end was predicted through a continuum approach assuming shock wave formation. This was found to only be applicable for certain combinations of height and impact velocity. Notwithstanding it can provide reasonable estimates of the average force for certain scenarios which allows the evaluation of the energy absorption.