Quasi-static crushing of eggbox, cube, and modified cube foldcore sandwich structures
Graphical abstract
Introduction
A rigid foldable origami pattern is an unbroken sheet that can realise a continuous rigid motion if its facets and fold lines are replaced by rigid panels and hinges [1]. Rigid foldable kirigami patterns possess the same property, but are not folded from a single, continuous sheet and so are characterised by the need to cut, stamp or punch the sheet before folding.
When an origami pattern consists of repeating, tessellated shapes, it is known as tessellation origami [2]. The Miura-ori pattern is the most widely known rigid-foldable, tessellated origami pattern and has been much-researched as engineering structures and devices [3]. Previous studies have identified and parameterised kirigami tessellations which may be suitable for engineering use, including sandwich panel construction [4], [5], [6].
Foldcore sandwich panels consist of a folded core sandwiched between two stiff facings. The key advantage of foldcore construction over honeycomb cores is that the cells are not closed, allowing moisture to escape through open channels and not become trapped [7], [8]. Additionally, foldcores possess the ability to be continuously manufactured from a flat sheet [9].
The only foldcore to be studied in detail is the Miura-type foldcore and its variants, including single-curved [10], [11], [12] and curved-crease [13], [14], [15] architectures. Experimental investigations have benchmarked the performance of these cores against honeycomb cores under out-of-plane quasi-static loading [15]. The standard Miura-core cannot match the energy-absorption or strength of a commercial honeycomb with comparable material and density. Curved-crease cores can potentially match honeycomb, but encounter manufacturing difficulties at the necessary optimum geometries.
Preliminary investigations into kirigami foldcores have identified two kirigami geometries with potential to match or exceed Miura-type foldcores [16], specifically the cube and eggbox type. However for manufacturing convenience, experiments were conducted with polypropylene sheet material and at different core effective densities and so their performance relative to typical Miura-type foldcores is unknown.
Origami design techniques have been shown to be effective at improving the energy-absorption capability of thin-walled devices. An effective energy-absorbing device should possess, amongst other properties [17], a peak reaction force from impact below the threshold which would cause damage, a high specific energy absorption, and a stable deformation mode. A high specific energy absorption can be generated from a high average reaction force with a long crush stroke. In [18], a pre-folded diamond lobe was introduced onto each corner edge of a conventional thin-walled square tube, to produce the origami tube. A conventional square tube under axial crushing causes each corner edge to form a single travelling plastic hinge line that sweeps through a certain surface area, dissipating a large amount of energy. The addition of the lobe successfully triggered a new failure mode involving two travelling plastic hinge lines at each corner. As a result, the overall energy dissipation was increased by 41%. Parametric optimisation of the square origami tube then generated an improved configuration with a further 47% increase in energy-absorption [19].
A similar technique has been applied to Miura foldcores to create the indented foldcore [20]. For the indented Miura foldcore, an indent was added along the top ridge of the Miura pattern. This geometric imperfection initiated a failure mode involving two top–down travelling hinge lines. This increased the uniformity of the force–displacement response compared to a basic Miura foldcore, which fails by plate buckling and generated a 39% increase in energy-absorption. However the new failure mode is suppressed in a complete sandwich panel with two attached skins. It therefore offers no significant advantage over the standard Miura foldcore in most applications.
The present paper conducts an experimental and numerical analysis on four kirigami sandwich core geometries. Two geometries are the cube and eggbox tessellated kirigami patterns. Two geometries are cube geometries altered with origami design techniques, aimed at triggering failure modes associated with higher energy absorption. All cores are constructed at a similar density and aluminium material to those used for previous Miura-type foldcore investigations to enable benchmarking relative to these existing core types. The geometry of each core structure is characterised in Section 2. Experimental analyses under quasi-static loading are conducted in Section 3. Numerical analyses are given in Section 4 followed by discussion in Section 5.
Section snippets
Cube
Various forms of the cube pattern are known [4] with a similar panel arrangement but different crease polarities. The cube crease pattern shown in Fig. 1(a) produces a folded configuration with continuity between adjacent vertical walls and so forms a square honeycomb-like tessellation. As with the eggbox pattern, the general form of the pattern has three side lengths, however the present study shall restrict consideration to the regular configuration in which all side lengths are s. The
Prototype manufacture
Three prototypes were manufactured for each of the above geometries. All foldcores were manufactured from the same pure aluminium sheet material used in previous study of Miura foldcores [15] and additionally were designed at approximately the same effective core density and core height at . Foldcore prototypes were also designed to contain a large number of unit cells, in order to avoid significant free-edge effects. They are shown in Fig. 2.
Cube prototypes were manufactured with
Numerical analysis
Finite element analysis was performed by means of a quasi-static, large-displacement analysis using ABAQUS/Explicit. The analysis was performed for a single unit cell, with periodic boundary constraints applied to nodes on the relevant edges. Unit cells were modelled using the same material and dimensions as the experimental prototypes. As no tearing was observed in the prototype experiments beyond that already present in eggbox cores from manufacture, an isotropic-hardening plasticity material
Kirigami foldcore comparison
The dimensionless stress–strain responses of the core experimental responses are shown in Fig. 4. Considering first the two unmodified kirigami patterns, the cube core is seen to have a 53% greater energy than the eggbox core. The poor eggbox performance is attributed to the extremely high sensitivity of the core geometry to periodic boundary conditions, with the numerical models showing a 63% reduction in energy absorption from to models.
Comparing cube and cube strip experimental
Conclusion
This paper presented an experimental and numerical investigation on four kirigami-inspired folded core structures under out-of-plane crushing. The cube and eggbox patterns were based directly on known kirigami patterns and displayed the lowest energy absorption capacity, compared to both other foldcores tested in the present study and those reported previously. The eggbox core additionally was seen to have extremely high sensitivity to geometric imperfections and boundary conditions.
Two
Acknowledgement
The authors are grateful for the financial support provided by the Air Force Office of Scientific Research R&D Project 134028.
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