7 June 2021
by Dr Parvez Alam FIMMM

Into the fold – mechanical metamaterials

Dr Parvez Alam FIMMM, at The University of Edinburgh, UK, on the potential of mechanical metamaterials with Japanese ancient arts.

© Hakase_/Getty

Mechanical metamaterials are a special breed of cellular solid with properties that are guided by the geometrical construction of solid matter, rather than solely by its composition.

Such materials consist of both pore space and matter and, as such, there is greater freedom for solid deformation into the pore space. Researchers can exploit this by judiciously designing the solid structure to work not only with other solid parts of the structure, but also with the air space.

Broadly speaking, mechanical metamaterials can be divided into two groups. The first is based on structures designed to optimise mechanical performance, examples of which include hierarchically architected metamaterials with heightened toughness and ultra-light-ultra-stiff metamaterials.

The second group comprises structures that exhibit unique properties of deformation, including negative stiffness metamaterials showing increased displacement with decreasing load; negative Poisson’s ratio (auxetic) metamaterials, where stretching the material makes it wider rather than thinner; chiral metamaterials that twist under uniaxial loading; and metamaterials that are able to stretch far beyond normal capacity for the host material (extreme stretch metamaterials).

While most design efforts focus on additive manufacturing of unique shapes and structures, there exists less research on origami and kirigami. Both are ancient arts with deep-set Shinto and Buddhist roots. While origami is focused on the folding (ori~) of sheet material such as paper (~kami), kirigami is more versatile as it includes cutting (kiri~) sheet material such as paper.

Origami and kirigami structures are advantageous as they are fabricated from simple sheet materials. From both manufacturing and transportation perspectives, there are obvious benefits in creating expandable materials and unit cells from simple sheets. Pre-cut materials have the potential to be built onsite, or used as sheets, only realising shape changes on loading.

Recent research in origami and kirigami at The University of Edinburgh, UK, is broad ranging with such structures forming the basis of several novel engineering designs. Recent application examples include impact softening, rocket airbrakes and sheet materials exhibiting extreme levels of lateral expansion.

Sticky behaviour

The deformation behaviours exhibited by mechanical metamaterials are evident in nature. Honeybees, for example, create light-weight, interlinked hexagonal structures with high out-of-plane stiffness properties. Auxetic effects of ‘re-entrant honeycombs’ are observed in the skins of salamanders and snakes, and certain structures in nature, when deformed along a primary axis, will simultaneously twist about this axis, such as goat horns, shells, cellulose and DNA.

Twist and turn

Recoverable impact softening is an area where there is growing interest as it may preserve the lifetime of impact-resisting laminates.

Many of these materials are designed to crush under impaction (crush-zones), and while this is an effective method for redistributing stress and enabling energy losses, the result is that even under small impactions, the material will often need to be replaced. The design of elastically recoverable, impact-softening metamaterials may be a route to improved longevity of impact-resisting materials.

Novel kirigami structures, developed at the University, aim to enable recoverable impact softening under low levels of impaction. The unit cells – made from cellulose-based card for this prototype stage – are sandwiched between two flat plates. The vertical walls of each unit cell have been designed with a subtle tilt, similar to the way a parallelogram changes both obtuse and acute angles as well as its open area from one open end to the other. This allows the structure to twist simultaneously with an out-of-plane deformation, and to untwist during unloading.

Freya Bauman, who worked on the design, notes, ‘The kirigami structure works well as it is designed to dissipate material strain via torsional compression. Even though it compresses along its axis, there is no change in the area of cross-section of the plates as the structure twists internally. When compared against other structures such as honeycombs, we found that, under impact, there was irrecoverable bifurcation of the core honeycomb structure, as well as failure of the plates. Since the number and size of kirigami unit cells between the plates can be varied independently, the stiffness of the sandwich can be modified to suit its intended application.’

Alone, impact-softening, kirigami, sandwich panels may not offer the same level of protection that a material designed to crush may provide. However, when laminated between different crush-panels, impact-softening panels preferentially deform, thus saving crush-panels from permanent damage during low-impact occurrences.

Loading and unloading of the elastic impact-softening structure © Freya Bauman/The University of Edinburgh
Closed (bottom left) and open (bottom right) forms of the origami Flasher, designed for use as an airbrake on Endeavour’s Darwin I rocket (top)
  © Ann (Hyeon) Lee, The University of Edinburgh

Propelling forward

Origami metamaterials are also being scaled up, specifically the origami Flasher, which is designed to act as an airbrake for the Darwin I rocket developed at the University.

The Endeavour team’s rocket is >2m in length with a mass of around 22kg and a fuselage made of carbon fibre reinforced plastic. Deployment of its airbrake would be expected to occur prior to reaching an apogee of 10,000ft.The airbrake must have the ability to (a) exert drag at an optimal value on deployment while maintaining rocket stability, (b) exert no drag on the rocket while in a folded state, and (c) withstand the mechanical stresses created by air pressures post-deployment.

The Flasher design is a good origami candidate, as in its closed (stowed) state, it is a 3D structure that aligns with the rocket fuselage. In its open state, it becomes a flat 2D plate that extends beyond the fuselage diameter, enabling increased drag. ‘The Flasher’ is a term coined by the American origami entertainer Jeremy Shafer for any structure that wraps in a spiral coil and opens up into a 2D flat plate.

Ann (Hyeon) Lee, who worked on the design, says, ‘I needed a structure that had a large deployed-to-stowed ratio as it had to be stowed in a limited volume of the rocket fuselage and have a large surface area to generate maximum drag when deployed.

‘The Flasher satisfied this specification and has a stowed shape of a cylinder, which makes integration to the rocket easier. The Flasher is capable of motion that other traditional structures would require more parts and joints to achieve. It was a massive advantage in terms of saving the mass and volume of the structure, which was critical for our rocketry application.’

Lateral expansion

The rotating square structure is known to laterally expand when stretched. This effect is a function of the maximum angle at which the individual squares can rotate, which, in turn, relates to the cut length that separates the squares and the hinges that develop between them. These hinges rotate when the material is stretched, and the structure resultantly expands.

Our recent research on rotating square structures shows that lateral expansion and contraction can be controlled by exploiting hinge rotation. This is made possible by constraining lateral movement of loaded squares of adjacent unit cells. This increases the rotation of material hinges located directly under the constrained squares, and causes an unprecedented lateral deformation in the thickness-direction, reaching well over the edge length of a single rotating square.

Lateral expansion in structures such as these are proportional to the edge lengths of the squares, meaning that larger or smaller structural strains are possible by controlling the sizes and constraints of the squares. The structure enables elastic straining that far exceeds the strain-to-failure of the base material – thin sheets of polypropylene – from which the metamaterial is made.   

The design of these structures must account for potential yielding of the material hinge in torsion, and ensure it is not surpassed. One potential application could be a non-pneumatic expansion – a pipe or similar hollow structure that can expand without the need for any air pressure.

Right: Sheet cuts of rotating squares (top left), typical width-direction expansion of rotating squares (bottom left) and extreme thickness-direction lateral expansion of rotating squares caused by selectively constraining rotating squares (right) © Pippa Hughes, The University of Edinburgh

A folding revolution

The idea that 2D materials can be designed with cuts and folds to enable the creation of never-before-seen material structures with unique properties, is a good reason for excitement. While new material discoveries are frequently being made in this field, there remains considerable ‘free-volume’ for R&D in other diverse areas. From programmable structures that shape-adapt to external stimuli, to buildings built up from sheet materials pulled out from the back of a van, the future of mechanical metamaterials is inspiring, and swiftly unfolding its way towards a new technology revolution.


Dr Parvez Alam FIMMM