Understanding the complexity of materials might help to solve the bendy phone problem.
Facebook and Twitter has been flooded with stories that the new iPhone 6 and 6 Plus bends during normal use. Dr Daniel Sutton and Professors Jonathan Dawes and Chris Bowen, look at the facts behind the headlines:
Twitter has carried a number of stories that the new iPhone 6 and 6 Plus bend during normal use. Traditional materials science suggests that light, thin phones will always run the risk of being ‘bendy’. Will the rapidly growing field of 'metamaterials’, artificially assembled composite materials, be able in the future to provide us with the unbendable phone?
The story, or #BendGate as it has become known, started with reports like the short YouTube video by Lewis Hilsenteger, of Unbox Therapy, investigating the force it would take to bend an iPhone. At the time of writing the video ‘iPhone 6 Plus Bend Test’ had accumulated 24 million hits. New iPhone owners are concerned that they could potentially bend their phone out of shape through normal everyday use, and reports of phones bending naturally have been circulating. Apple has described the devices’ unibody aluminium chassis as having been hardened and reinforced for extra endurance.
Is the aluminium body in fact so thin and light that Apple sacrificed stiffness and strength for lightness? Apple have defended the new iPhone, pointing to their rigorous design, development and testing process which ensures that such failures are incredibly rare. The aluminium alloy used by Apple appears to be a reliable industry standard choice. But aluminium has its limitations, and the design demands of phones is an example of pushing materials to their limits. In this article we comment on the possibility that metamaterials, a rapidly growing interdisciplinary scientific field, could help to create the unbendable phone.
What are metamaterials?
Mankind has always tailored the material world to its advantage. Half a million years ago it was trying to find the best materials to make spearheads; today we’re finding the best uses for carbon fibre, titanium, and graphene. Technology has always been impatiently waiting for scientific advances, not least demanding materials with new properties; whether that be materials that are harder, transmit information faster, or are lighter, or shinier, or more light-absorbing.
It’s hard to change the physical characteristics of most commonly used materials, such as aluminium. The mathematics of elasticity theory shows that if you halve the thickness of the casing of a phone, for example, then the stiffness drops by a factor of eight. To go for a stiffer material without increasing the weight, you have to sacrifice other desirable properties such as resistance to fracture (ceramics, for example).
As we reach the limits of naturally occurring materials however, we are also understanding much more about them. Enter the science of metamaterials. A metamaterial is an artificially engineered material with properties often significantly different from its constitutive components. Metamaterials are built by taking identical microscopic units and assembling them into repeating periodic structures.
The exact size and shape of the microscopic units allows the material to respond in often surprising ways to electromagnetic or acoustic waves, on large scales. It’s not a traditional alloy because the assembly is at a micron scale not an atomic scale, and it often needs to be precisely periodic in order to achieve the desired effect.
The best known potential application for metamaterials is to be able to bend light rays, holding out the possibility of creating ‘invisibility cloaks’. But there are mechanical possibilities as well (for example the ability to produce materials having a negative 'Poisson's ratio'). The impact of metamaterials potentially could stretch from stronger, lighter prosthetic limbs to the design and construction of the space suit that will take the first humans to Mars.
Where's the mathematics?
For metamaterials, both laboratory experimentation and computer simulation turn out to be expensive. For computer simulations the difficulty is that the range of spatial scales involved, down to the fine details on the micron scale, often make the simulation option out of reach of even the most advanced supercomputers. Luckily, mathematics can help; in fact mathematical techniques can be developed precisely by exploiting the range of spatial scales in this problem: the computational disadvantage becomes a theoretical advantage.
By taking averages in careful ways, one can homogenise the material, blending the small-scale structures into a simpler overall material that has different coarse-grained material properties. The coarse-grained material properties can be calculated mathematically through the homogenization procedure – this might involve numerical simulation still, but on a vastly simpler problem that can be run on a desktop PC, not a supercomputer. Even better, the mathematics of homogenization gives us direct theoretical links between the original problem and the coarse-grained one, so our understanding grows and theory can be checked against experiment.
The University of Bath carries out research in materials science across the whole range of these issues, from how best to use composites in the aerospace industry through to the mathematics of homogenization theory. Most excitingly, a good piece of mathematics often finds uses all over the sciences: in this case, homogenization can help understand soft matter problems such as how drugs are absorbed through cellular membranes as well as how to make faster, lighter, stronger materials so that your phone won’t drive you round the bend.