New formula to help scientists advance artificial muscles, soft robotics – and Batman’s bat cape

Professor Michel Destrade, School of Mathematics, Statistics and Applied Mathematics, NUI Galway.
Feb 17 2017 Posted: 10:03 GMT

NUI Galway publish new mathematical formula on soft ‘dielectric’ membranes

Applied mathematicians from NUI Galway have today published a formula which will be of huge benefit to materials scientists and soft robotics engineers. The team have worked out how much voltage and deformation soft ‘dielectric’ membranes can take before they break.

Soft ‘dielectric’ membranes are used on the cutting edge of science to develop artificial muscles, soft robotics, energy harvesters and ‘smart clothes’. These lightweight soft materials deploy and stiffen when put under high voltage, but until now, there has been a big challenge in knowing what the breaking point of these membranes is. 

Professor Michel Destrade, at the School of Mathematics, Statistics and Applied Mathematics in NUI Galway explains: “If you can remember the scene in Batman Begins where this huge bat cape emerges from a tiny folded piece of material, that’s the kind of technology which is being developed currently in some labs around the world, especially in Harvard University and in China. It’s the electric voltage that allows these special membranes to expand.

Until now it was not fully understood how much voltage these membranes could sustain. Some are a millimetre thick, but if they thin out too much when they stretch with the voltage, it can lead to a short-circuit and a catastrophic breakdown. We hope our mathematical formula will help advance science in this area.”

Dr Giuseppe Zurlo of NUI Galway, co-author of the study, adds: “The very near and real applications for these materials are artificial human muscles, or soft robots which can help organs function.”

Together with collaborators at Politecnico di Bari in Italy, the mathematicians worked out a simple formula to link the physical properties of the membrane to the breakdown amount of stretch. “The final equation is very compact”, says Dr Zurlo, “and it will provide most useful safety guidelines for future experiments on these fascinating materials.”

The problem had stumped material scientists for years and its solution is published today in the prestigious Physical Review Letters. Professor Destrade and Dr Zurlo are now working on experiments with engineering colleagues at Xi’an Jiaotong University in China.

To view the full paper in Physical Review Letters visit: or 

Video link of a membrane deforming under a voltage: 


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