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How can mathematics help us make more resilient materials?

Modern materials often contain inclusions: bits of other materials or holes embedded within the bulk material in order to enhance the overall properties. This can bring benefits such as a high strength to weight ratio or increased chemical resistance. But mechanical stress can build up in the host material surrounding the inclusion, and this can lead to material failure.

Watch the video and play the game to find out how we can use maths to design special coatings for inclusions that protect the surrounding material from stress.

The princess and the… neutral inclusion?!

Neutral Inclusion Game: See how the tale of the Princess and the Pea could be very different if the pea had a neutral effect on the mattresses! Follow the story and then use the slider to vary the firmness of the pea’s coating. What effect does the firmness of the coating have on the mattresses? Find the value for which the firmness of the coating leads to no effect on the mattresses, i.e. the mattresses become flat, as if the pea isn’t there!

How can we see stress? Forces act on materials all the time, and too much force can cause a material to fail, or break. The amount of force per unit of area is called the stress. Stress tends to concentrate around holes and inclusions, so these are common points of failure. In some materials we can make the stress show up in a rainbow of colours using polarising films.

Watch this short video and find out more:


Suitable for ages 7+.

Activity Information

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We are the Mathematics of Waves and Materials, a research group in the Department of Mathematics at The University of Manchester. We use Applied Maths alongside ideas from Materials Science, Chemistry, Engineering and Physics to model and test the properties of materials and waves. We use mathematical modelling to design novel materials called metamaterials, with properties that are not found in everyday materials. This can help us find solutions that are more environmentally sustainable.

Why not visit the Maths of Waves and Materials learning pages for more fun things to try!

If you haven’t already done it, how about checking out Feeling the heat – Part 1!

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