Mathematics Key to 4D Printing

Although some of us are just getting our heads around the amazing potential in 3D printing, the next step is already on the horizon.    A leading mathematician has started working on the formulas required to step into an extra dimension!

Three D printing is already revolutionizing all sorts of areas from manufacturing, medicine to science and engineering.  It’s now fairly simple and inexpensive and has the potential to create all sorts of intricate objects quickly and cheaply.   There are printer parts in our machines and indeed people are having printed body replacement parts transplanted into their bodies with great success.

However there is always a next step, and now mathematicians are working on taking us in to the world of 4d printing.  Just to clarify we are talking about the possibility of fabricating objects with a programmable shape over time.  It’s always been theoretically possible however no-one had really starting looking at working through the complexities involved.

This seems to be changing as Professor Pasquale Ciarletta from Milan has just published a paper in ‘Nature Communications’ where he has started working through the numbers about a specific problem with this.  The professor has been focusing on how to control the sudden nucleation of localised furrows in the soft solids produced in 3d printing.

The advantages and possibilities of these developments may not be initially apparent.  However in addition to the advantages to the field of engineering there is huge potential to have the ability to design and print objects which can morph over time.  The paper related the development to the field of development biology as particular interest.  Here we could look at things like tissue morphogenesis and other areas such as issues in the brain or tumour control.

Ciarletta has acknowledged that there are great complexities behind making this work.  There has already been lots of experimental investigation of the issues involved – the physics behind the concept of ‘creasing’ being particularly challenging.  His study proposes a unique mathematical approach to predicting the experimental conditions required to trigger the onset and how creases change over time.  This is the key to being able to control their appearance on a specific scale and ultimately to be able to print them in 4d.

There are parallel advancements being made in the area of 3d printing too.  You can already sit down and watch the football on Match of the Day live like this on a completely 3d printed television set.  It is also now possible to edit specific printed objects after they have been created.  This is achieved by repeatedly changing the colours of 3d printed objects after thy have been printed.

The concept is currently being developed under the name ColorFab and it involves using a specially created 3d printable ink which can actually change colour under certain conditions – primarily after being exposed to UV light.  This of course has a time delay currently estimated at around 20 minutes, however the researchers are hoping to improve on this substantially in further development.

Further Reading: Available on British TV