dear fellow scholars, this is two minute paperswith kã¡roly zsolnai-fehã©r. we are back! and in this episode, we shall talk about auxeticmaterials. auxetic materials are materials that whenstretched, thicken perpendicular to the direction we're stretching them.
3d printing without support material, in other words, instead of thinning, theyget fatter when stretched. really boggles the mind, right? they are excellent at energy absorption andresisting fracture, and are therefore widely used in body armor design, and i've read aresearch paper stating that even our tendons
also show auxetic behavior. these auxetic patterns can be cut out froma number of different materials, and are also used in footwear design and actuated electronicmaterials. however, all of these applications are restrictedto rather limited shapes. furthermore, even the simplest objects, likethis sphere cannot be always approximated by inextensible materials. however, if we remove parts of this surfacein a smart way, this inextensible material becomes auxetic, and can approximate not onlythese rudimentary objects, but much more complicated shapes as well.
however, achieving this is not trivial. if we try the simplest possible solution,which would basically be shoving the material onto a human head like a paperbag, but asit is aptly demonstrated in these images, it would be a fruitless endeavor. this method tries to solve this problem byflattening the target surface with an operation that mathematicians like to call a conformalmapping. for instance, the world map in our geographytextbooks is also a very astutely designed conformal mapping from a geoid object, theearth, to a 2d plane which can be shown on a sheet of paper.
however, this mapping has to make sense sothat the information seen on this sheet of paper actually makes sense in the original3d domain as well. this is not trivial to do. after this mapping, our question is wherethe individual points would have to be located so that they satisfy three conditions:one: the resulting shape has to approximate the target shape, for instance, the humanhead, as faithfully as possible two: the construction has to be rigidthree: when we stretch the material, the triangle cuts have to make sense and not intersecteach other, so huge chasms and degenerate shapes are to be avoided.
this work is using optimization to obtaina formidable solution that satisfies these constraints. if you remember our earlier episode aboutoptimization, i said there will be a ton of examples of that in the series. this is one fine example of that! and the results are absolutely amazing - thepossibility of creating a much richer set of auxetic material designs is now withinthe realm of possibility, and i expect that it will have applications from designing microscopicmaterials, to designing better footwear and leather garments.
and we are definitely just scratching thesurface! the method supports copper, aluminum, plasticand leather designs, and i am sure there will be mind blowing applications that we cannoteven fathom so early in the process. as an additional selling point, the materialsare also reconfigurable, meaning that from the same piece of material, we can createa number of different shapes. even non-trivial shapes with holes, such asa torus, can be created. note that in mathematics, the torus is basicallya fancy name for a donut. a truly fantastic piece of work, definitelyhave a look at the paper, it has a lot of topological calculations, which is an awesomesubfield of mathematics.
and, the authors' presentation video is excellent,make sure to have a look at that. let me know if you have found this episodeunderstandable, we always get a lot of awesome feedback and we love reading your comments. thanks for watching, and for your generoussupport, and i'll see you next time!
