Since the 1600s, chocolatiers have been perfecting the art of the bonbon, passing down techniques for crafting a perfectly smooth, even chocolaty shell.

Now, a theory and a simple fabrication technique derived by MIT engineers may help chocolate artisans create uniformly smooth shells and precisely tailor their thickness. The research should also have uses far beyond the chocolate shop: By knowing just a few key variables, engineers could predict the mechanical response of many other types of shells, from small pharmaceutical capsules to large airplane and rocket bodies. The team’s results are reported today in the journal Nature Communications.

The researchers developed a fabrication technique to quickly create thin, rubbery shells, which involved drizzling liquid polymer over dome-shaped molds and spheres such as ping pong balls. They allowed the liquid to coat each mold and cure, or solidify, over 15 minutes. They then peeled the resulting shell off the mold and observed that it was smooth — virtually free of noticeable defects — with a nearly uniform thickness throughout.

Combining this simple technique with the theory they derived, the team created shells of various thicknesses by changing certain variables, such as the size of the mold and the polymer’s density. Surprisingly, they found that the shell’s final thickness does not depend on the volume of liquid or the height from which it is poured onto the mold.

“Think of this formula as a recipe,” says Pedro Reis, the Gilbert W. Winslow Associate Professor of mechanical engineering and civil and environmental engineering at MIT. “I’m sure chocolatiers have come up with techniques that give empirically a set of instructions that they know will work. But our theory provides a a much better, quantitative understanding of what’s going on, and one can now be predictive.”

Reis hopes that the group’s theory will reinvigorate studies in shell mechanics, a field that saw significant development in the 1950s and 60s.

“This is a really simple, robust, rapid prototyping technique, and we’ve established design principles together with a predictive framework that characterizes the fabrication of thin shells,” Reis says. “I think that will be powerful. We’re revisiting an old topic with new eyes.”

Reis’ co-authors include lead author and graduate student Anna Lee, postdoc Joel Marthelot, and applied mathematics instructor Pierre-Thomas Brun, along with graduate student Gioele Balestra and Professor François Gallaire at the Swiss Federal Institute of Technology in Lausanne, Switzerland.