Shrinkage and swelling during 3D printing

3D printing has led to a manufacturing revolution by enabling complex objects to be rapidly created at a low cost. A large number of 3D printers work by using a single wavelength of light to convert liquid into solid in a layer-by-layer fashion. That is, a layer of liquid is placed on top of an existing solid structure and then exposed to light to create a new solid layer. Mathematical modelling plays a critical role in 3D printing by predicting the experimental conditions, such as the light intensity and exposure time, that are needed to grow a given shape.

During 3D printing, the solid structure can shrink or swell. On one hand, shrinkage and swelling are detrimental because they lead to large distortions. 3D printers must take this distortion into account in order to produce desired shapes. On the other hand, shrinkage and swelling can lead to bending and mechanical instabilities such as wrinkling. These instabilities can be harnessed to self-assemble complex shapes that are difficult to produce using conventional 3D printers.

The overall goal of this project is to develop a new suite of models for 3D printing that account for shrinkage and swelling. These models will be used to create a software package that takes as input the 3D shape to be produced and outputs the required experimental conditions. Specific objectives include:

• Building discrete and continuum models of 3D printing that account for the mechanics of shrinkage and swelling
• Numerically solving these models in Python or Matlab and carrying out relevant mathematical analyses
• Solving inverse and optimal control problems to determine how to 3D print specific shapes, possibly with machine learning

This project will be carried out in collaboration with researchers at Imperial College London.