Slicing vector fields into tool paths for additive manufacturing of nematic elastomers

During additive manufacturing, it is normally assumed that the tool path does not affect the material properties, which is thus chosen to achieve the target geometry/strength while minimising the print time. However, in anisotropic materials the printing direction can be used to direct the anisotropy, for example, shear stresses during extrusion align liquid crystal elastomers (LCEs) along the print direction, which then dictates the direction of anisotropic deformations under thermal stimulation. By patterning the print direction, and hence the contraction direction, one can fabricate LCE sheets programmed to undergo complex deformations. Therefore, the slicing algorithm needs to provide control over both the geometry of the sample and the printing direction. In this work, we present a slicing algorithm which translates arbitrary planar unit vector fields into sets of print-paths, by seeding paths based on the divergence of the desired pattern. The manuscript is accompanied by an open-source implementation called Vector Slicer, and we demonstrate its capabilities by printing numerous LCE designs that reversibly morph from flat sheets into complex 3D shapes on heating. Previously, AM of LCEs has been limited to extremely elementary patterns sliced by hand. Our approach to slicing arbitrary patterns is thus a significant advancement for AM of LCEs and will enable similar patterned AM in a range of other materials.