Results - Densification

After obtaining previous simulation, we realized that there is no simple analytical solution to beam bending problem with newly imposed boundary conditions caused by nanotube contact. Physically, nanotubes exert mechanical forces and van der Waals forces on each other when they collide. Therefore we decided to incorporate Finite Element method to predict that shape of nanotubes for each step. 2-dimensional frame elements were used instead of 1-dimensional beam elements to properly capture large deformations the nanotubes have to undergo. The frame elements used have quadratic shape functions to account for element rotation [3]. The advantage of the frame elements is that they can have idividual orientations; by updating the shape of the CNT after each incremental interface migation step, we were able to model large deformations. Moreover, the boundary conditions after collision was succesfully incorporated in the model by applying a zero-relative displacement in the transverse direction for each set of colliding nodes similar to an attractive van der Waals.

After incorporating Finite Element model for the nanotubes, the whole phenomenon of densification could be simulated. The video showing two nanotubes pulling together and forming experimentally observed shape is shown below. The m-file needed for this simulation can be downloaded here.