The Material Point Method (MPM) is a quasi Eulerian-Lagrangian approach to solve solid mechanics problems involving large deformations. In order to improve the stability of the MPM, several extensions have been proposed in the last decade. In these extensions, the sudden change of stiffness when a point crossing an element boundary in the standard MPM is avoided by replacing a material point with a deformable particle domain. The latest extensions are Convected Particle Domain Interpolation approaches, primarily including the CPDI1 and recently published CPDI2. We have unified the standard MPM and CPDI approaches into one implicit computational framework, and here investigate their ability to model problems involving large rotational deformation, which is essential in the installation of screw pile foundations. It was found that the CPDI2 approach can produce erroneous results due to particle domain distortion, while the CPDI1 approach and standard MPM can predict more physically realistic mechanical responses.