On the use of the material point method to model problems involving large rotational deformation

The Material Point Method (MPM) is a quasi Eulerian-Lagrangian approach to solve solid
mechanics problems involving large deformations. The standard MPM [1] discretises the
physical domain using material points which are advected through a standard finite element
background mesh. The method of mapping state variables back and forth between the material
points and background mesh nodes in the MPM significantly influences the results. In the
standard MPM (sMPM), a material point only influences its parent element (i.e. the
background element in which it is located), which can cause spurious stress oscillations when
material points cross between elements. The instability is due to the sudden transfer of
stiffness between elements. It can also result in some elements having very little stiffness or
some internal elements loosing all stiffness. Therefore, several extensions to the sMPM have
been proposed, each of which replaces the material point with a deformable particle domain.
The most notable of these extensions are the Generalised Interpolation Material Point
(GIMP), the Convected Particle Domain Interpolation (CPDI1) and Second-order CPDI
(CPDI2) methods [2]. In this paper, the sMPM, CPDI1 and CPDI2 approaches are unified for
geometrically non-linear elasto-plastic problems using an implicit solver and their
performance investigated for large rotational problems. This type of deformation is common
in applications in the area of soil mechanics, for example the vane shear test and, specifically
of interest here, the installation of screw piles. Screw piles are currently used as an onshore
foundation solution and research being undertaken at Durham, Dundee and Southampton
universities is exploring their use in the area of offshore renewables. The numerical modelling
using the MPM aims to predict the installation torque and vertical force as well as
understanding the “state” of the soil around the screw pile which is critical in understanding
the long term performance of the foundation. In the analysis, the pile is assumed to be a rigid
body and no-slip boundary condition is used at the pile-soil interface. The boundary condition
is imposed using the moving mesh concept within an unstructured mesh fixed to the pile. It
will be shown that the CPDI2 approach produces erroneous torque due to particle domain
distortion, while the CPDI1 approach and sMPM predict physically realistic mechanical
responses.