Effectiveness and limitations of Taylor particle-in-cell transfer and kernel correction for material point method

  • Nakamura, Keita (Port and Airport Research Institute)

Please login to view abstract download link

The material point method (MPM) has been extensively used to solve problems involving large displacements and deformations. The original MPM formulation [1], which adopts fluid-implicit-particle (FLIP) transfer [2], is less dissipative but also less stable than particle-in-cell (PIC) transfer [3]. The affine PIC (APIC) transfer [4] introduces the affine velocity and was developed to realize stable simulations while overcoming dissipations of the angular momentum in PIC. Recently, the Taylor PIC (TPIC) transfer, which is a type of APIC transfer that combines the affine velocity based on the first-order Taylor series approximation and PIC transfer, was proposed by Nakamura et al. [5] TPIC is simple (only the particle velocity gradient is required) and inherits the key advantages of the original APIC, such as less dissipation and stability. Furthermore, the MPM can cause stress oscillations near boundaries when boundary conditions are explicitly imposed, e.g., when the boundary grid velocity (or momentum) is set to zero. When affine-type transfers are used, this instability is exacerbated, and simulations can easily fail. A kernel correction method proposed by Nakamura et al. [5] is a simple approach to solve this problem. The method was developed so that the corrected kernels satisfy not only the partition of unity but also the linear field reproduction by using the weighted least squares for particles near boundaries. In this study, effectiveness and limitations of the TPIC transfer and the kernel correction are discussed through several numerical examples.