Material point method enhanced by modified gradient of shape function

Mitigating kinematic locking in the material point method

“…The cell-crossing error is caused by the sudden jump in strain rate as a particle moves from one cell to another. A potential solution to the cell-crossing error is to counteract the discontinuity of the gradient at the interface between adjacent cells by introducing an enhanced gradient field [63]. Alternatively, the particle can be represented using a finite domain, effectively smoothing out the discontinuity.…”

Temporal and null‐space filter for the material point method

“…The characteristic functions in GIMP give the material points domains (red square in Figure ) and continuous gradients. Another approach, which reduces the cell‐crossing errors, is DDMP . The DDMP replaces the gradient ∇S ip with a continuous function between the grid cells while leaving the shape functions intact.…”

“…However, in the simulations made with the original MPM, there are numerical noises when material points crossing the cell boundaries. These numerical inaccuracies led to the development of other MPM variants, including the generalized interpolation material point method (GIMP), the dual domain material point method (DDMP), and the B‐spline MPM . Those implementations improved the errors directly related to cell‐crossing, yet some high frequency noises are still present in the solutions.…”

Technical Report on NETL's Non Newtonian Multiphase Slurry Workshop: A path forward to understanding non-Newtonian multiphase slurry flows

“…can be naturally incorporated as well. In the MPPIC [16] and Material Point Method (MPM) methodology [17,18], parcels or notional particles are used to statistically describe the solid-phase, wherein each parcel represents more than one real particle. Although the statistical representation of solid phase by parcels representing more than one particle reduces the computational cost of MPPIC or MPM methodologies, it has the drawback that particle-particle interactions cannot be easily incorporated and need to be modeled.…”