All material point method (MPM) codes approximate the full mass matrix with a lumped mass matrix. Because this approach causes dissipation, most MPM simulations rely on so-called FLIP methods to limit dissipation. Recent work to deal with noise caused by those FLIP methods derived the XPIC method (for extended particle in cell method) that filters null space noise from particle velocities using a projection operator. This paper shows that the XPIC projection operator is equivalent to doing grid calculations using an asymptotic expansion of the full mass matrix inverse. From that insight, we derived FMPM(k) for full mass matrix MPM of order k (where the mass matrix inverse is expanded to k terms). Compared to prior MPM algorithms, FMPM changes the methods used to update particle velocities, positions, stresses, and strains. Several examples show that FMPM is more stable and accurate, has less dissipation than XPIC, and with high enough k has less dissipation than FLIP methods. One challenge in MPM is imposing velocity conditions on the grid and those challenges are amplified in FMPM. This paper describes a new moving-wall approach that improves grid boundary conditions and is beneficial to both FMPM and prior MPM. Finally, the use of FMPM for multimaterial mode MPM, with explicit cracks, and with affine extrapolation options is each discussed. (C) 2021 Elsevier B.V. All rights reserved.
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