Implicit time integration for the material point method: Quantitative and algorithmic comparisons with the finite element method

An implicit integration strategy was developed and implemented for use with the material point method (MPM). An incremental‐iterative solution strategy was developed around Newton's method to solve the equations of motion with Newmark integration to update the kinematic variables. Test problems directly compared the implicit MPM solutions with those obtained using an explicit MPM code and implicit finite element (FE) code. Results demonstrated very good agreement with FE predictions and also illustrated several advantages in comparison to calculations using the explicit MPM code. In particular, the accuracy of the implicit solution was superior to the explicit MPM when compared to validated FE solutions, and by definition the implicit time integration is unconditionally stable. Similarities between the assembly of the implicit MPM equations and those of the FE method were identified and should allow further algorithmic improvement.