Implicit MPM with second-order convected particle domain interpolation

An implicit material point method (MPM) with the second-order convected particle interpolation (CPDI2) is presented in this paper. In the MPM a body is described by a number of Lagrangian material points, at which state variables are stored and tracked. Calculations are then carried out on a background Eulerian computational mesh. A mapping and re-mapping algorithm is employed, to allow the state variables and other information to be mapped back and forth between the material points and background mesh nodes during an analysis. To reduce the error during these mappings, there are several extensions. The latest extension is termed CPDI2, which uses a quadrilateral particle domain to replace a material point. The CPDI2 extension has been implemented explicitly with using regular grids in published papers. This work develops an implicit CPDI2 method with an elasto-plastic material model. The motivation is that an implicit scheme can reduce the computational cost by allowing a large time step, while enforcing the yield condition accurately and increase stability. Both quadrilateral and triangular particle domains are used. An example shows that the use of a triangular particle domain is more flexible than the quadrilateral particle domain.