Implicit formulation of material point method for analysis of incompressible materials

Material point method (MPM) is a particle based numerical technique with application to solid mechanics problems involving large deformations. Recently, MPM has been successfully applied in many engineering applications including solid and solid-fluid interaction problems due to its capability to model complex history dependent material behaviours. However, the conventional explicit MPM approach exhibits numerical limitations in incompressible or near incompressible material behaviour problems. We study an implicit treatment of the pressure in MPM algorithm to simulate material incompressibility avoiding artificial pressure oscillations and significantly small time steps present in the explicit MPM approach. Applying Chorin's projection method to the velocity-pressure coupled equations, an elliptic equation is solved for the pressure which is then used to solve the divergence free velocity field. The results of dam break problem show no spurious pressure oscillations and large time steps compared to the traditional explicit MPM. The ability of the present implicit MPM formulation to model incompressible materials will be an additional advantage in simulating materials with complex constitutive equations which exhibit a time dependent memory.