Despite the presence of a background mesh, the MPM does not encounter the drawbacks of mesh-based methods (high deformation tangling, advection errors etc.)
Motivated by the need for better simulating penetration problems in solid dynamics, Sulsky, Chen and Schreyer started in 1993 to reformulate the PIC and develop the MPM, with funding from Sandia National Laboratories.
Recently, an MPM implementation based on a micro-polar Cosserat continuum[7] has been used to simulate high-shear granular flow, such as silo discharge.
The PIC method has been used to simulate a wide range of fluid-solid interactions, including sea ice dynamics,[9] penetration of biological soft tissues,[10] fragmentation of gas-filled canisters,[11] dispersion of atmospheric pollutants,[12] multiscale simulations coupling molecular dynamics with MPM,[13][14] and fluid-membrane interactions.
[15] In addition, the PIC-based FLIP code has been applied in magnetohydrodynamics and plasma processing tools, and simulations in astrophysics and free-surface flow.
[20][21] MPM has also become a widely used method within the field of soil mechanics: it has been used to simulate granular flow, quickness test of sensitive clays,[22] landslides,[23][24][25] silo discharge, pile driving, fall-cone test,[26][27][28][29] bucket filling, and material failure; and to model soil stress distribution,[30] compaction, and hardening.
It is now being used in wood mechanics problems such as simulations of transverse compression on the cellular level including cell wall contact.
Purely Eulerian methods, on the other hand, employ a framework in which the motion of material is described relative to a mesh that remains fixed in space throughout the calculation.
Unlike FEM, MPM does not require periodical remeshing steps and remapping of state variables, and is therefore better suited to the modeling of large material deformations.
Therefore, no numerical error results from the mesh returning to its original position after each calculation cycle, and no remeshing algorithm is required.
Spurious oscillation may occur as particles cross the boundaries of the mesh in MPM, although this effect can be minimized by using generalized interpolation methods (GIMP).