The Dual-Domain Material Point Method for Triangular Meshes

The Dual-Domain Material Point Method (DDMP), introduced by Zhang in 2011, was designed to resolve the cell-crossing instability in the Material Point Method (MPM). DDMP calculates internal nodal forces using a continuous modified gradient of the shape function, preventing sign changes in nodal forces as a material point crosses cell boundaries and thus reducing numerical noise seen in classical MPM calculations. To date, DDMP has been implemented and studied with quadrilateral meshes in 2D and hexahedron meshes in 3D. In this work, we have extended and implemented DDMP using triangular background meshes and demonstrated its advantages over classical MPM.