A mesh-grading material point method and its parallelization for problems with localized extreme deformation

As a kind of meshless method, material point method (MPM) applies an Eulerian background grid served as a finite element mesh in each time step, and therefore its accuracy and efficiency are mainly dependent on the cell size setting of background grid. However, the conventional MPM commonly uses a regular background grid with uniform cells, which is not apposite for localized extreme deformation problems from the view point of computation efficiency, where, in fact, a local refined background grid is preferable. Hence, a mesh-grading material point method (MGMPM) is proposed here for such problems to supply MPM with the ability for local refinement simulation. The edge displacement continuity associated with mesh grading is embedded in the nodal shape functions. Besides, the truss element is incorporated into MGMPM to model the steel reinforcement bars in reinforced concrete impacting problems, based on our previous work. Furthermore, the proposed method is parallelized using OpenMP (Open Multi-Processing) to take advantage of PC power with multi-core and hyper threading technologies for large scale engineering problems, where both loop-level parallelism and code-block parallelism are used. Several numerical examples including stress wave propagation, Taylor bar impact, and penetration problems, are studied, which show that the efficiency of MGMPM is much higher than that of conventional MPM, and with lower memory requirement.