Examination and analysis of implementation choices within the material point method (MPM)

Journal ArticleThe Material Point Method (MPM) has shown itself to be a powerful tool in the simulation of large deformation problems, especially those involving complex geometries and contact where typical finite element type methods frequently fail. While these large complex problems lead to some impressive simulations and solutions, there has been a lack of basic analysis characterizing the errors present in the method, even on the simplest of problems

Improved contact algorithm for the material point method and application to stress propagation in granular material

Journal ArticleContact between deformable bodies is a difficult problem in the analysis of engineering systems. A new approach to contact has been implemented using the Material Point Method for solid mechanics, Bardenhagen, Brackbill, and Sulsky (2000a). Here two improvements to the algorithm are described. The first is to include the normal traction in the contact logic to more appropriately determine the free separation criterion. The second is to provide numerical stability by scaling the contact impulse when computational grid information is suspect, a condition which can be expected to occur occasionally as material bodies move through the computational grid. The modifications described preserve important properties of the original algorithm, namely conservation of momentum, and the use of global quantities which obviate the need for neighbor searches and result in the computational cost scaling linearly with the number of contacting bodies. The algorithm is demonstrated on several examples. Deformable body solutions compare favorably with several problems which, for rigid bodies, have analytical solutions. A much more demanding simulation of stress propagation through idealized granular material, for which high fidelity data has been obtained, is examined in detail. Excellent qualitative agreement is found for a variety of contact conditions. Important material parameters needed for more quantitative comparisons are identified

Improved velocity projection for the Material Point Method

Journal ArticleThe standard velocity projection scheme for the Material Point Method (MPM) and a typical form of the GIMP Method are examined. It is demonstrated that the fidelity of information transfer from a particle representation to the computational grid is strongly dependent on particle density and location. In addition, use of non-uniform grids and even non-uniform particle sizes are shown to introduce error