Structured mesh refinement in generalized interpolation material point (GIMP) method for simulation of dynamic problems

The generalized interpolation material point (GIMP) method, recently developed using, a C-1 continuous weighting function, has solved the numerical noise problem associated with material points just crossing the cell borders, so that it is suitable for simulation of relatively large deformation problems. However, this method typically uses a uniform mesh in computation when one level of material points, is used, thus limiting its effectiveness in dealing with structures involving areas of high stress gradients. In this paper, a spatial refinement scheme of the structured grid for GIMP is presented for simulations with highly localized stress gradients. A uniform structured background grid is used in each refinement zone for interpolation in GIMP for ease of generating and duplicating structured grid in parallel processing. The concept of influence zone for the background node and transitional node is introduced for the mesh size transition. The grid shape function for the transitional node is modified accordingly, whereas the computation of the weighting function in GIMP remains the same. Two other issues are also addressed to improve the GIMP method. The displacement boundary conditions are introduced into the discretization of the momentum conservation equation in GIMP, and a method is implemented to track the deformation of the material particles by tracking the position of the particle corners to resolve the problem of artificial separation of material particles in GIMP simulations. Numerical simulations of several problems, such as tension, indentation, stress concentration and stress distribution near a crack (mode I crack problem) are presented to verify this refinement scheme.