Post-Processing in the Material-Point Method

The material-point method (MPM) is a numerical method for dynamic or static analysis of solids using a discretization in time and space. The method has shown to be successful in modelling physical problems involving large deformations, which are difficult to model with traditional numerical tools such as the finite element method. In the material-point method, a set of material points is utilized to track the problem in time and space, while a computational background grid is utilized to obtain spatial derivatives relevant to the physical problem. Currently, the research within the material-point method focusses on establishing its accuracy and robustness. For easy evaluation of results, a good visualization of the deformation pattern as well as an accurate way to obtain the stresses is essential. This article introduces new ideas to improve the post-processing of results obtained by the material-point method. The first idea involves associating a volume with each material point and displaying the deformation of this volume. In the discretization process, the physical domain is divided into a number of smaller volumes each represented by a simple shape; here quadrilaterals are chosen for the presented two-dimensional problems. At the centroid of each of these sub domains, a material point is defined. The deformation gradient tensor associated with the material point is used to display deformation of the sub domain. This type of visualization is shown to dramatically improve visualization of large strain problems. It is noted, that this idea is also relevant for other point based methods, such as smoothed particle hydrodynamics, where the history dependent variables are tracked by a set of particles. The second idea introduced in the article involves the fact that while the stresses may oscillate in an unphysical fashion at the individual material points, a physically realistic stress field may often be obtained at the grid nodes. Further, a new way of remapping the stresses via the grid nodes is introduced to obtain more meaningful stress fields in the post processing. The new ideas are shown to improve the visual presentation of results from material-point method simulations and hence the understanding of the underlying physical problems to which the method is applied. Further, the way the stresses can be extracted reveals some pitfalls for the method and suggests a place to direct future research.