Analysis of Stress Updates in the Material-point Method

The material-point method (MPM) is a new numerical method for analysis of large strain engineering problems. The MPM applies a dual formulation, where the state of the problem (mass, stress, strain, velocity etc.) is tracked using a finite set of material points while the governing equations are solved on a background computational grid. Several references state, that one of the main advantages of the material-point method is the easy application of complicated material behaviour as the constitutive response is updated individually for each material point. However, as discussed here, the MPM way updating and integrating stresses in time is problematic. This is discussed using an example of the dynamical collapse of a soil column.