Validation and Applications of the Material Point Method

The Material Point Method (MPM) is a modern finite element method that is classified as a point based method or meshless method, while it takes the advantage of two kinds of spatial discretisation that are based on an arbitrary Eulerian-Lagrangian description of motion. The referenced continuum is represented by the material points, and the motions are tracked through a computational background mesh, that is an arbitrary constant mesh which does not move the material. Hence, in the MPM mesh distortion especially in the large deformation analysis is naturally avoided. However, MPM has been employed to simulate difficult problems in the literature, many are still unsatisfactory due to the lack of rigorous validation. Therefore, this thesis firstly provides a series of simple case studies which any numerical method must pass to test the validity of the MPM, and secondly demonstrate the capability of the MPM in simulating difficult problems such as degradation of highly swellable polymers during large swelling that is currently difficult to handle by the standard finite element method. Flory’s theory is incorporated into the material point method to study large swelling of polymers, and degradation of highly swellable polymers is modelled by the MPM as a random phenomenon based on the normal distribution of the volumetric strain. These numerical developments represent adaptability of the MPM and enabling the method to be used in more complicated simulations. Furthermore, the advantages of this powerful numerical tool are studied in the modelling of an additive manufacturing technology called Selective Laser Melting (SLM). It is shown the MPM is an ideal numerical method to study SLM manufacturing technique. The focus of this thesis is to validate the MPM and exhibit the simplicity, strength, and accuracy of this numerical tool compared with standard finite element method for very complex problems which requires a complicated topological system.