Augmented MPM for Phase-Change and Varied Materials

In this paper, we introduce a novel material point method for heat transport, melting and solidifying materials. This brings a wider range of material behaviors into reach of the already versatile mate- rial point method. This is in contrast to best-of-breed fluid, solid or rigid body solvers that are difficult to adapt to a wide range of ma- terials. Extending the material point method requires several contributions. We introduce a dilational/deviatoric splitting of the constitutive model and show that an implicit treatment of the Eulerian evolution of the dilational part can be used to simulate arbitrarily in- compressible materials. Furthermore, we show that this treatment reduces to a parabolic equation for moderate compressibility and an elliptic, Chorin-style projection at the incompressible limit. Since projections are naturally done on marker and cell (MAC) grids, we devise a staggered grid MPM method. Lastly, to generate varying material parameters, we adapt a heat-equation solver to a material point framework.