A. Stomakhin, C. Schroeder, C. Jiang, L. Chai, J. Teran, A. Selle.
Augmented MPM for Phase-Change and Varied Materials.
ACM SIGGRAPH 2014.
In this paper, we introduce a novel material point method
(MPM) for heat transport, melting and solidifying
materials. This brings a wider range of material behaviors
into reach of the already versatile material 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 materials. 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 incompressible 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.