MPM for melting and solidifying materials using a heat solver to capture the underlying thermodynamics and alter mechanical parameters
Abstract
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 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.
Author
Alexey Stomakhin, Walt Disney Animation Studios
Craig Schroeder, University of California Los Angeles
Chenfanfu Jiang, University of California Los Angeles
Lawrence Chai, Walt Disney Animation Studios
Joseph Teran, Walt Disney Animation Studios and University of California Los Angeles
Andrew Selle, Walt Disney Animation Studios
Journal/Conference
ACM Transactions on Graphics (TOG), Volume 33 Issue 4, July 2014
Summary
MPM for melting and solidifying materials using a heat solver to capture the underlying thermodynamics and alter mechanical parameters
Abstract
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 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.
Author
Journal/Conference
ACM Transactions on Graphics (TOG), Volume 33 Issue 4, July 2014
Link