Heuristic scheme in material point method for simulating material

Methods, apparatus, and computer readable storage medium for simulating and rendering a material with a modified material point method are described. The method includes, for each of a plurality of time-steps of simulating a material: transferring states of particles representing the material at a N-th time-step to a grid, determining a plurality of grid-node velocities at the N-th time-step using a particle-to-grid computation based on the states of the particles at the N-th time-step, updating the plurality of grid-node velocities at a (N+1)-th time-step based on grid forces, and updating the states of the particles at the (N+1)-th time-step using a grid-to-particle computation based on the states of the particles at the N-th time-step, the plurality of grid-node velocities at the N-th and (N+1)-th time-steps. The method further includes rendering one or more image depicting the material based on the states of the particles at the plurality of time-steps.