In this paper we describe a point-based approach for animating elastoplastic materials. Our primary contribution
is a simple method for computing the deformation gradient for each particle in the simulation. The deformation
gradient is computed for each particle by finding the affine transformation that best approximates the motion
of neighboring particles over a single timestep. These transformations are then composed to compute the total
deformation gradient that describes the deformation around a particle over the course of the simulation. Given
the deformation gradient we can apply arbitrary constitutive models and compute the resulting elastic forces. Our
method has two primary advantages: we do not store or compare to an initial rest configuration and we work
directly with the deformation gradient. The first advantage avoids poor numerical conditioning and the second
naturally leads to a multiplicative model of deformation appropriate for finite deformations. We demonstrate our
approach on a number of examples that exhibit a wide range of material behaviors.
D Gerszewski, H Bhattacharya, A. W. Bargteil
"A Point-based Method for Animating Elastoplastic Solids."
In ACM SIGGRAPH/Eurographics Symposium on Computer Animation 2009