Figure 1: Sand falls through the narrow neck of an hourglass, accumulating at the bottom. AbstractWe simulate sand dynamics using an elastoplastic, continuum assumption. We demonstrate that the Drucker-Prager plastic flow model combined with a Hencky-strain-based hyperelasticity accurately recreates a wide range of visual sand phenomena with moderate computational expense. We use the Material Point Method (MPM) to discretize the governing equations for its natural treatment of contact, topological change and history dependent constitutive relations. The Drucker-Prager model naturally represents the frictional relation between shear and normal stresses through a yield stress criterion. We develop a stress projection algorithm used for enforcing this condition with a non-associative flow rule that works naturally with both implicit and explicit time integration. We demonstrate the efficacy of our approach on examples undergoing large deformation, collisions and topological changes necessary for producing modern visual effects.
Fig. 1. Ink drop. We compare from left to right FLIP, APIC, and PolyPIC for an inkjet in an ambient incompressible fluid. PolyPIC more effectively resolves the vorticial details.Recently the Affine Particle-In-Cell (APIC) Method was proposed by 2017b] to improve the accuracy of the transfers in Particle-In-Cell (PIC) [Harlow 1964] techniques by augmenting each particle with a locally affine, rather than locally constant description of the velocity. This reduced the dissipation of the original PIC without suffering from the noise present in the historic alternative, Fluid-Implicit-Particle (FLIP) [Brackbill and Ruppel 1986]. We present a generalization of APIC by augmenting each particle with a more general local function. By viewing the grid-to-particle transfer as a linear and angular momentum conserving projection of the particle-wise local grid velocities onto a reduced basis, we greatly improve the energy and vorticity conservation over the original APIC. Furthermore, we show that the cost of the generalized projection is negligible over APIC when using a particular class of local polynomial functions. Lastly, we note that our method retains the filtering property of APIC and PIC and thus has similar robustness to noise.
Fig. 1. Dam breach. Water pours in from a reservoir and slowly erodes a dam. As water seeps into the sand, its cohesivity decreases. When it eventually breaks, the landslide creates interesting dynamics in the debris flow. We present a multi-species model for the simulation of gravity driven landslides and debris flows with porous sand and water interactions. We use continuum mixture theory to describe individual phases where each species individually obeys conservation of mass and momentum and they are coupled through a momentum exchange term. Water is modeled as a weakly compressible fluid and sand is modeled with an elastoplastic law whose cohesion varies with water saturation. We use a two-grid Material Point Method to discretize the governing equations. The momentum exchange term in the mixture theory is relatively stiff and we use semi-implicit time stepping to avoid associated small time steps. Our semi-implicit treatment is explicit in plasticity and preserves symmetry of force linearizations. We develop a novel regularization of the elastic part of the sand constitutive model that better mimics plasticity during the implicit solve to prevent numerical cohesion artifacts that would otherwise have occurred. Lastly, we develop
Fig. 1. Shell Montage. Upper left : simulation of shells coupled with granular materials. Center left : a walk cycle benchmark for clothing simulation. Bottom right : a T-shirt twisted to induce many self-collisions. Center : the effect of increasing bending stiffness (from left to right) for six collapsing elastic cylinders. 147:2 • Q. Guo et. al. Fig. 2. Elastic spheres on diving boards. We demonstrate appealing dynamics achieved with self-collision and appreciable bending for shells. Both the spheres and the diving boards are simulated as thin shells.
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