Month: July 2020

Doug L. James

Physics-based simulations of deforming tetrahedral meshes are widely used to animate detailed embedded geometry. Unfortunately most practitioners still use linear interpolation (or other low-order schemes) on tetrahedra, which can produce undesirable visual artifacts, e.g., faceting and shading artifacts, that necessitate increasing the simulation’s spatial resolution and, unfortunately, cost. In this paper, we propose Phong Deformation, a simple, robust and practical vertex-based quadratic interpolation scheme that, while still only C0 continuous like linear interpolation, greatly reduces visual artifacts for embedded geometry. The method first averages element-based linear deformation models to vertices, then barycentrically interpolates the vertex models while also averaging with the traditional linear interpolation model. The method is a fast, robust, and easily implemented replacement for linear interpolation that produces visually better results for embedded deformation with irregular tetrahedral meshes.

Phong Deformation: A better C0 interpolant for embedded deformation

Joshuah Wolper, Yunuo Chen, Minchen Li, Yu Fang, Ziyin Qu, Jiecong Lu, Meggie Cheng, Chenfanfu Jiang

Dynamic fracture surrounds us in our day-to-day lives, but animating this phenomenon is notoriously difficult and only further complicated by anisotropic materials—those with underlying structures that dictate preferred fracture directions. Thus, we present AnisoMPM: a robust and general approach for animating the dynamic fracture of isotropic, transversely isotropic, and orthotropic materials. AnisoMPM has three core components: a technique for anisotropic damage evolution, methods for anisotropic elastic response, and a coupling approach. For anisotropic damage, we adopt a non-local continuum damage mechanics (CDM) geometric approach to crack modeling and augment this with structural tensors to encode material anisotropy. Furthermore, we discretize our damage evolution with explicit and implicit integration, giving a high degree of computational efficiency and flexibility. We also utilize a QR-decomposition based anisotropic constitutive model that is inversion safe, more efficient than SVD models, easy to implement, robust to extreme deformations, and that captures all aforementioned modes of anisotropy. Our elasto-damage coupling is enforced through an additive decomposition of our hyperelasticity into a tensile and compressive component in which damage is used to degrade the tensile contribution to allow for material separation. For extremely stiff fibered materials, we further introduce a novel Galerkin weak form discretization that enables embedded directional inextensibility. We present this as a hard-constrained grid velocity solve that poses an alternative to our anisotropic elasticity that is locking-free and can model very stiff materials.

AnisoMPM: Animating Anisotropic Damage Mechanics

Jan Bender, Tassilo Kugelstadt, Marcel Weiler, Dan Koschier

In this paper, we present a novel method for the robust handling of static and dynamic rigid boundaries in Smoothed Particle Hydrodynamics (SPH) simulations. We build upon the ideas of the density maps approach which has been introduced recently by Koschier and Bender. They precompute the density contributions of solid boundaries and store them on a spatial grid which can be efficiently queried during runtime. This alleviates the problems of commonly used boundary particles, like bumpy surfaces and inaccurate pressure forces near boundaries. Our method is based on a similar concept but we precompute the volume contribution of the boundary geometry. This maintains all benefits of density maps but offers a variety of advantages which are demonstrated in several experiments. Firstly, in contrast to the density maps method we can compute derivatives in the standard SPH manner by differentiating the kernel function. This results in smooth pressure forces, even for lower map resolutions, such that precomputation times and memory requirements are reduced by more than two orders of magnitude compared to density maps. Furthermore, this directly fits into the SPH concept so that volume maps can be seamlessly combined with existing SPH methods. Finally, the kernel function is not baked into the map such that the same volume map can be used with different kernels. This is especially useful when we want to incorporate common surface tension or viscosity methods that use different kernels than the fluid simulation.

Implicit Frictional Boundary Handling for SPH