Month: September 2021

Seung Heon Sheen, Egor Larionov, Dinesh K. Pai

Simulation of human soft tissues in contact with their environment is essential in many fields, including visual effects and apparel design. Biological tissues are nearly incompressible. However, standard methods
employ compressible elasticity models and achieve incompressibility indirectly by setting Poisson’s ratio to be close to 0.5. This approach can produce results that are plausible qualitatively but inaccurate quantatively.
This approach also causes numerical instabilities and locking in coarse discretizations or otherwise poses a prohibitive restriction on the size of the time step. We propose a novel approach to alleviate these issues by replacing indirect volume preservation using Poisson’s ratios with direct enforcement of zonal volume constraints, while controlling fine-scale volumetric deformation through a cell-wise compression penalty.
To increase realism, we propose an epidermis model to mimic the dramatically higher surface stiffness on real skinned bodies. We demonstrate that our method produces stable realistic deformations with precise volume preservation but without locking artifacts. Due to the volume preservation not being tied to mesh discretization, our method also allows a resolution consistent simulation of incompressible materials. Our method improves the stability of the standard neo-Hookean model and the general compression recovery in the Stable neo-Hookean model.

Volume Preserving Simulation of Soft Tissue with Skin

Sheldon Andrews, Loic Nassif, Kenny Erleben, Paul Kry

We present a novel meso-scale model for computing anisotropic and asymmetric friction for contacts in rigid body simulations that is based on surface facet orientations. The main idea behind our approach is to compute a direction dependent friction coefficient that is determined by an object’s roughness. Specifically, where the friction is dependent on asperity interlocking, but at a scale where surface roughness is also a visual
characteristic of the surface. A GPU rendering pipeline is employed to rasterize surfaces using a shallow depth orthographic projection at each contact point in order to sample facet normal information from both surfaces, which we then combine to produce direction dependent friction coefficients that can be directly used in typical LCP contact solvers, such as the projected Gauss-Seidel method. We demonstrate our approach with a variety of rough textures, where the roughness is both visible in the rendering and in the motion produced by the physical simulation.

Coupling Friction with Visual Appearance

Tassilo Kugelstadt, Jan Bender, José Antonio Fernández-Fernández, Stefan Rhys Jeske, Fabian Löschner and Andreas Longva

We develop a new operator splitting formulation for the simulation of corotated linearly elastic solids with Smoothed Particle Hydrodynamics (SPH). Based on the technique of Kugelstadt et al. [2018] originally devel-
oped for the Finite Element Method (FEM), we split the elastic energy into two separate terms corresponding to stretching and volume conservation, and based on this principle, we design a splitting scheme compatible with
SPH. The operator splitting scheme enables us to treat the two terms separately, and because the stretching forces lead to a stiffness matrix that is constant in time, we are able to prefactor the system matrix for the
implicit integration step. Solid-solid contact and fluid-solid interaction is achieved through a unified pressure solve. We demonstrate more than an order of magnitude improvement in computation time compared to a
state-of-the-art SPH simulator for elastic solids. We further improve the stability and reliability of the simulation through several additional contributions. We introduce a new implicit penalty mechanism that suppresses zero-energy modes inherent in the SPH formulation for elastic solids, and present a new, physics-inspired sampling algorithm for generating high-quality particle distributions for the rest shape of an elastic solid. We finally also devise an efficient method for interpolating vertex positions of a high-resolution surface mesh based on the SPH particle positions for use in high-fidelity visualization.

Fast Corotated Elastic SPH Solids with Implicit Zero-Energy Mode Control

Tao Du, Kui Wu, Pingchuan Ma, Sebastien Wah, Andrew Spielberg, Daniela Rus, Wojciech Matusik

We present a novel, fast differentiable simulator for soft-body learning and control applications. Existing differentiable soft-body simulators can be classified into two categories based on their time integration methods: Simulators using explicit time-stepping scheme require tiny time steps to avoid numerical instabilities in gradient computation, and simulators using implicit time integration typically compute gradients by employing the adjoint method and solving the expensive linearized dynamics. Inspired by Projective Dynamics (PD), we present Differentiable Projective Dynamics (DiffPD), an efficient differentiable soft-body simulator based on PD with implicit time integration. The key idea in DiffPD is to speed up backpropagation by exploiting the prefactorized Cholesky decomposition in forward PD simulation. In terms of contact handling, DiffPD supports two types of contacts: a penalty-based model describing contact and friction forces and a complementarity-based model enforcing non-penetration conditions and static friction. We evaluate the performance of DiffPD and observe it is 4-19 times faster compared to the standard Newton’s method in various applications including system identification, inverse design problems, trajectory optimization, and closed-loop control. We also apply DiffPD in a real-to-sim example with contact and collisions and show its capability of reconstructing a digital twin of real-world scenes.

DiffPD: Differentiable Projective Dynamics