Physics-Based Animation

Yinwei Du, Yue Li, Stelian Coros, Bernhard Thomaszewski,

Modeling contact between deformable solids is a fundamental problem in computer animation, mechanical design, and robotics. Existing methods based on C0-discretizations—piece-wise linear or polynomial surfaces—suffer from discontinuities and irregularities in tangential contact forces, which can significantly affect simulation outcomes and even prevent convergence. In this work, we show that these limitations can be overcome with a smooth surface representation based on Implicit Moving Least Squares (IMLS). In particular, we propose a self collision detection scheme tailored to IMLS surfaces that enables robust and efficient handling of challenging self contacts. Through a series of test cases, we show that our approach offers advantages over existing methods in terms of accuracy and robustness for both forward and inverse problems.

Robust and Artefact-Free Deformable Contact with Smooth Surface Representations

Alexandre Mercier-Aubin, Paul G. Kry

We present a novel multi-layer method for extended position-based dynamics that exploits a sequence of reduced models consisting of rigid and elastic parts to speed up convergence. Taking inspiration from concepts like adaptive rigidification and long-range constraints, we automatically generate different rigid bodies at each layer based on the current strain rate. During the solve, the rigid bodies provide coupling between progressively less distant vertices during layer iterations, and therefore the fully elastic iterations at the final layer start from a lower residual error. Our layered approach likewise helps with the treatment of contact, where the mixed solves of both rigid and elastic in the layers permit fast propagation of impacts. We show several experiments that guide the selection of parameters of the solver, including the number of layers, the iterations per layers, as well as the choice of rigid patterns. Overall, our results show lower compute times for achieving a desired residual reduction across a variety of simulation models and scenarios.

A Multi-Layer Solver for XPBD

Lukas Westhofen, José Antonio Fernández-Fernández, Stefan Rhys Jeske, Jan Bender

We present a strongly coupled method for the robust simulation of linear magnetic rigid bodies. Our approach describes the magnetic effects as part of an incremental potential function. This potential is inserted into the reformulation of the equations of motion for rigid bodies as an optimization problem. For handling collision and friction, we lean on the Incremental Potential Contact (IPC) method. Furthermore, we provide a novel, hybrid explicit / implicit time integration scheme for the magnetic potential based on a distance criterion. This reduces the fill-in of the energy Hessian in cases where the change in magnetic potential energy is small, leading to a simulation speedup without compromising the stability of the system. The resulting system yields a strongly coupled method for the robust simulation of magnetic effects. We showcase the robustness in theory by analyzing the behavior of the magnetic attraction against the contact resolution. Furthermore, we display stability in practice by simulating exceedingly strong and arbitrarily shaped magnets. The results are free of artifacts like bouncing for time step sizes larger than with the equivalent weakly coupled approach. Finally, we showcase the utility of our method in different scenarios with complex joints and numerous magnets.

Strongly Coupled Simulation of Magnetic Rigid Bodies

Quoc-Minh Ton-That, Paul G. Kry, Sheldon Andrews

Traditional mesh-based methods for cutting deformable bodies rely on modifying the simulation mesh by deleting, duplicating, deforming or subdividing its elements. Unfortunately, such topological changes eventually lead to instability, reduced accuracy, or computational efficiency challenges. Hence, state of the art algorithms favor the extended finite element method (XFEM), which decouples the cut geometry from the simulation mesh, allowing for stable and accurate cuts at an additional computational cost that is local to the cut region. However, in the 3-dimensional setting, current XFEM frameworks are limited by the cutting configurations that they support. In particular, intersecting cuts are either prohibited or require sophisticated special treatment. Our work presents a general XFEM formulation that is applicable to the 1-, 2-, and 3-dimensional setting without sacrificing the desirable properties of the method. In particular, we propose a generalized enrichment which supports multiple intersecting cuts of various degrees of non-linearity by leveraging recent advances in robust mesh-Boolean technology. This novel strategy additionally enables analytic discontinuous integration schemes required to compute mass, force and elastic energy. We highlight the simplicity, expressivity and accuracy of our XFEM implementation across various scenarios in which intersecting cutting patterns are featured.

Generalized eXtended Finite Element Method for Deformable Cutting via Boolean Operations

Yalan Zhang, Long Shen, Yanrui Xu, and Xiaokun Wang, Chao Yao, Jiri Kosinka, Alexandru Telea, Steffen Frey, Xiaojuan Ban

We propose a method for simulating viscoelastic non-Newtonian fluids within a multiphase framework. For this, we use mixture models to handle component transport and conformation tensor methods to handle the fluid’s viscoelastic stresses. In addition, we consider a bonding effects network to handle the impact of microscopic chemical bonds on phase transport. Our method supports the simulation of both steady-state viscoelastic fluids and discontinuous shear behavior. Compared to previous work on single-phase viscous non-Newtonian fluids, our method can capture more complex behavior, including material mixing processes that generate non-Newtonian fluids. We adopt a uniform set of variables to describe shear thinning, shear thickening, and ordinary Newtonian fluids while automatically calculating local rheology in inhomogeneous solutions. In addition, our method can simulate large viscosity ranges under explicit integration schemes, which typically requires implicit viscosity solvers under earlier single-phase frameworks.

Multiphase Viscoelastic Non-Newtonian Fluid Simulation

Fabian Löschner, José Antonio Fernández-Fernández, Stefan Rhys Jeske, Jan Bender

Continuum-based shell models are an established approach for the simulation of thin deformables in computer graphics. However, existing research in physically-based animation is mostly focused on shear-rigid Kirchhoff-Love shells. In this work we explore three-director Cosserat (micropolar) shells which introduce additional rotational degrees of freedom. This microrotation field models transverse shearing and in-plane drilling rotations. We propose an incremental potential formulation of the Cosserat shell dynamics which allows for strong coupling with frictional contact and other physical systems. We evaluate a corresponding finite element discretization for non-planar shells using second-order elements which alleviates shear-locking and permits simulation of curved geometries. Our formulation and the discretization, in particular of the rotational degrees of freedom, is designed to integrate well with typical simulation approaches in physically-based animation. While the discretization of the rotations requires some care, we demonstrate that they do not pose significant numerical challenges in Newton’s method. In our experiments we also show that the codimensional shell model is consistent with the respective three-dimensional model. We qualitatively compare our formulation with Kirchhoff-Love shells and demonstrate intriguing use cases for the additional modes of control over dynamic deformations offered by the Cosserat model such as directly prescribing rotations or angular velocities and influencing the shell’s curvature.

Curved Three-Director Cosserat Shells with Strong Coupling

• Multiphase Viscoelastic Non-Newtonian Fluid Simulation
• Reconstruction of implicit surfaces from fluid particles using convolutional neural networks
• Unerosion: Simulating Terrain Evolution Back in Time
• Curved Three-Director Cosserat Shells with Strong Coupling
• Generalized eXtended Finite Element Method for Deformable Cutting via Boolean Operations
• Strongly Coupled Simulation of Magnetic Rigid Bodies
• A Multi-Layer Solver for XPBD
• Robust and Artefact-Free Deformable Contact with Smooth Surface Representations

Xuan Li, Minchen Li, Xuchen Han, Huamin Wang, Yin Yang, Chenfanfu Jiang

This paper presents a novel method to couple Finite Element Methods (FEM), typically employed for modeling Lagrangian solids such as flesh, cloth, hair, and rigid bodies, with Material Point Methods (MPM), which are well-suited for simulating materials undergoing substantial deformation and topology change, including Newtonian/non-Newtonian fluid, granular materials, and fracturing materials. The challenge of coupling these diverse methods arises from their contrasting computational needs: implicit FEM integration is often favored to enjoy stability and large timesteps, while explicit MPM integration benefits from its allowance for efficient GPU optimization and flexibility of applying different plasticity models, which only allows for moderate timesteps. To bridge this gap, a mixed implicit-explicit time integration (IMEX) approach is proposed, utilizing principles from time splitting for partial differential equations and optimization-based time integrators. This method adopts incremental potential contact (IPC) to define a variational frictional contact model between the two materials, serving as the primary coupling mechanism. Our method enables implicit FEM and explicit MPM to coexist with significantly different timestep sizes while preserving two-way coupling. Experimental results demonstrate the potential of our method as a strong foundation for future exploration and enhancement in the field of multi-material simulation.

A Dynamic Duo of Finite Elements and Material Points

Xing Shen, Runyuan Cai, Mengxiao Bi Tangjie Lv

The linear conjugate gradient method is widely used in physical simulation, particularly for solving large-scale linear systems derived from Newton’s method. The nonlinear conjugate gradient method generalizes the conjugate gradient method to nonlinear optimization, which is extensively utilized in solving practical large-scale unconstrained optimization problems. However, it is rarely discussed in physical simulation due to the requirement of multiple vector-vector dot products. Fortunately, with the advancement of GPU-parallel acceleration techniques, it is no longer a bottleneck. In this paper, we propose a Jacobi preconditioned nonlinear conjugate gradient method for elastic deformation using interior-point methods. Our method is straightforward, GPU-parallelizable, and exhibits fast convergence and robustness against large time steps. The employment of the barrier function in interior-point methods necessitates continuous collision detection per iteration to obtain a penetration-free step size, which is computationally expensive and challenging to parallelize on GPUs. To address this issue, we introduce a line search strategy that deduces an appropriate step size in a single pass, eliminating the need for additional collision detection. Furthermore, we simplify and accelerate the computations of Jacobi preconditioning and Hessian-vector product for hyperelasticity and barrier function. Our method can accurately simulate objects comprising over 100,000 tetrahedra in complex self-collision scenarios at real-time speeds.

Preconditioned Nonlinear Conjugate Gradient Method for Real-time Interior-point Hyperelasticity

Yushan Han, Yizhou Chen, Carmichael Ong, Jingyu Chen, Jennifer Hicks, Joseph Teran

We present a comprehensive neural network to model the deformation of human soft tissues including muscle, tendon, fat and skin. Our approach provides kinematic and active correctives to linear blend skinning [Magnenat-Thalmann et al. 1989] that enhance the realism of soft tissue deformation at modest computational cost. Our network accounts for deformations induced by changes in the underlying skeletal joint state as well as the active contractile state of relevant muscles. Training is done to approximate quasistatic equilibria produced from physics-based simulation of hyperelastic soft tissues in close contact. We use a layered approach to equilibrium data generation where deformation of muscle is computed first, followed by an inner skin/fascia layer, and lastly a fat layer between the fascia and outer skin. We show that a simple network model which decouples the dependence on skeletal kinematics and muscle activation state can produce compelling behaviors with modest training data burden. Active contraction of muscles is estimated using inverse dynamics where muscle moment arms are accurately predicted using the neural network to model kinematic musculotendon geometry. Results demonstrate the ability to accurately replicate compelling musculoskeletal and skin deformation behaviors over a representative range of motions, including the effects of added weights in body building motions.

A Neural Network Model for Efficient Musculoskeletal-Driven Skin Deformation