Physics-Based Animation

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

Marcelo Martins, Lucas Morais, Rafael Torchelsen, Luciana Nedel, Anderson Maciel

Current endoscopy simulators oversimplify navigation and interaction within tubular anatomical structures to maintain interactive frame rates, neglecting the intricate dynamics of permanent contact between the organ and the medical tool. Traditional algorithms fail to represent the complexities of long, slender, deformable tools like endoscopes and hollow organs, such as the human colon, and their interaction.  In this paper, we address longstanding challenges hindering the realism of surgery simulators, explicitly focusing on these structures. One of the main components we introduce is a new model for the overall shape of the organ, which is challenging to retain due to the complex surroundings inside the abdomen. Our approach uses eXtended Position-Based Dynamics (XPBD) with a Cosserat rod constraint combined with a mesh of tetrahedrons to retain the colon’s shape. We also introduce a novel contact detection algorithm for tubular structures, allowing for real-time performance. This comprehensive representation captures global deformations and local features, significantly enhancing simulation fidelity compared to previous works. Results showcase that navigating the endoscope through our simulated colon seemingly mirrors real-world operations. Additionally, we use real-patient data to generate the colon model, resulting in a highly realistic virtual colonoscopy simulation. Integrating efficient simulation techniques with practical medical applications arguably advances surgery simulation realism.

Efficient Position-Based Deformable Colon Modeling for Endoscopic Procedures Simulation

Vismay Modi, Nicholas Sharp, Or Perel, Shinjiro Sueda, David I. W. Levin

The proliferation of 3D representations, from explicit meshes to implicit neural fields and more, motivates the need for simulators agnostic to representation. We present a data-, mesh-, and grid-free solution for elastic simulation for any object in any geometric representation undergoing large, nonlinear deformations. We note that every standard geometric representation can be reduced to an occupancy function queried at any point in space, and we define a simulator atop this common interface. For each object, we fit a small implicit neural network encoding spatially varying weights that act as a reduced deformation basis. These weights are trained to learn physically significant motions in the object via random perturbations. Our loss ensures we find a weight-space basis that best minimizes deformation energy by stochastically evaluating elastic energies through Monte Carlo sampling of the deformation volume. At runtime, we simulate in the reduced basis and sample the deformations back to the original domain. Our experiments demonstrate the versatility, accuracy, and speed of this approach on data including signed distance functions, point clouds, neural primitives, tomography scans, radiance fields, Gaussian splats, surface meshes, and volume meshes, as well as showing a variety of material energies, contact models, and time integration schemes.

Simplicits: Mesh-Free, Geometry-Agnostic, Elastic Simulation

Yizhou Chen, Yushan Han, Jingyu Chen, Zhan Zhang, Alex Mcadams, Joseph Teran

Position based dynamics [Müller et al. 2007] is a powerful technique for simulating a variety of materials. Its primary strength is its robustness when run with limited computational budget. Even though PBD is based on the projection of static constraints, it does not work well for quasistatic problems. This is particularly relevant since the efficient creation of large data sets of plausible, but not necessarily accurate elastic equilibria is of increasing importance with the emergence of quasistatic neural networks [Bailey et al. 2018; Chentanez et al. 2020; Jin et al. 2022; Luo et al. 2020]. Recent work [Macklin et al. 2016] has shown that PBD can be related to the Gauss-Seidel approximation of a Lagrange multiplier formulation of backward Euler time stepping, where each constraint is solved/projected independently of the others in an iterative fashion. We show that a position-based, rather than constraint-based nonlinear Gauss-Seidel approach resolves a number of issues with PBD, particularly in the quasistatic setting. Our approach retains the essential PBD feature of stable behavior with constrained computational budgets, but also allows for convergent behavior with expanded budgets. We demonstrate the efficacy of our method on a variety of representative hyperelastic problems and show that both successive over relaxation (SOR), Chebyshev and multiresolution-based acceleration can be easily applied.

Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity