We present a family of mixed Material Point Methods well suited for the CFL-rate simulation of stiff elastoviscoplastic materials, up to the incompressible limit. Our work builds upon the mixed discretization from Daviet and Bertails-Descoubes [2016a] and extends it to handle finite-strain vis-coelasticity and more general flow rules, allowing the simulation of a much wider range of materials. Our implicit integration scheme leads to a well-posed, symmetric optimization problem with compact stencils for which we propose an efficient GPU solver. We demonstrate our method on a variety of examples ranging from granular materials and snow to elastic solids, including two-way coupling with rigid-body solvers.

We introduce SimAvatar, a framework designed to generate simulation-ready clothed 3D human avatars from a text prompt. Current text-driven human avatar generation methods either model hair, clothing, and the human body using a unified geometry or produce hair and garments that are not easily adaptable for simulation within existing simulation pipelines. The primary challenge lies in representing the hair and garment geometry in a way that allows leveraging established prior knowledge from foundational image diffusion models (e.g., Stable Diffusion) while being simulation-ready using either physics or neural simulators. To address this task, we propose a two-stage framework that combines the flexibility of 3D Gaussians with simulation-ready hair strands and garment meshes. Specifically, we first employ three text-conditioned 3D generative models to generate garment mesh, body shape and hair strands from the given text prompt. To leverage prior knowledge from foundational diffusion models, we attach 3D Gaussians to the body mesh, garment mesh, as well as hair strands and learn the avatar appearance through optimization. To drive the avatar given a pose sequence, we first apply physics simulators onto the garment meshes and hair strands. We then transfer the motion onto 3D Gaussians through carefully designed mechanisms for each body part. As a result, our synthesized avatars have vivid texture and realistic dynamic motion. To the best of our knowledge, our method is the first to produce highly realistic, fully simulation-ready 3D avatars, surpassing the capabilities of current approaches. Project page: https://research.nvidia.com/labs/dair/simavatar/

We present an elastic simulator for domains defined as evolving implicit functions, which is efficient, robust, and differentiable with respect to both shape and material. This simulator is motivated by applications in 3D reconstruction: it is increasingly effective to recover geometry from observed images as implicit functions, but physical applications require accurately simulating and optimizing-for the behavior of such shapes under deformation, which has remained challenging. Our key technical innovation is to train a small neural network to fit quadrature points for robust numerical integration on implicit grid cells. When coupled with a Mixed Finite Element formulation, this yields a smooth, fully differentiable simulation model connecting the evolution of the underlying implicit surface to its elastic response. We demonstrate the efficacy of our approach on forward simulation of implicits, direct simulation of 3D shapes during editing, and novel physics-based shape and topology optimizations in conjunction with differentiable rendering.

We introduce Loki, a new framework for robust simulation of fluid, rigid, and deformable objects with non-compromising fidelity on any single element, and capabilities for coupling and representation transitions across multiple elements. Loki adapts multiple best-in-class solvers into a unified framework driven by a declarative state machine where users declare 'what' is simulated but not 'when,' so an automatic scheduling system takes care of mixing any combination of objects. This leads to intuitive setups for coupled simulations such as hair in the wind or objects transitioning from one representation to another, for example bulk water FLIP particles to SPH spray particles to volumetric mist. We also provide a consistent treatment for components used in several domains, such as unified collision and attachment constraints across 1D, 2D, 3D deforming and rigid objects. Distribution over MPI, custom linear equation solvers, and aggressive application of sparse techniques keep performance within production requirements. We demonstrate a variety of solvers within the framework and their interactions, including FLIPstyle liquids, spatially adaptive volumetric fluids, SPH, MPM, and mesh-based solids, including but not limited to discrete elastic rods, elastons, and FEM with state-of-the-art constitutive models. Our framework has proven powerful and intuitive enough for voluntary artist adoption and has delivered creature and FX simulations for multiple major movie productions in the preceding four years.

Frictional contacts are the primary way by which physical bodies interact, yet they pose many numerical challenges. Previous works have devised robust methods for handling collisions in elastic bodies, cloth, or fiber assemblies such as hair, but the performance of many of those algorithms degrades when applied to objects with different topologies or constitutive models, or simply cannot scale to high-enough numbers of contacting points. In this work we propose a unified approach, able to handle a large class of dynamical objects, that can solve for millions of contacts with unbiased Coulomb friction while keeping computation time and memory usage reasonable. Our method allows seamless coupling between the various simulated components that comprise virtual characters and their environment. Furthermore, our proposed approach is simple to implement and can be easily integrated in popular time integrators such as Projected Newton or ADMM.

Cloth dynamics plays an important role in the visual appearance of moving characters. Properly accounting for contact and friction is of utmost importance to avoid cloth-body and cloth-cloth penetration and to capture typical folding and stick-slip behavior due to dry friction. We present here the first method able to account for cloth contact with exact Coulomb friction, treating both cloth self-contacts and contacts occurring between the cloth and an underlying character. Our key contribution is to observe that for a nodal system like cloth, the frictional contact problem may be formulated based on velocities as primary variables, without having to compute the costly Delassus operator. Then, by reversing the roles classically played by the velocities and the contact impulses, conical complementarity solvers of the literature can be adapted to solve for compatible velocities at nodes. To handle the full complexity of cloth dynamics scenarios, we have extended this base algorithm in two ways: first, towards the accurate treatment of frictional contact at any location of the cloth, through an adaptive node refinement strategy; second, towards the handling of multiple constraints at each node, through the duplication of constrained nodes and the adding of pin constraints between duplicata. Our method allows us to handle the complex cloth-cloth and cloth-body interactions in full-size garments with an unprecedented level of realism compared to former methods, while maintaining reasonable computational timings.

We present a new continuum-based method for the realistic simulation of large-scale free-flowing granular materials. We derive a compact model for the rheology of the material, which accounts for the exact nonsmooth Drucker-Prager yield criterion combined with a varying volume fraction. Thanks to a semi-implicit time-stepping scheme and a careful spatial discretization of our rheology built upon the Material-Point Method, we are able to preserve at each time step the exact coupling between normal and tangential stresses, in a stable way. This contrasts with previous approaches which either regularize or linearize the yield criterion for implicit integration, leading to unrealistic behaviors or visible grid artifacts. Remarkably, our discrete problem turns out to be very similar to the discrete contact problem classically encountered in multibody dynamics, which allows us to leverage robust and efficient nonsmooth solvers from the literature. We validate our method by successfully capturing typical macroscopic features of some classical experiments, such as the discharge of a silo or the collapse of a granular column. Finally, we show that our method can be easily extended to accommodate more complex scenarios including two-way rigid body coupling as well as anisotropic materials.

In the latest years, considerable progress has been achieved for accurately acquiring the geometry of human hair, thus largely improving the realism of virtual characters. In parallel, rich physics-based simulators have been successfully designed to capture the intricate dynamics of hair due to contact and friction. However, at the moment there exists no consistent pipeline for converting a given hair geometry into a realistic physics-based hair model. Current approaches simply initialize the hair simulator with the input geometry in the absence of external forces. This results in an undesired sagging effect when the dynamic simulation is started, which basically ruins all the efforts put into the accurate design and/or capture of the input hairstyle. In this paper we propose the first method which consistently and robustly accounts for surrounding forces---gravity and frictional contacts, including hair self-contacts---when converting a geometric hairstyle into a physics-based hair model. Taking an arbitrary hair geometry as input together with a corresponding body mesh, we interpret the hair shape as a static equilibrium configuration of a hair simulator, in the presence of gravity as well as hair-body and hair-hair frictional contacts. Assuming that hair parameters are homogeneous and lie in a plausible range of physical values, we show that this large underdetermined inverse problem can be formulated as a well-posed constrained optimization problem, which can be solved robustly and efficiently by leveraging the frictional contact solver of the direct hair simulator. Our method was successfully applied to the animation of various hair geometries, ranging from synthetic hairstyles manually designed by an artist to the most recent human hair data automatically reconstructed from capture.

We focus on the challenging problem of simulating thin elastic rods in contact, in the presence of friction. Most previous approaches in computer graphics rely on a linear complementarity formulation for handling contact in a stable way, and approximate Coulombs's friction law for making the problem tractable. In contrast, following the seminal work by Alart and Curnier in contact mechanics, we simultaneously model contact and exact Coulomb friction as a zero finding problem of a nonsmooth function. A semi-implicit time-stepping scheme is then employed to discretize the dynamics of rods constrained by frictional contact: this leads to a set of linear equations subject to an equality constraint involving a nondifferentiable function. To solve this one-step problem we introduce a simple and practical nonsmooth Newton algorithm which proves to be reasonably efficient and robust for systems that are not overconstrained. We show that our method is able to finely capture the subtle effects that occur when thin elastic rods with various geometries enter into contact, such as stick-slip instabilities in free configurations, entangling curls, resting contacts in braid-like structures, or the formation of tight knots under large constraints. Our method can be viewed as a first step towards the accurate modeling of dynamic fibrous materials.

Dry friction between hair fibers plays a major role in the collective hair dynamic behavior as it accounts for typical nonsmooth features such as stick-slip instabilities. However, due the challenges posed by the modeling of nonsmooth friction, previous mechanical models for hair either neglect friction or use an approximate smooth friction model, thus losing important visual features. In this paper we present a new generic robust solver for capturing Coulomb friction in large assemblies of tightly packed fibers such as hair. Our method is based on an iterative algorithm where each single contact problem is efficiently and robustly solved by introducing a hybrid strategy that combines a new zero-finding formulation of (exact) Coulomb friction together with an analytical solver as a fail-safe. Our global solver turns out to be very robust and highly scalable as it can handle up to a few thousand densely packed fibers subject to tens of thousands frictional contacts at a reasonable computational cost. It can be conveniently combined to any fiber model with various rest shapes, from smooth to curly. Our results, visually validated against real hair motions, depict typical hair collective effects and greatly enhance the realism of standard hair simulators.