Stable Neo-Hookean Flesh Simulation

Smith, Breannan; Goes, Fernando de; Kim, Theodore

doi:10.1145/3180491

Cited by 126 publications

(109 citation statements)

References 46 publications

(51 reference statements)

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“…During the Newton solve we evaluate N at each iteration and perform a direct inversion of it to obtain E. A practical consideration for hyperelastic materials is that, as E is the inverse of a Hessian it may be indefinite, in which case it may be necessary to project it back to the positive definite cone before including it in our system matrices [Teran et al 2005], although we have also found that a simple diagonal approximation to E is often sufficient. In Appendix B we give the derivation of E = ( ∂ 2 U ∂s 2 ) −1 for the stable Neo-Hookean model presented by Smith et al [2018].…”

Section: Hyperelasticmentioning

confidence: 99%

“…While solving LCP problems efficiently is still the subject of active research, as a model they may not capture all of the dynamics we wish to simulate. For example, hyperelastic materials have highly nonlinear forces that significantly affect behavior compared to linear models [Smith et al 2018]. In addition, contact models themselves may be nonlinear particularly when considering compliance and deformation [Li and Kao 2001].…”

Section: Introductionmentioning

confidence: 99%

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Non-smooth Newton Methods for Deformable Multi-body Dynamics

et al. 2019

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Fig. 1. The Fetch robot picking up and transferring a tomato to a mechanical scale. The tomato is modeled using tetrahedral FEM, while the robot and working mechanical scale are modeled as rigid bodies connected by revolute and prismatic joints. Our method provides full two-way coupling that allows for stable grasping and force sensing on the gripper. The robot is controlled by a human operator in real-time. Model provided courtesy of Fetch Robotics, Inc.We present a framework for the simulation of rigid and deformable bodies in the presence of contact and friction. Our method is based on a non-smooth Newton iteration that solves the underlying nonlinear complementarity problems (NCPs) directly. This approach allows us to support nonlinear dynamics models, including hyperelastic deformable bodies and articulated rigid mechanisms, coupled through a smooth isotropic friction model. The fixed-point nature of our method means it requires only the solution of a symmetric linear system as a building block. We propose a new complementarity preconditioner for NCP functions that improves convergence, and we develop an efficient GPU-based solver based on the conjugate residual (CR) method that is suitable for interactive simulations. We show how to improve robustness using a new geometric stiffness approximation and evaluate our method's performance on a number of robotics simulation scenarios, including dexterous manipulation and training using reinforcement learning.

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Section: Hyperelasticmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Non-smooth Newton Methods for Deformable Multi-body Dynamics

et al. 2019

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“…Comparison to the Finite Element Method - Figure 16. We compare the VIPER discretization to a tetrahedral FEM discretization with the hyperelastic NeoHookean model of Smith et al [2018]. As the two methods have different parameterizations of the material properties, we chose values for the FEM sheet that produce similar behaviour to the VIPER sheet: For the FEM sheet we use a Young's modulus of Y = 10 6 Pa and Poisson's ratio of ν = 0.49.…”

Section: E Further Evaluationsmentioning

confidence: 99%

Viper

Angles

Rebain

Macklin

et al. 2019

Proc. ACM Comput. Graph. Interact. Tech.

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a) (b) (c) (d) Fig. 1. (a) We compactly model muscles as a collection of generalized rods, where volume conservation is expressed by a radius function defined on curve's vertices -vis sphere's radii. (b) The rods create a subspace on which physics is solved, and its effects later propagated to the muscle mesh via linear blend skinning; please see the animation in our supplemental video. The anatomical model is courtesy of Ziva Dynamics. (c) We show how rods and/or bundles can be skinned to a surface mesh to drive its deformation (d), resulting in an alternative to cages for real-time volumetric deformation.We extend the formulation of position-based rods to include elastic volumetric deformations. We achieve this by introducing an additional degree of freedom per vertex -isotropic scale (and its velocity). Including scale enriches the space of possible deformations, allowing the simulation of volumetric effects, such as a reduction in cross-sectional area when a rod is stretched. We rigorously derive the continuous formulation of its elastic energy potentials, and hence its associated position-based dynamics (PBD) updates to realize this model, enabling the simulation of up to 26000 DOFs at 140 Hz in our GPU implementation. We further show how rods can provide a compact alternative to tetrahedral meshes for the representation of complex muscle deformations, as well as providing a convenient representation for collision detection. This is achieved by modeling a muscle as a bundle of rods, for which we also introduce a technique to automatically convert a muscle surface mesh into a rods-bundle. Finally, we show how rods and/or bundles can be skinned to a surface mesh to drive its deformation, resulting in an alternative to cages for real-time volumetric deformation. The source code of our physics engine will be openly available 1 .

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“…The gradients of the continuous material constraints are associated with the first Piola‐Kirchhoff stress tensor ( P ( F ) = dψ( F )/∂ F ). The foundations and detailed derivations of the first Piola‐Kirchhoff stress tensors can be found in [SB12] and [SGK18].…”

Section: Constraintsmentioning

confidence: 99%

“…For all those reasons, we derive our method independently from the numerical integration method and simulation step‐size. In order to test our method, we have implemented many different potential energy constraint types such as Hookean spring potential [LBOK13], St. Venant ‐ Kirchhoff (StVK) spring potential [RLK18] and many continuous material constraints from [BKCW14], [WY16], [SGK18]. Since our algorithm is based on XPBD method, they share the common features, including similar computation performances.…”

Section: Introductionmentioning

confidence: 99%

Position‐Based Simulation of Elastic Models on the GPU with Energy Aware Gauss‐Seidel Algorithm

Cetinaslan

2019

Computer Graphics Forum

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In this paper, we provide a smooth extension of the energy aware Gauss‐Seidel iteration to the Position‐Based Dynamics (PBD) method. This extension is inspired by the kinetic and potential energy changes equalization and uses the foundations of the recent extended version of PBD algorithm (XPBD). The proposed method is not meant to conserve the total energy of the system and modifies each position constraint based on the equality of the kinetic and potential energy changes within the Gauss‐Seidel process of the XPBD algorithm. Our extension provides an implicit solution for relatively better stiffness during the simulation of elastic objects. We apply our solution directly within each Gauss‐Seidel iteration and it is independent of both simulation step‐size and integration methods. To demonstrate the benefits of our proposed extension with higher frame rates, we develop an efficient and practical mesh coloring algorithm for the XPBD method which provides parallel processing on a GPU. During the initialization phase, all mesh primitives are grouped according to their connectivity. Afterwards, all these groups are computed simultaneously on a GPU during the simulation phase. We demonstrate the benefits of our method with many spring potential and strain‐based continuous material constraints. Our proposed algorithm is easy to implement and seamlessly fits into the existing position‐based frameworks.

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Stable Neo-Hookean Flesh Simulation

Cited by 126 publications

References 46 publications

Non-smooth Newton Methods for Deformable Multi-body Dynamics

Non-smooth Newton Methods for Deformable Multi-body Dynamics

Viper

Position‐Based Simulation of Elastic Models on the GPU with Energy Aware Gauss‐Seidel Algorithm

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