Category: Shells

Parallel Multigrid for Nonlinear Cloth Simulation

Zhendong Wang, Longhua Wu, Marco Fratarcangeli, Min Tang, Huamin Wang

Accurate high-resolution simulation of cloth is a highly desired computational tool in graphics applications. As single resolution simulation starts to reach the limit of computational power, we believe the future of cloth simulation is in multi-resolution simulation. In this paper, we explore nonlinearity, adaptive smoothing, and parallelization under a full multigrid (FMG) framework. The foundation of this research is a novel nonlinear FMG method for unstructured meshes. To introduce nonlinearity into FMG, we propose to formulate the smoothing process at each resolution level as the computation of a search direction for the original high-resolution nonlinear optimization problem. We prove that our nonlinear FMG is guaranteed to converge under various conditions and we investigate the improvements to its performance. We present an adaptive smoother which is used to reduce the computational cost in the regions with low residuals already. Compared to normal iterative solvers, our nonlinear FMG method provides faster convergence and better performance for both Newton’s method and Projective Dynamics. Our experiment shows our method is efficient, accurate, stable against large time steps, and friendly with GPU parallelization. The performance of the method has a good scalability to the mesh resolution, and the method has good potential to be combined with multi-resolution collision handling for real-time simulation in the future.

Parallel Multigrid for Nonlinear Cloth Simulation

Inverse Elastic Shell Design with Contact and Friction

Mickaël Ly, Romain Casati, Florence Bertails-Descoubes, Mélina Skouras, Laurence Boissieux

We propose an inverse strategy for modeling thin elastic shells physically, just from the observation of their geometry. Our algorithm takes as input an arbitrary target mesh, and interprets this configuration automatically as a stable equilibrium of a shell simulator under gravity and frictional contact constraints with a given external object. Unknowns are the natural shape of the shell (i.e., its shape without external forces) and the frictional contact forces at play, while the material properties (mass density, stiffness, friction coefficients) can be freely chosen by the user. Such an inverse problem formulates as an ill-posed nonlinear system subject to conical constraints. To select and compute a plausible solution, our inverse solver proceeds in two steps. In a first step, contacts are reduced to frictionless bilateral constraints and a natural shape is retrieved using the adjoint method. The second step uses this result as an initial guess and adjusts each bilateral force so that it projects onto the admissible Coulomb friction cone, while preserving global equilibrium. To better guide minimization towards the target, these two steps are applied iteratively using a degressive regularization of the shell energy. We validate our approach on simulated examples with reference material parameters, and show that our method still converges well for material parameters lying within a reasonable range around the reference, and even in the case of arbitrary meshes that are not issued from a simulation. We finally demonstrate practical inversion results on complex shell geometries freely modeled by an artist or automatically captured from real objects, such as posed garments or soft accessories.

Inverse Elastic Shell Design with Contact and Friction

Physical Simulation of Environmentally Induced Thin Shell Deformation

Hsiao-yu Chen, Arnav Sastry, Wim M. van Rees, Etienne Vouga

We present a physically accurate low-order elastic shell model that incorporates active material response to dynamically changing stimuli such as heat, moisture, and growth. Our continuous formulation of the geometrically non-linear elastic energy derives from the principles of differential geometry, and as such naturally incorporates shell thickness, non-zero rest curvature, and physical material properties. By modeling the environmental stimulus as local, dynamic changes in the rest metric of the material, we are able to solve for the corresponding shape changes by integrating the equations of motions given this non-Euclidean rest state. We present models for differential growth and shrinking due to moisture and temperature gradients along and across the surface, and incorporate anisotropic growth by defining an intrinsic machine direction within the material. Comparisons with experiments and volumetric finite elements show that our simulations achieve excellent qualitative and quantitative agreement. By combining the reduced-order shell theory with appropriate physical models, our approach accurately captures all the physical phenomena while avoiding expensive volumetric discretization of the shell volume.

Physical Simulation of Environmentally Induced Thin Shell Deformation

A Material Point Method for Thin Shells with Frictional Contact

Qi Guo, Xuchen Han, Chuyuan Fu, Theodore Gast, Rasmus Tamstorf, Joseph Teran

We present a novel method for simulation of thin shells with frictional contact using a combination of the Material Point Method (MPM) and subdivision finite elements. The shell kinematics are assumed to follow a continuum shell model which is decomposed into a Kirchhoff-Love motion that rotates the mid-surface normals followed by shearing and compression/extension of the material along the mid-surface normal. We use this decomposition to design an elastoplastic constitutive model to resolve frictional contact by decoupling resistance to contact and shearing from the bending resistance components of stress. We show that by resolving frictional contact with a continuum approach, our hybrid Lagrangian/Eulerian approach is capable of simulating challenging shell contact scenarios with hundreds of thousands to millions of degrees of freedom. Without the need for collision detection or resolution, our method runs in a few minutes per frame in these high resolution examples. Furthermore we show that our technique naturally couples with other traditional MPM methods for simulating granular and related materials.

A Material Point Method for Thin Shells with Frictional Contact

Eulerian-on-Lagrangian Cloth Simulation

Nicholas J. Weidner, Kyle Piddington, David I. W. Levin, Shinjiro Sueda

We resolve the long-standing problem of simulating the contact-mediated interaction of cloth and sharp geometric features by introducing an Eulerian-on-Lagrangian (EOL) approach to cloth simulation. Unlike traditional Lagrangian approaches to cloth simulation, our EOL approach permits bending exactly at and sliding over sharp edges, avoiding parasitic locking caused by over-constraining contact constraints. Wherever the cloth is in contact with sharp features, we insert EOL vertices into the cloth, while the rest of the cloth is simulated in the standard Lagrangian fashion. Our algorithm manifests as new equations of motion for EOL vertices, a contact-conforming remesher, and a set of simple constraint assignment rules, all of which can be incorporated into existing state-of-the-art cloth simulators to enable smooth, inequality-constrained contact between cloth and objects in the world.

Eulerian-on-Lagrangian Cloth Simulation

Inequality Cloth

Ning Jin, Wenlong Lu, Zhenglin Geng, Ronald Fedkiw

As has been noted and discussed by various authors, numerical simulations of deformable bodies often adversely suffer from so-called “locking” artifacts. We illustrate that the “locking” of out-of-plane bending motion that results from even an edge-spring-only cloth simulation can be quite severe, noting that the typical remedy of softening the elastic model leads to an unwanted rubbery look. We demonstrate that this “locking” is due to the well-accepted notion that edge springs in the cloth mesh should preserve their lengths, and instead propose an inequality constraint that stops edges from stretching while allowing for edge compression as a surrogate for bending. Notably, this also allows for the capturing of bending modes at scales smaller than those which could typically be represented by the mesh. Various authors have recently begun to explore optimization frameworks for deformable body simulation, which is particularly germane to our inequality cloth framework. After exploring such approaches, we choose a particular approach and illustrate its feasibility in a number of scenarios including contact, collision, and self-collision. Our results demonstrate the efficacy of the inequality approach when it comes to folding, bending, and wrinkling, especially on coarser meshes, thus opening up a plethora of interesting possibilities.

Inequality Cloth

Anisotropic Elastoplasticity for Cloth, Knit and Hair Frictional Contact

Chenfanfu Jiang, Theodore Gast, Joseph Teran

The typical elastic surface or curve simulation method takes a Lagrangian approach and consists of three components: time integration, collision detection and collision response. The Lagrangian view is beneficial because it naturally allows for tracking of the codimensional manifold, however collision must then be detected and resolved separately. Eulerian methods are promising alternatives because collision processing is automatic and while this is effective for volumetric objects, advection of a codimensional manifold is too inaccurate in practice. We propose a novel hybrid Lagrangian/Eulerian approach that preserves the best aspects of both views. Similar to the Drucker-Prager and Mohr-Coulomb models for granular materials, we define our collision response with a novel elastoplastic constitutive model. To achieve this, we design an anisotropic hyperelastic constitutive model that separately characterizes the response to manifold strain as well as shearing and compression in the directions orthogonal to the manifold. We discretize the model with the Material Point Method and a novel codimensional Lagrangian/Eulerian update of the deformation gradient. Collision intensive scenarios with millions of degrees of freedom require only a few minutes per frame and examples with up to one million degrees of freedom run in less than thirty seconds per frame.

Anisotropic Elastoplasticity for Cloth, Knit and Hair Frictional Contact

Interactive Paper Tearing

Camille Schreck, Damien Rohmer, Stefanie Hahmann

We propose an efficient method to model paper tearing in the context of interactive modeling. The method uses geometrical information to automatically detect potential starting points of tears. We further introduce a new hybrid geometrical and physical-based method to compute the trajectory of tears while procedurally synthesizing high resolution details of the tearing path using a texture based approach. The results obtained are compared with real paper and with previous studies on the expected geometric paths of paper that tears.

Interactive Paper Tearing

Non-smooth developable geometry for interactively animating paper crumpling

Camille Schreck, Damien Rohmer, Stefanie Hahmann, Marie-Paule Cani, Shuo Jin, Charlie Wang, Jean-Francois Bloch

We present the first method to animate sheets of paper at interactive rates, while automatically generating a plausible set of sharp features when the sheet is crumpled. The key idea is to interleave standard physically-based simulation steps with procedural generation of a piecewise continuous developable surface. The resulting hybrid surface model captures new singular points dynamically appearing during the crumpling process, mimicking the effect of paper fiber fracture. Although the model evolves over time to take these irreversible damages into account, the mesh used for simulation is kept coarse throughout the animation, leading to efficient computations. Meanwhile, the geometric layer ensures that the surface stays almost isometric to its original 2D pattern. We validate our model through measurements and visual comparison with real paper manipulation, and show results on a variety of crumpled paper configurations.

Non-smooth developable geometry for interactively animating paper crumpling

Real-time Hair Mesh Simulation

Kui Wu, Cem Yuksel

We present a robust real-time hair simulation method using hair meshes. Leveraging existing simulation models for sheet-based cloth, we introduce a volumetric force model for incorporating hair interactions inside the hair mesh volume. We also introduce a position correction method that minimizes the local deformation of the hair mesh due to collision handling. We demonstrate the robustness of our hair simulation method using large time steps with fast motion, and we show that our method can recover the initial hair shape even when the hair mesh goes through substantial deformation.

Real-Time Hair Mesh Simulation