Month: June 2022

Linxu Fan, Lloyd M. Chitalu, Taku Komura

Large-scale topological changes play a key role in capturing the fine debris of fracturing virtual brittle material. Real-world, tough brittle fractures have dynamic branching behaviour but numerical simulation of this phenomena is notoriously challenging. In order to robustly capture these
visual characteristics, we simulate brittle fracture by combining elastodynamic continuum mechanical models with rigid-body methods: A continuum damage mechanics (CDM) problem is solved, following rigid-body impact, to simulate crack propagation by tracking a damage field. We combine the result of this elastostatic continuum model with a novel technique to approximate cracks as a non-manifold mid-surface, which enables accurate and robust modelling of material fragment volumes to compliment fast-and-rigid shatter effects. For enhanced realism, we add fracture detail, incorporating particle damage-time to inform localised perturbation of the crack surface with artistic control. We evaluate our method with numerous examples and comparisons, showing that it produces a breadth of brittle material fracture effects and with low simulation resolution to require much less time compared to fully elastodynamic simulations.

Simulating Brittle Fracture with Material Points

Zhen Chen, Hsiao-yu Chen, Danny M Kaufman, Mélina Skouras, Etienne Vouga

We propose a new model and algorithm to capture the high-definition statics of thin shells via coarse meshes. This model predicts global, fine-scale wrinkling at frequencies much higher than the resolution of the coarse mesh; moreover, it is grounded in the geometric analysis of elasticity, and does not require manual guidance, a corpus of training examples, nor tuning of ad hoc parameters. We first approximate the coarse shape of the shell using tension field theory, in which material forces do not resist compression. We then augment this base mesh with wrinkles, parameterized by an amplitude and phase field that we solve for over the base mesh, which together characterize the geometry of the wrinkles. We validate our approach against both physical experiments and numerical simulations, and we show that our algorithm produces wrinkles qualitatively similar to those predicted by traditional shell solvers requiring orders of magnitude more degrees of freedom.

Fine Wrinkling on Coarsely Meshed Thin Shells

Michael Tao, Christopher Batty, Mirela Ben-Chen, Eugene Fiume, David I. W. Levin

The comprehensive visual modeling of fluid motion has historically been a challenging task, due in no small part to the difficulties inherent in geometries that are non-manifold, open, or thin. Modern geometric cut-cell mesh generators have been shown to produce, both robustly and quickly, workable volumetric elements in the presence of these problematic geometries, and the resulting volumetric representation would seem to offer an ideal infrastructure with which to perform fluid simulations. However, cut-cell mesh elements are general polyhedra that often contain holes and are non-convex; it is therefore difficult to construct the explicit function spaces required to employ standard functional discretizations, such as the Finite Element Method. The Virtual Element Method (VEM) has recently emerged as a functional discretization that successfully operates with complex polyhedral elements through a weak formulation of its function spaces. We present a novel cut-cell fluid simulation framework that exactly represents boundary geometry during the simulation. Our approach enables, for the first time, detailed fluid simulation with “in-the-wild” obstacles, including ones that contain non-manifold parts, self-intersections, and extremely thin features. Our key technical contribution is the generalization of the Particle-In-Cell fluid simulation methodology to arbitrary polyhedra using VEM. Coupled with a robust cut-cell generation scheme, this produces a fluid simulation algorithm that can operate on previously infeasible geometries without requiring any additional mesh modification or repair.

VEMPIC: Particle-in-Polyhedron Fluid Simulation for Intricate Solid Boundaries

Alejandro Rodriguez, Gabriel Cirio

Seams play a fundamental role in the way a garment looks, fits, feels and behaves. Seams can have very different shapes and mechanical properties depending on how fabric is overlapped, folded and stitched together, with garment designers often choosing specific seam and stitch type combinations depending on the appearance and behavior they want for the garment. Yet, virtually all 3D CAD tools for fashion and visual effects ignore most of the visual and mechanical complexity of seams, and just treat them as joint edges, their simplest possible form, drastically limiting the fidelity of digital garments. In this paper, we present a method that models seams following their true, real-life construction. Each seam brings together and overlaps the fabric pieces to be sewn, folds the fabric according to the type of seam, and stitches the resulting assembly following the type of stitch. To avoid dealing with the complexities of folding in 3D space, we cast the problem into a sequence of simpler 2D problems where we can easily shape the seam and produce a result free of self-intersections, before lifting the folded geometry back to 3D space. We run a series of constrained optimizations to enforce spatial properties in these 2D settings, allowing us to treat asymmetric seams, gatherings and overlapping construction orders. Using a variety of common seams and stitches, we show how our approach substantially improves the visual appearance of full garments, for a better and more predictive digital replica.

True Seams: Modeling Seams in Digital Garments

Botao Wu, Zhendong Wang, Huamin Wang

In this paper, we wish to push the limit of real-time cloth and deformable body simulation to a higher level with 50K to 500K vertices, based on the development of a novel GPU-based multilevel additive Schwarz (MAS) preconditioner. Similar to other preconditioners under the MAS framework, our preconditioner naturally adopts multilevel and domain decomposition concepts. But contrary to previous works, we advocate the use of small, non-overlapping domains that can well explore the parallel computing power on a GPU. Based on this idea, we investigate and invent a series of algorithms for our preconditioner, including multilevel domain construction using Morton codes, low-cost matrix precomputation by one-way Gauss-Jordan elimination, and conflict-free symmetric-matrix-vector multiplication in runtime preconditioning. The experiment shows that our preconditioner is effective, fast, cheap to precompute and scalable with respect to stiffness and problem size. It is compatible with many linear and nonlinear solvers used in cloth and deformable body simulation with dynamic contacts, such as PCG, accelerated gradient descent and L-BFGS. On a GPU, our preconditioner speeds up a PCG solver by approximately a factor of four, and its CPU version outperforms a number of competitors, including ILU0 and ILUT.

A GPU-Based Multilevel Additive Schwarz Preconditioner for Cloth and Deformable Body Simulation

Alexandre Mercier-Aubin, Alexander Winter, David I.W. Levin, Paul G. Kry

We present a method for reducing the computational cost of elastic solid simulation by treating connected sets of non-deforming elements as rigid bodies. Non-deforming elements are identified as those where the strain rate squared Frobenius norm falls below a threshold for several frames. Rigidification uses a breadth first search to identify connected components while avoiding connections that would form hinges between rigid components. Rigid elements become elastic again when their approximate strain velocity rises above a threshold, which is fast to compute using a single iteration of conjugate gradient with a fixed Laplacian-based incomplete Cholesky preconditioner. With rigidification, the system size to solve at each time step can be greatly reduced, and if all elastic element become rigid, it reduces to solving the rigid body system. We demonstrate our results on a variety of 2D and 3D examples, and show that our method is likewise especially beneficial in contact rich examples.

Adaptive Rigidification of Elastic Solids