Real-time large-deformation substructuring

Abstract

This paper shows a method to extend 3D nonlinear elasticity model reduction to open-loop multi-level reduced deformable structures. Given a volumetric mesh, we decompose the mesh into several subdomains, build a reduced deformable model for each domain, and connect the domains using inertia coupling. This makes model reduction deformable simulations much more versatile: localized deformations can be supported without prohibitive computational costs, parts can be re-used and precomputation times shortened. Our method does not use constraints, and can handle large domain rigid body motion in addition to large deformations, due to our derivation of the gradient and Hessian of the rotation matrix in polar decomposition. We show real-time examples with multi-level domain hierarchies and hundreds of reduced degrees of freedom.

Physics-Based Character Skinning Using Multidomain Subspace Deformations

“…In concurrent work, [BZ11] proposes a reduced-order domain-decomposition method. It addresses the special case of passive models that can be partitioned into tree-structured reduced-order domains that are connected by interfaces which are small and/or have negligible near-rigid defor-mations.…”

“…the National Science Foundation (CAREER-0430528, EMT-CompBio-0621999), the National Institutes of Health (NIBIB/NIH R01EB006615), NSERC (Many-core Physically Based Simulations), the Alfred P. Sloan Foundation, and donations from Intel, Pixar, and Autodesk. DLJ acknowledges early discussions with Dinesh Pai on precomputation-based domain decomposition and the rotation-sandwich problem [JP02a], and also collaborations with students under CAREER-0430528: early work with Christopher Twigg on articulated tree-structured reduced-order domains for Krysl-style simulation (unpublished) and data-driven animation of botanical systems [JTCW07], and later with Jernej Barbic on simulating reduced-order StVK models [BJ05] in the context of articulated tree-structured reduced-order domains (that led to [BZ11]). Reduced-order domain decomposition work was supported in part by NIBIB/NIH R01EB006615, and we thank Jaydev Desai for his infinite patience and support.…”

Coupling time-varying modal analysis and FEM for real-time cutting simulation of objects with multi-material sub-domains

“…So far, its widespread use has been enabling many downstream graphics applications such as computer games, virtual reality systems, computer animation, virtual surgery simulators, etc. To faithfully and efficiently simulate the object's physical behaviors of 5 deformation and arbitrary cutting, many fundamental methodologies, ranging from accurate finite element methods (FEM) together with their GPU acceleration [1] to various types of flexible mesh-free methods, have been well devised to accommodate the application-specific requirements.…”

“…However, when handling complex homogeneous objects, a naively-transplanted way requires a large number of carefully-divided elements to accurately represent all the involved physical states, which gives rise to expensive computation expenses in modal reduction, and what is even worse is that, the above-documented extra efforts may not facilitate the corresponding global modal analysis towards physical realism due to 25 massive elements from various sub-domains. Therefore, it naturally needs a divide-and-rule scheme [5,6] to independently model the involved heterogeneous physical domains in an approximated sense.…”

“…Based on the open-source framework (SOFA) [14], Allard et al [8] proposed a series of numerical methods to implicitly solve FEM-based deformation systems on GPU. Barbič et al [5] used co-rotational finite element method to accommodate large-scale deformations. And Wang et al [15] proposed to capture and model the deformations of soft objects by integrating FEM-based simulation into a physics-based tracking framework.…”