Although mesh-based methods are efficient for simulating simple hyperelasticity, maintaining and adapting a mesh-based representation is less appealing in more complex scenarios, e.g. collision, plasticity and fracture. Thus, meshless or point-based methods have enjoyed recent popularity due to their added flexibility in dealing with these situations. Our approach begins with an initial mesh that is either conforming (as generated by one’s favorite meshing algorithm) or non-conforming (e.g. a BCC background lattice). We then propose a framework for embedding arbitrary sample points into this initial mesh allowing for the straightforward handling of collisions, plasticity and fracture without the need for complex remeshing. A straightforward consequence of this new framework is the ability to naturally handle T-junctions alleviating the requirement for a manifold initial mesh. The arbitrarily added embedded points are endowed with full simulation capability allowing them to collide, interact with each other, and interact with the parent geometry in the fashion of a particle-centric simulation system. We demonstrate how this formulation facilitates tasks such as arbitrary refinement or resampling for collision processing, the handling of multiple and possibly conflicting constraints (e.g. when cloth is nonphysically pinched between two objects), the straightforward treatment of fracture, and sub-element resolution of elasticity and plasticity.
Category: Deformables
Arbitrary Cutting of Deformable Tetrahedralized Objects
We propose a flexible geometric algorithm for placing arbitrary cracks and incisions on tetrahedralized deformable objects. Although techniques based on remeshing can also accommodate arbitrary fracture patterns, this flexibility comes at the risk of creating sliver elements leading to models that are inappropriate for subsequent simulation. Furthermore, interactive applications such as virtual surgery simulation require both a relatively low resolution mesh for efficient simulation of elastic deformation and highly detailed surface geometry to facilitate accurate manipulation and cut placement. Thus, we embed a high resolution material boundary mesh into a coarser tetrahedral mesh using our cutting algorithm as a meshing tool, obtaining meshes that can be efficiently simulated while preserving surface detail. Our algorithm is similar to the virtual node algorithm in that we avoid sliver elements and their associated stringent timestep restrictions, but it is significantly more general allowing for the arbitrary cutting of existing cuts, sub-tetrahedron resolution (e.g. we cut a single tetrahedron into over a thousand pieces), progressive introduction of cuts while the object is deforming, and moreover the ability to accurately cut the high resolution embedded mesh.
Adaptive Deformations with Fast Tight Bounds
“Simulation of deformations and collision detection are two highly intertwined problems that are often treated separately. This is especially true in existing elegant adaptive simulation techniques, where standard collision detection algorithms cannot leverage the adaptively selected degrees of freedom.We propose a seamless integration of multi-grid algorithms and collision detection that identifies boundary conditions while inherently exploiting adaptivity. We realize this integration through multiscale bounding hierarchies, a novel unified hierarchical representation, together with an adaptive multigrid algorithm for irregular meshes and an adaptivity-aware hierarchical collision detection algorithm. Our solution produces detailed deformations with adapted computational cost, but it also enables robust interactive simulation of self-colliding deformable objects with high-resolution surfaces.”
A Finite Element Method on Convex Polyhedra
“We present a method for animating deformable objects using a novel finite element discretization on convex polyhedra. Our finite element approach draws upon recently introduced 3D mean value coordinates to define smooth interpolants within the elements. The mathematical properties of our basis functions guarantee convergence. Our
method is a natural extension to linear interpolants on tetrahedra: for tetrahedral elements, the methods are identical. For fast and robust computations, we use an elasticity model based on Cauchy strain and stiffness warping. This more flexible discretization is particularly useful for simulations that involve topological changes, such as cutting or fracture. Since splitting convex elements along a plane produces convex elements, remeshing or subdivision schemes used in simulations based on tetrahedra are not necessary, leading to less elements after such operations. We propose various operators for cutting the polyhedral discretization. Our method can handle arbitrary cut trajectories, and there is no limit on how often elements can be split.”
FastLSM: Fast Lattice Shape Matching for Robust Real-Time Deformation
“We introduce a simple technique that enables robust approximation of volumetric, large-deformation dynamics for real-time or large-scale offline simulations. We propose Lattice Shape Matching, an extension of deformable shape matching to regular lattices with embedded geometry; lattice vertices are smoothed by convolution of rigid shape matching operators on local lattice regions, with the effective mechanical stiffness specified by the amount of smoothing via region width. Since the naive method can be very slow for stiff models — per-vertex costs scale cubically with region width — we provide a fast summation algorithm, Fast Lattice Shape Matching (FastLSM), that exploits the inherent summation redundancy of shape matching and can provide large-region matching at constant per-vertex cost. With this approach, large lattices can be simulated in linear time. We present several examples and benchmarks of an efficient CPU implementation, including many dozens of soft bodies simulated at real-time rates on a typical desktop machine.”
FastLSM: Fast Lattice Shape Matching for Robust Real-Time Deformation
Volume Conserving Finite Element Simulations of Deformable Models
“We propose a numerical method for modeling highly deformable nonlinear incompressible solids that conserves the volume locally near each node in a finite element mesh. Our method works with arbitrary constitutive models, is applicable to both passive and active materials (e.g. muscles), and works with simple tetrahedra without
the need for multiple quadrature points or stabilization techniques. Although simple linear tetrahedra typically suffer from locking when modeling incompressible materials, our method enforces incompressibility per node (in a one-ring), and we demonstrate that it is free from locking. We correct errors in volume without introducing oscillations by treating position and velocity in separate implicit solves. Finally, we propose a novel method for treating both object contact and self-contact as linear constraints during
the incompressible solve, alleviating issues in enforcing multiple possibly conflicting constraints.”
Volume Conserving Finite Element Simulations of Deformable Models
A Finite Element Method for Animating Large Viscoplastic Flow
“We present an extension to Lagrangian finite element methods to allow for large plastic deformations of solid materials. These behaviors are seen in such everyday materials as shampoo, dough, and clay as well as in fantastic gooey and blobby creatures in special effects scenes. To account for plastic deformation, we explicitly update the linear basis functions defined over the finite elements during each simulation step. When these updates cause the basis functions to become ill-conditioned, we remesh the simulation domain to produce a new high-quality finite-element mesh, taking care to preserve the original boundary. We also introduce an enhanced plasticity model that preserves volume and includes creep and work hardening/softening. We demonstrate our approach with simulations of synthetic objects that squish, dent, and flow. To validate our methods, we compare simulation results to videos of real materials.”
A Finite Element Method for Animating Large Viscoplastic Flow