Category: Fracture

Simulating Rigid Body Fracture with Surface Meshes

Yufeng Zhu, Robert Bridson, Chen Greif

We present a new brittle fracture simulation method based on a boundary integral formulation of elasticity and recent explicit surface mesh evolution algorithms. Unlike prior physically-based simulations in graphics, this avoids the need for volumetric sampling and calculations, which aren’t reflected in the rendered output. We represent each quasi-rigid body by a closed triangle mesh of its boundary, on which we solve quasi-static linear elasticity via boundary integrals in response to boundary conditions and loads such as impact forces and gravity. A fracture condition based on maximum tensile stress is subsequently evaluated at mesh vertices, while crack initiation and propagation are formulated as an interface tracking procedure in material space. Existing explicit mesh tracking methods are modified to support evolving cracks directly in the triangle mesh representation, giving highly detailed fractures with sharp features, independent of any volumetric sampling (unlike tetrahedral mesh or level set approaches); the triangle mesh representation also allows simple integration into rigid body engines. We also give details on our well-conditioned integral equation treatment solved with a kernel-independent Fast Multipole Method for linear time summation. Various brittle fracture scenarios demonstrate the efficacy and robustness of our new method.

Simulating Rigid Body Fracture with Surface Meshes

An Adaptive Virtual Node Algorithm with Robust Mesh Cutting

Yuting Wang, Chenfanfu Jiang, Craig Schroeder, Joseph Teran

We present a novel virtual node algorithm (VNA) for changing tetrahedron mesh topology to represent arbitrary cutting triangulated surfaces. Our approach addresses a number of shortcomings in the original VNA of [MBF04]. First, we generalize the VNA so that cuts can pass through tetrahedron mesh vertices and lie on mesh edges and faces. The original algorithm did not make sense for these cases and required often ambiguous perturbation of the cutting surface to avoid them. Second, we develop an adaptive approach to the definition of embedded material used for element duplication. The original algorithm could only handle a limited number of configurations which restricted cut surfaces to have curvature at the scale of the tetrahedron elements. Our adaptive approach allows for cut surfaces with curvatures independent of the embedding tetrahedron mesh resolution. Finally, we present a novel, provably-robust floating point mesh intersection routine that accurately registers triangulated surface cuts against the background tetrahedron mesh without the need for exact arithmetic.

An Adaptive Virtual Node Algorithm with Robust Mesh Cutting

A Peridynamic Perspective on Spring-Mass Fracture

Joshua A. Levine, Adam W. Bargteil, Christopher Corsi, Jerry Tessendorf, Robert Geist 

The application of spring-mass systems to the animation of brittle fracture is revisited. The motivation arises from the recent popularity of peridynamics in the computational physics community. Peridynamic systems can be regarded as spring-mass systems with two specific properties. First, spring forces are based on a simple strain metric, thereby decoupling spring stiffness from spring length. Second, masses are connected using a distance-based criterion. The relatively large radius of influence typically leads to a few hundred springs for every mass point. Spring-mass systems with these properties are shown to be simple to implement, trivially parallelized, and well-suited to animating brittle fracture.

A Peridynamic Perspective on Spring-Mass Fracture

Physics-Inspired Adaptive Fracture Refinement

Zhili Chen, Miaojun Yao, Renguo Feng, Huamin Wang

Physically based animation of detailed fracture effects is not only computationally expensive, but also difficult to implement due to numerical instability. In this paper, we propose a physics-inspired approach to enrich low-resolution fracture animation by realistic fracture details. Given a custom-designed material strength field, we adaptively refine a coarse fracture surface into a detailed one, based on a discrete gradient descent flow. Using the new fracture surface, we then generate a high-resolution fracture animation with details on both the fracture surface and the exterior surface. Our experiment shows that this approach is simple, fast, and friendly to user design and control. It can generate realistic fracture animations within a few seconds.

Physics-Inspired Adaptive Fracture Refinement

Adaptive Tetrahedral Meshes for Brittle Fracture Simulation

Dan Koschier, Sebastian Lipponer, Jan Bender

We present a method for the adaptive simulation of brittle fracture of solid objects based on a novel reversible tetrahedral mesh refinement scheme. The refinement scheme preserves the quality of the input mesh to a large extent, it is solely based on topological operations, and does not alter the boundary, i.e. any geometric feature. Our fracture algorithm successively performs a stress analysis and increases the resolution of the input mesh in regions of high tensile stress. This results in an accurate location of crack origins without the need of a general high resolution mesh which would cause high computational costs throughout the whole simulation. A crack is initiated when the maximum tensile stress exceeds the material strength. The introduced algorithm then proceeds by iteratively recomputing the changed stress state and creating further cracks. Our approach can generate multiple cracks from a single impact but effectively avoids shattering artifacts. Once the tensile stress decreases, the mesh refinement is reversed to increase the performance of the simulation. We demonstrate that our adaptive method is robust, scalable and computes highly realistic fracture results.

Adaptive Tetrahedral Meshes for Brittle Fracture Simulation

Adaptive Tearing and Cracking of Thin Sheets

Tobias Pfaff, Rahul Narain, Juan Miguel de Joya, and James F. O’Brien

This paper presents a method for adaptive fracture propagation in thin sheets. A high-quality triangle mesh is dynamically restructured to adaptively maintain detail wherever it is required by the simulation. These requirements include refining where cracks are likely to either start or advance. Refinement ensures that the stress distribution around the crack tip is well resolved, which is vital for creating highly detailed, realistic crack paths. The dynamic meshing framework allows subsequent coarsening once areas are no longer likely to produce cracking. This coarsening allows efficient simulation by reducing the total number of active nodes and by preventing the formation of thin slivers around the crack path. A local reprojection scheme and a substepping fracture process help to ensure stability and prevent a loss of plasticity during remeshing. By including bending and stretching plasticity models, the method is able to simulate a large range of materials with very different fracture behaviors.

Adaptive Tearing and Cracking of Thin Sheets

Fracture animation based on high-dimensional Voronoi diagrams

Sara Schvartzmann, Miguel Otaduy

We propose a novel algorithm to simulate brittle fracture. It augments previous methods based on Voronoi diagrams, improving their versatility and their ability to adapt fracture patterns automatically to diverse collision scenarios and object properties. We cast brittle fracture as the computation of a high-dimensional Centroidal Voronoi Diagram (CVD), where the distribution of fracture fragments is guided by the deformation field of the fractured object. By formulating the problem in high dimensions, we support robustly object and crack concavities, as well as intuitive artist control. We further accelerate the fracture animation process with example-based learning of the fracture degree, and a highly parallel tessellation algorithm. As a result, we obtain fast animations of detailed and rich fractures, with fracture patterns that adapt to each particular collision scenario.

Fracture animation based on high-dimensional Voronoi diagrams

A Level Set Method for Ductile Fracture

Jan Hegemann, Chenfanfu Jiang, Craig Schroeder, Joseph M. Teran

We utilize the shape derivative of the classical Griffith’s energy in a level set method for the simulation of dynamic ductile fracture. The level set is defined in the undeformed configuration of the object, and its evolution is designed to represent a transition from undamaged to failed material. No re-meshing is needed since the resulting topological changes are handled naturally by the level set method. We provide a new mechanism for the generation of fragments of material during the progression of the level set in the Griffith’s energy minimization. Collisions between different material pieces are resolved with impulses derived from the material point method over a background Eulerian grid. This provides a stable means for colliding with embedded interfaces. Simulation of corotational elasticity is based on an implicit finite element discretization.

A Level Set Method for Ductile Fracture

Adaptive Fracture Simulation of Multi-Layered Thin Plates

Oleksiy Busaryev, Tamal K. Dey, Huamin Wang

The fractures of thin plates often exhibit complex physical behaviors in the real world. In particular, fractures caused by tearing are different from fractures caused by in-plane motions. In this paper, we study how to make thin-plate fracture animations more realistic from three perspectives. We propose a stress relaxation method, which is applied to avoid shattering artifacts after generating each fracture cut. We formulate a fracture-aware remeshing scheme based on constrained Delaunay triangulation, to adaptively provide more fracture details. Finally, we use our multi-layered model to simulate complex fracture behaviors across thin layers. Our experiment shows that the system can efficiently and realistically simulate the fractures of multi-layered thin plates.

Adaptive Fracture Simulation of Multi-Layered Thin Plates

Real-Time Dynamic Fracture with Volumetric Approximate Convex Decompositions

Matthias Mueller, Nuttapong Chentanez, Tae-Yong Kim

We propose a new fast, robust and controllable method to simulate the dynamic destruction of large and complex objects in real time. The common method for fracture simulation in computer games is to pre-fracture models and replace objects by their pre-computed parts at run-time. This popular method is computationally cheap but has the disadvantages that the fracture pattern does not align with the impact location and that the number of hierarchical fracture levels is fixed. Our method allows dynamic fracturing of large objects into an unlimited number of pieces fast enough to be used in computer games. We represent visual meshes by volumetric approximate convex decompositions (VACD) and apply user-defined fracture patterns dependent on the impact location. The method supports partial fracturing meaning that fracture patterns can be applied locally at multiple locations of an object. We propose new methods for computing a VACD, for approximate convex hull construction and for detecting islands in the convex decomposition after partial destruction in order to determine support structures.

Real-Time Dynamic Fracture with Volumetric Approximate Convex Decompositions