A peridynamic perspective on spring-mass fracture

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.

[1]  翔貴 宮川.  ”Fast Simulation of Mass-Spring Systems”の研究報告 , 2016 .

[2]  Koichi Hirota,et al.  Generation of crack patterns with a physical model , 1998, The Visual Computer.

[3]  James F. Blinn,et al.  A Generalization of Algebraic Surface Drawing , 1982, TOGS.

[4]  Markus H. Gross,et al.  Optimized Spatial Hashing for Collision Detection of Deformable Objects , 2003, VMV.

[5]  Dong-Ming Yan,et al.  Efficient computation of clipped Voronoi diagram for mesh generation , 2013, Comput. Aided Des..

[6]  Koichi Hirota,et al.  Simulation of three-dimensional cracks , 2000, The Visual Computer.

[7]  Pat Hanrahan,et al.  An efficient representation for irradiance environment maps , 2001, SIGGRAPH.

[8]  Huamin Wang,et al.  Bilateral blue noise sampling , 2013, ACM Trans. Graph..

[9]  Ross T. Whitaker,et al.  Topology, Accuracy, and Quality of Isosurface Meshes Using Dynamic Particles , 2007, IEEE Transactions on Visualization and Computer Graphics.

[10]  Jessica K. Hodgins,et al.  Graphical modeling and animation of brittle fracture , 1999, SIGGRAPH.

[11]  Robert Bacon,et al.  Animation of fracture by physical modeling , 1991, The Visual Computer.

[12]  Yue Gao,et al.  A Level-Set Method for Skinning Animated Particle Data , 2011, IEEE Transactions on Visualization and Computer Graphics.

[13]  Stewart Andrew Silling,et al.  Peridynamic Modeling of Impact Damage , 2004 .

[14]  Eitan Grinspun,et al.  Asynchronous contact mechanics , 2009, ACM Trans. Graph..

[15]  Miguel A. Otaduy,et al.  Fracture animation based on high-dimensional Voronoi diagrams , 2014, I3D.

[16]  Murat Cenk Cavusoglu,et al.  Determination of elasticity parameters in lumped element (mass-spring) models of deformable objects , 2010, Graph. Model..

[17]  Saty Raghavachary,et al.  Fracture generation on polygonal meshes using Voronoi polygons , 2002, SIGGRAPH '02.

[18]  S. Silling.  Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces , 2000 .

[19]  Etienne Emmrich,et al.  Peridynamics: a nonlocal continuum theory. , 2013 .

[20]  L. Guibas,et al.  Meshless animation of fracturing solids , 2005, ACM Trans. Graph..

[21]  Maud Marchal,et al.  Real-Time Simulation of Brittle Fracture Using Modal Analysis , 2013, IEEE Transactions on Visualization and Computer Graphics.

[22]  James F. O'Brien,et al.  Real-time deformation and fracture in a game environment , 2009, SCA '09.

[23]  Markus H. Gross,et al.  Interactive Virtual Materials , 2004, Graphics Interface.

[24]  Eitan Grinspun,et al.  Enrichment textures for detailed cutting of shells , 2009, ACM Trans. Graph..

[25]  Jessica K. Hodgins,et al.  Graphical modeling and animation of ductile fracture , 2002, SIGGRAPH.

[26]  James F. O'Brien,et al.  Graphical modeling and animation of ductile fracture , 2002, SIGGRAPH '02.

[27]  S. Silling,et al.  A meshfree method based on the peridynamic model of solid mechanics , 2005 .

[28]  K HodginsJessica,et al.  Graphical modeling and animation of ductile fracture , 2002 .

[29]  Andrew P. Witkin,et al.  Fast and Controllable Simulation of the Shattering of Brittle Objects , 2001, Comput. Graph. Forum.

[30]  Christopher D. Twigg,et al.  Point Cloud Glue: constraining simulations using the procrustes transform , 2010, SCA '10.

[31]  Jihun Yu,et al.  Reconstructing surfaces of particle-based fluids using anisotropic kernels , 2010, SCA '10.

[32]  Nuttapong Chentanez,et al.  Real time dynamic fracture with volumetric approximate convex decompositions , 2013, ACM Trans. Graph..

[33]  Samir Akkouche,et al.  Procedural modeling of cracks and fractures , 2004, Proceedings Shape Modeling Applications, 2004..

[34]  Huamin Wang,et al.  Adaptive fracture simulation of multi-layered thin plates , 2013, ACM Trans. Graph..

[35]  Pat Hanrahan,et al.  Interactive k-d tree GPU raytracing , 2007, SI3D.

[36]  Gábor Székely,et al.  Identification of Spring Parameters for Deformable Object Simulation , 2007, IEEE Transactions on Visualization and Computer Graphics.

[37]  Demetri Terzopoulos,et al.  Modeling inelastic deformation: viscolelasticity, plasticity, fracture , 1988, SIGGRAPH.

[38]  宮川翔貴.  ”Fast Simulation of Mass‐Spring Systems”の研究報告 , 2016 .

[39]  W. Kabsch.  A discussion of the solution for the best rotation to relate two sets of vectors , 1978 .

[40]  Mark Meyer,et al.  Artistic simulation of curly hair , 2013, SCA '13.

[41]  Ronald Fedkiw,et al.  A virtual node algorithm for changing mesh topology during simulation , 2004, ACM Trans. Graph..

[42]  Andrew Selle,et al.  To appear in the ACM SIGGRAPH conference proceedings A Mass Spring Model for Hair Simulation , 2008 .

[43]  W. C. Swope,et al.  A computer simulation method for the calculation of equilibrium constants for the formation of physi , 1981 .