Unified simulation of elastic rods, shells, and solids

We develop an accurate, unified treatment of elastica. Following the method of resultant-based formulation to its logical extreme, we derive a higher-order integration rule, or elaston, measuring stretching, shearing, bending, and twisting along any axis. The theory and accompanying implementation do not distinguish between forms of different dimension (solids, shells, rods), nor between manifold regions and non-manifold junctions. Consequently, a single code accurately models a diverse range of elastoplastic behaviors, including buckling, writhing, cutting and merging. Emphasis on convergence to the continuum sets us apart from early unification efforts.

[1]  Jos Stam,et al.  Nucleus: Towards a unified dynamics solver for computer graphics , 2009, 2009 11th IEEE International Conference on Computer-Aided Design and Computer Graphics.

[2]  Leonard McMillan,et al.  Stable real-time deformations , 2002, SCA '02.

[3]  Xavier Provot,et al.  Deformation Constraints in a Mass-Spring Model to Describe Rigid Cloth Behavior , 1995 .

[4]  M. Rubin.  On the Theory of a Cosserat Point and Its Application to the Numerical Solution of Continuum Problems , 1985 .

[5]  Rakesh K. Kapania,et al.  A survey of recent shell finite elements , 2000 .

[6]  Paolo Fiorini,et al.  Calibration of mass spring models for organ simulations , 2007, 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[7]  Markus H. Gross,et al.  Efficient Animation of Point‐Sampled Thin Shells , 2005, Comput. Graph. Forum.

[8]  M. Gross,et al.  Unified simulation of elastic rods, shells, and solids , 2010, ACM Trans. Graph..

[9]  E. Grinspun,et al.  Discrete elastic rods , 2008, SIGGRAPH 2008.

[10]  Dinesh K. Pai,et al.  STRANDS: Interactive Simulation of Thin Solids using Cosserat Models , 2002, Comput. Graph. Forum.

[11]  Wolfgang Straßer,et al.  Corotational Simulation of Deformable Solids , 2004, WSCG.

[12]  Ronald Fedkiw,et al.  Volume conserving finite element simulations of deformable models , 2007, ACM Trans. Graph..

[13]  Adam W. Bargteil,et al.  A point-based method for animating elastoplastic solids , 2009, SCA '09.

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

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

[16]  John C. Platt,et al.  Elastically deformable models , 1987, SIGGRAPH.

[17]  Ronald Fedkiw,et al.  Simulation of clothing with folds and wrinkles , 2003, SCA '03.

[18]  Motoji Yamamoto,et al.  An edge-based computationally efficient formulation of Saint Venant-Kirchhoff tetrahedral finite elements , 2009, ACM Trans. Graph..

[19]  S. P. Lloyd,et al.  Least squares quantization in PCM , 1982, IEEE Trans. Inf. Theory.

[20]  Hans-Peter Seidel,et al.  Meshless modeling of deformable shapes and their motion , 2008, SCA '08.

[21]  Steve Marschner,et al.  Strands and hair: modeling, animation, and rendering , 2007, SIGGRAPH Courses.

[22]  J. Spillmann,et al.  CoRdE: Cosserat rod elements for the dynamic simulation of one-dimensional elastic objects , 2007, SCA '07.

[23]  Wolfgang Straßer,et al.  Interactive physically-based shape editing , 2009, Comput. Aided Geom. Des..

[24]  Venkat Devarajan,et al.  1D and 2D structured mass-spring models with preload , 2005, The Visual Computer.

[25]  Greg Turk,et al.  A finite element method for animating large viscoplastic flow , 2007, SIGGRAPH 2007.

[26]  Petr Krysl,et al.  A Pragmatic Introduction to the Finite Element Method for Thermal And Stress Analysis: With the Matlab Toolkit Sofea , 2006 .

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

[28]  Ronald Fedkiw,et al.  Eurographics/ Acm Siggraph Symposium on Computer Animation (2007) Hybrid Simulation of Deformable Solids , 2022 .

[29]  G. Turk,et al.  Fast viscoelastic behavior with thin features , 2008, SIGGRAPH 2008.

[30]  B. D. Veubeke,et al.  The dynamics of flexible bodies , 1976 .

[31]  Theodore Kim,et al.  Optimizing cubature for efficient integration of subspace deformations , 2008, SIGGRAPH Asia '08.

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

[33]  M. Ortiz,et al.  Subdivision surfaces: a new paradigm for thin‐shell finite‐element analysis , 2000 .

[34]  Hyun Gyu Kim,et al.  Analysis of thin beams, using the meshless local Petrov–Galerkin method, with generalized moving least squares interpolations , 1999 .

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

[36]  Hong Qin,et al.  Meshless thin-shell simulation based on global conformal parameterization , 2006, IEEE Transactions on Visualization and Computer Graphics.

[37]  Ronald Fedkiw,et al.  A virtual node algorithm for changing mesh topology during simulation , 2004, SIGGRAPH 2004.

[38]  YANQING CHEN,et al.  Algorithm 8 xx : CHOLMOD , supernodal sparse Cholesky factorization and update / downdate ∗ , 2006 .

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

[40]  Markus H. Gross,et al.  Eurographics/ Acm Siggraph Symposium on Computer Animation (2006) Fast Arbitrary Splitting of Deforming Objects , 2022 .

[41]  Wolfgang Straßer,et al.  Deriving a Particle System from Continuum Mechanics for the Animation of Deformable Objects , 2003, IEEE Trans. Vis. Comput. Graph..

[42]  Allen Van Gelder,et al.  Approximate Simulation of Elastic Membranes by Triangulated Spring Meshes , 1998, J. Graphics, GPU, & Game Tools.

[43]  Andrew P. Witkin,et al.  Large steps in cloth simulation , 1998, SIGGRAPH.

[44]  H. Matthies,et al.  Classification and Overview of Meshfree Methods , 2004 .

[45]  L. E. Malvern.  Introduction to the mechanics of a continuous medium , 1969 .

[46]  Marc Alexa,et al.  Point based animation of elastic, plastic and melting objects , 2004, SCA '04.

[47]  Matthias Müller,et al.  Position based dynamics , 2007, J. Vis. Commun. Image Represent..

[48]  Nadia Magnenat-Thalmann,et al.  A simple approach to nonlinear tensile stiffness for accurate cloth simulation , 2009, TOGS.

[49]  Mathieu Desbrun,et al.  Discrete shells , 2003, SCA '03.

[50]  Hervé Delingette,et al.  Triangular Springs for Modeling Nonlinear Membranes , 2008, IEEE Transactions on Visualization and Computer Graphics.