Tetrahedral and hexahedral invertible finite elements

We review an algorithm for the finite element simulation of elastoplastic solids which is capable of robustly and efficiently handling arbitrarily large deformation. In fact, the model remains valid even when large parts of the mesh are inverted. The algorithm is straightforward to implement and can be used with any material constitutive model, and for both volumetric solids and thin shells such as cloth. We also discuss a mechanism for controlling plastic deformation, which allows a deformable object to be guided towards a desired final shape without sacrificing realistic behavior, and an improved method for rigid body collision handling in the context of mixed explicit/implicit time-stepping. Finally, we present a novel extension of our method to arbitrary element types including specific details for hexahedral elements.

[1]  Steven M. Seitz,et al.  Interactive manipulation of rigid body simulations , 2000, SIGGRAPH.

[2]  Michael I. Jordan.  Graphical Models , 1998 .

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

[4]  F. Armero,et al.  An arbitrary Lagrangian–Eulerian finite element method for finite strain plasticity , 2003 .

[5]  Dimitris N. Metaxas,et al.  Controlling fluid animation , 1997, Proceedings Computer Graphics International.

[6]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[7]  Z. Popovic,et al.  Interactive skeleton-driven dynamic deformations , 2002, ACM Trans. Graph..

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

[9]  Demetri Terzopoulos,et al.  Deformable models , 2000, The Visual Computer.

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

[11]  Ronald Fedkiw,et al.  Robust treatment of collisions, contact and friction for cloth animation , 2002, SIGGRAPH Courses.

[12]  David Zeltzer,et al.  Pump it up: computer animation of a biomechanically based model of muscle using the finite element method , 1992, SIGGRAPH.

[13]  Wolfgang Straßer,et al.  A fast finite element solution for cloth modelling , 2003, 11th Pacific Conference onComputer Graphics and Applications, 2003. Proceedings..

[14]  Eitan Grinspun,et al.  CHARMS: a simple framework for adaptive simulation , 2002, ACM Trans. Graph..

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

[16]  E. A. S. Neto,et al.  F‐bar‐based linear triangles and tetrahedra for finite strain analysis of nearly incompressible solids. Part I: formulation and benchmarking , 2005 .

[17]  B. Boroomand,et al.  On using linear elements in incompressible plane strain problems: a simple edge based approach for triangles , 2004 .

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

[19]  Doug Griffin,et al.  Jiggly bits and motion retargeting: bringing the motion of Hyde to life in Van Helsing with dynamics: Copyright restrictions prevent ACM from providing the full text for this work. , 2004, SIGGRAPH '04.

[20]  Lee Cooper.  Preventing collapse within mass-spring-damper models of deformable objects , 1997 .

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

[22]  Steve Capell,et al.  A multiresolution framework for dynamic deformations , 2002, SCA '02.

[23]  Doug L. James,et al.  Precomputing interactive dynamic deformable scenes , 2003, ACM Trans. Graph..

[24]  Matthias Müller,et al.  A versatile and robust model for geometrically complex deformable solids , 2004, Proceedings Computer Graphics International, 2004..

[25]  L. Taylor,et al.  Modeling of impact problems using an h-adaptive, explicit Lagrangian finite element method in three dimensions , 2003 .

[26]  Andrew P. Witkin,et al.  Untangling cloth , 2003, ACM Trans. Graph..

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

[28]  Jagnow Robert Carl,et al.  Real-time simulation of deformation and fracture of stiff materials , 2001 .

[29]  Adrien Treuille,et al.  Keyframe control of smoke simulations , 2003, ACM Trans. Graph..

[30]  Kwang-Jin Choi,et al.  Stable but responsive cloth , 2002, SIGGRAPH Courses.

[31]  C. Hirsch,et al.  Introduction to “Towards the Ultimate Conservative Difference Scheme. V. A Second-Order Sequel to Godunov's Method” , 1997 .

[32]  M. Ortiz,et al.  Adaptive Lagrangian modelling of ballistic penetration of metallic targets , 1997 .

[33]  Ronald Fedkiw,et al.  A Crystalline, Red Green Strategy for Meshing Highly Deformable Objects with Tetrahedra , 2003, IMR.

[34]  E. A. de Souza Neto,et al.  On the finite element prediction of damage growth and fracture initiation in finitely deforming ductile materials , 2004 .

[35]  B. Palmerio.  An attraction-repulsion mesh adaption model for flow solution on unstructured grids , 1994 .

[36]  J. M. González-Yuste,et al.  Simultaneous untangling and smoothing of tetrahedral meshes , 2003 .

[37]  Mathieu Desbrun,et al.  Dynamic real-time deformations using space & time adaptive sampling , 2001, SIGGRAPH.

[38]  Arie E. Kaufman,et al.  Real‐time Biomechanically‐based Muscle Volume Deformation using FEM , 1998, Comput. Graph. Forum.

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

[40]  Henry Fuchs,et al.  An implicit finite element method for elastic solids in contact , 2001, Proceedings Computer Animation 2001. Fourteenth Conference on Computer Animation (Cat. No.01TH8596).

[41]  Ronald Fedkiw,et al.  Creating and simulating skeletal muscle from the visible human data set , 2005, IEEE Transactions on Visualization and Computer Graphics.

[42]  H. Espinosa,et al.  Adaptive FEM computation of geometric and material nonlinearities with application to brittle failure , 1998 .

[43]  Ted Belytschko,et al.  Triangular composite finite elements , 2000 .

[44]  Daniel Thalmann,et al.  Simulation of object and human skin formations in a grasping task , 1989, SIGGRAPH.

[45]  Ronald Fedkiw,et al.  Finite volume methods for the simulation of skeletal muscle , 2003, SCA '03.

[46]  E. A. Repetto,et al.  Tetrahedral composite finite elements , 2002 .

[47]  Jessica K. Hodgins,et al.  Animating explosions , 2000, SIGGRAPH.

[48]  Dinesh K. Pai,et al.  DyRT: dynamic response textures for real time deformation simulation with graphics hardware , 2002, SIGGRAPH.

[49]  R. D. Wood,et al.  Nonlinear Continuum Mechanics for Finite Element Analysis , 1997 .

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

[51]  C. W. Hirt,et al.  An Arbitrary Lagrangian-Eulerian Computing Method for All Flow Speeds , 1997 .

[52]  Marie-Paule Cani,et al.  Controlling Anisotropy in Mass-Spring Systems , 2000, Computer Animation and Simulation.

[53]  Hervé Delingette,et al.  Nonlinear and anisotropic elastic soft tissue models for medical simulation , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[54]  R. Garimella,et al.  Untangling of 2D meshes in ALE simulations , 2004 .

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

[56]  Ronald Fedkiw,et al.  Invertible finite elements for robust simulation of large deformation , 2004, SCA '04.