article

Tetrahedral and hexahedral invertible finite elements

Authors:

R. FedkiwAuthors Info & Claims

Graphical Models, Volume 68, Issue 2

Pages 66 - 89

https://doi.org/10.1016/j.gmod.2005.03.007

Published: 01 March 2006 Publication History

Abstract

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.

References

[1]

{1} C. Hirt, A. Amsden, J. Cook, An arbitrary Lagrangian-Eulerian computing method for all flow speeds, J. Comput. Phys. 135 (1974) 227-253.

[2]

{2} G. Camacho, M. Ortiz, Adaptive Lagrangian modelling of ballistic penetration of metallic targets, Comput. Meth. Appl. Mech. Eng. 142 (1997) 269-301.

[3]

{3} H. Espinosa, P. Zavattieri, G. Emore, Adaptive FEM computation of geometric and material nonlinearities with application to brittle failure, Mech. Mater. 29 (1998) 275-305.

[4]

{4} G. Bessette, E. Becker, L. Taylor, D. Littlefield, Modeling of impact problems using an h-adaptive, explicit Lagrangian finite element method in three dimensions, Comput. Meth. Appl. Mech. Eng. 192 (2003) 1649-1679.

[5]

{5} P. Vachal, R. Garimella, M. Shashkov, Untangling of 2D meshes in ALE simulation, J. Comput. Phys. 196 (2004) 627-644.

Digital Library

[6]

{6} J. Escobar, E. Rodríguez, R. Montenegro, G. Montero, J. González-Yuste, Simultaneous untangling and smoothing of tetrahedral meshes, Comput. Meth. Appl. Mech. Eng. 192 (2003) 2775-2787.

[7]

{7} N. Molino, R. Bridson, J. Teran, R. Fedkiw, A crystalline, red green strategy for meshing highly deformable objects with tetrahedra, in: 12th International Meshing Roundtable, 2003, pp. 103-114.

[8]

{8} R. Kautzman, A. Maiolo, D. Griffin, A. Bueker, Jiggly bits and motion retargetting: bringing the motion of hyde to life in Van Helsing with dynamics, in: SIGGRAPH 2004 Sketches and Applications, ACM Press, New York, 2004.

Digital Library

[9]

{9} M. Teschner, B. Heidelberger, M. Muller, M. Gross, A versatile and robust model for geometrically complex deformable solids, in: Proceedings of the Computer Graphics International, 2004.

[10]

{10} M. Muller, M. Gross, Interactive virtual materials, in: Graph. Interface, 2004.

[11]

{11} G. Irving, J. Teran, R. Fedkiw, Invertible finite elements for robust simulation of large deformation, in: Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation, 2004, pp. 131-140.

Digital Library

[12]

{12} D. Terzopoulos, J. Platt, A. Barr, K. Fleischer, Elastically deformable models, Comput. Graph. (Proc. SIGGRAPH 87) 21 (4) (1987) 205-214.

Digital Library

[13]

{13} D. Terzopoulos, K. Fleischer, Modeling inelastic deformation: viscoelasticity, plasticity, fracture, Comput. Graph. (SIGGRAPH Proc.) (1998) 269-278.

[14]

{14} D. Terzopoulos, K. Fleischer, Deformable models, Visual Comput. (4) (1988) 306-331.

[15]

{15} J.-P. Gourret, N. Magnenat-Thalmann, D. Thalmann, Simulation of object and human skin deformations in a grasping task, Comput. Graph. (SIGGRAPH Proc.) (1989) 21-30.

Digital Library

[16]

{16} D. Chen, D. Zeltzer, Pump it up: computer animation of a biomechanically based model of muscle using the finite element method, Comput. Graph. (SIGGRAPH Proc.) (1992) 89-98.

Digital Library

[17]

{17} G. Picinbono, H. Delingette, N. Ayache, Non-linear and anisotropic elastic soft tissue models for medical simulation, in: IEEE International Conference on Robot. and Automation, 2001.

[18]

{18} Q. Zhu, Y. Chen, A. Kaufman, Real-time biomechanically-based muscle volume deformation using FEM, Comput. Graph. Forum 190 (3) (1998) 275-284.

[19]

{19} G. Hirota, S. Fisher, A. State, C. Lee, H. Fuchs, An implicit finite element method for elastic solids in contact, in: Proceedings of the Computer Animation, 2001, pp. 136-146.

[20]

{20} J. O'Brien, J. Hodgins. Graphical modeling and animation of brittle fracture, in: Proceedings of the SIGGRAPH 99, vol. 18, 1999, pp. 137-146.

[21]

{21} J. O'Brien, A. Bargteil, J. Hodgins, Graphical modeling of ductile fracture, ACM Trans. Graph. (SIGGRAPH Proc.) 21 (2002) 291-294.

Digital Library

[22]

{22} G. Yngve, J. O'Brien, J. Hodgins, Animating explosions, in: Proceedings of the SIGGRAPH 2000, vol. 19, 2000, pp. 29-36.

[23]

{23} M. Muller, L. McMillan, J. Dorsey, R. Jagnow. Real-time simulation of deformation and fracture of stiff materials, in: Comput. Anim. Sim. '01, Proceedings of the Eurographics Workshop, Eurographics Association, 2001, pp. 99-111.

[24]

{24} G. Debunne, M. Desbrun, M. Cani, A. Barr, Dynamic real-time deformations using space and time adaptive sampling, in: Proceedings of the SIGGRAPH 2001, vol. 20, 2001, pp. 31-36.

[25]

{25} M. Muller, J. Dorsey, L. McMillan, R. Jagnow, B. Cutler. Stable real-time deformations, in: ACM SIGGRAPH Symposium on Computer Animation, 2002, pp. 49-54.

Digital Library

[26]

{26} S. Capell, S. Green, B. Curless, T. Duchamp, Z. Popović, Interactive skeleton-driven dynamic deformations, ACM Trans. Graph. (SIGGRAPH Proc.) 21 (2002) 586-593.

Digital Library

[27]

{27} S. Capell, S. Green, B. Curless, T. Duchamp, Z. Popović, A multiresolution framework for dynamic deformations, in: ACM SIGGRAPH Symposium on Computer Animation, ACM Press, New York, 2002, pp. 41-48.

Digital Library

[28]

{28} J. Teran, S. Blemker, V. Ng, R. Fedkiw, Finite volume methods for the simulation of skeletal muscle, in: Proceedings of the 2003 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, 2003, pp. 68-74.

Digital Library

[29]

{29} D. James, D. Pai, DyRT: dynamic response textures for real time deformation simulation with graphics hardware, ACM Trans. Graph. (SIGGRAPH Proc.) 21 (2002) 582-585.

Digital Library

[30]

{30} D. James, K. Fatahalian, Precomputing interactive dynamic deformable scenes, ACM Trans. Graph. (SIGGRAPH Proc.) 22 (2003) 879-887.

Digital Library

[31]

{31} B. Palmerio, An attraction-repulsion mesh adaption model for flow solution on unstructured grids, Comput. Fluids 23 (3) (1994) 487-506.

[32]

{32} D. Bourguignon, M.P. Cani, Controlling anisotropy in mass-spring systems, in: Eurographics, Eurographics Association, 2000, pp. 113-123.

[33]

{33} L. Cooper, S. Maddock, Preventing collapse within mass-spring-damper models of deformable objects, in: The 5th International Conference in Central Europe on Computer Graphics and Vis., 1997.

[34]

{34} O. Etzmuss, M. Keckeisen, W. Strasser, A fast finite element solution for cloth modelling, in: Pacific Graph., 2003, pp. 244-251.

[35]

{35} R. Bridson, S. Marino, R. Fedkiw, Simulation of clothing with folds and wrinkles, in: Proceedings of the 2003 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, 2003, pp. 28-36.

Digital Library

[36]

{36} E. Grinspun, A. Hirani, M. Desbrun, P. Schroder, Discrete shells, in: Proceedings of the 2003 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, 2003, pp. 62-67.

[37]

{37} R. Bridson, R. Fedkiw, J. Anderson, Robust treatment of collisions, contact and friction for cloth animation, ACM Trans. Graph.(SIGGRAPH Proc.) 21 (2002) 594-603.

Digital Library

[38]

{38} D. Baraff, A. Witkin, Large steps in cloth simulation, in: Proceedings of the SIGGRAPH 98, 1998, pp. 1-12.

[39]

{39} K.-J. Choi, H.-S. Ko, Stable but responsive cloth, ACM Trans. Graph. (SIGGRAPH Proc.) 21 (2002) 604 611.

[40]

{40} E. Grinspun, P. Krysl, P. Schroder, CHARMS: a simple framework for adaptive simulation, ACM Trans. Graph. (SIGGRAPH Proc.) 21 (2002) 281-290.

Digital Library

[41]

{41} D. Baraff, A. Witkin, M. Kass, Untangling cloth, ACM Trans. Graph. (SIGGRAPH Proc.) 22 (2003) 862-870.

Digital Library

[42]

{42} T. Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1987.

[43]

{43} J. Bonet, R. Wood, Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge University Press, Cambridge, 1997.

[44]

{44} J. Teran, E. Sifakis, S. Salinas-Blemker, V. Ng-Thow-Hing, C. Lau, R. Fedkiw, Creating and simulating skeletal muscle from the visible human data set, IEEE Trans. Vis. Comput. Graph. 11 (3) (2005) 317-328.

Digital Library

[45]

{45} F. Armero, E. Love, An arbitrary Lagrangian Eulerian finite element method for finite strain plasticity, Int. J. Numer. Meth. Eng. 57 (2003) 471-508.

[46]

{46} N. Molino, J. Bao, R. Fedkiw, A virtual node algorithm for changing mesh topology during simulation, ACM Trans. Graph. (SIGGRAPH Proc.) 23 (2004) 385-392.

Digital Library

[47]

{47} N. Foster, D. Metaxas, Controlling fluid animation, in: Computer Graphics International 1997, 1997, pp. 178-188.

Digital Library

[48]

{48} J. Popović, S. Seitz, M. Erdmann, Z. Popović, A. Witkin, Interactive manipulation of rigid body simulations, ACM Trans. Graph. (SIGGRAPH Proc.) 19 (2000) 209-217.

[49]

{49} A. Treuille, A. McNamara, Z. Popovic, J. Stam, Keyframe control of smoke simulations, ACM Trans. Graph. (SIGGRAPH Proc.) 22 (2003) 716-723.

Digital Library

[50]

{50} B. Boroomand, B. Khalilian, On using linear elements in incompressible plane strain problems: a simple edge based approach for triangles, Int. J. Numer. Meth. Eng. 61 (2004) 1710 1740.

[51]

{51} E. de Souza Neto, F.A. Pires, D. Owen, F-bar-based linear triangles and tetrahedra for finite strain analysis of nearly incompressible solids. Part I: formulation and benchmarking, Int. J. Numer. Meth. Eng. 62 (2005) 353-383.

[52]

{52} F.A. Pires, E. de Souza Neto, D. Owen, On the finite element prediction of damage growth and fracture initiation in finitely deforming ductile materials, Comput. Meth. Appl. Mech. Eng. 193 (2004) 5223-5256.

[53]

{53} Y. Guo, M. Ortiz, T. Belytschko, E. Repetto, Triangular composite finite elements, Int. J. Numer. Meth. Eng. 47 (2000) 287-316.

[54]

{54} P. Thoutireddy, J. Molinari, E. Repetto, M. Ortiz, Tetrahedral composite finite elements, Int. J. Numer. Meth. Eng. 53 (2002) 1337-1351.

Cited By

Lin HChitalu FKomura T(2024)Analytic rotation-invariant modelling of anisotropic finite elementsACM Transactions on Graphics10.1145/366608643:5(1-20)Online publication date: 9-Aug-2024
https://dl.acm.org/doi/10.1145/3666086
Li XLi MHan XWang HYang YJiang C(2024)A Dynamic Duo of Finite Elements and Material PointsACM SIGGRAPH 2024 Conference Papers10.1145/3641519.3657449(1-11)Online publication date: 13-Jul-2024
https://dl.acm.org/doi/10.1145/3641519.3657449
Du TBrunvand E(2023)Deep Learning for Physics SimulationACM SIGGRAPH 2023 Courses10.1145/3587423.3595518(1-25)Online publication date: 24-Jul-2023
https://dl.acm.org/doi/10.1145/3587423.3595518
Show More Cited By

Index Terms

Tetrahedral and hexahedral invertible finite elements
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Partial differential equations
    2. Numerical analysis
      1. Computations in finite fields

Recommendations

Stabilized tetrahedral elements for crystal plasticity finite element analysis overcoming volumetric locking

Image-based CPFE modeling involves computer generation of virtual polycrystalline microstructures from experimental data, followed by discretization into finite element meshes. Discretization is commonly accomplished using three-dimensional four-node ...
A general three-dimensional L-section beam finite element for elastoplastic large deformation analysis

In this paper, the development of a general three-dimensional L-section beam finite element for elastoplastic large deformation analysis is presented. We propose the generalized interpolation scheme for the isoparametric formulation of three-dimensional ...
Relations among stiffness coefficients of hexahedral 8-noded finite elements: A simple and efficient way to reduce the integration time

Computing coefficients in stiffness matrices of finite element analysis in computational mechanics is time consuming, especially in large non-linear dynamic problems involving large meshes. Thus, any improvement in computational procedures to reduce the ...

Comments

Information & Contributors

Information

Published In

cover image Graphical Models

Graphical Models Volume 68, Issue 2

Special issue on SCA 2004

March 2006

170 pages

ISSN:1524-0703

Issue’s Table of Contents

Publisher

Academic Press Professional, Inc.

United States

Publication History

Published: 01 March 2006

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

18
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 10 Nov 2024

Other Metrics

View Author Metrics

Citations

Cited By

Lin HChitalu FKomura T(2024)Analytic rotation-invariant modelling of anisotropic finite elementsACM Transactions on Graphics10.1145/366608643:5(1-20)Online publication date: 9-Aug-2024
https://dl.acm.org/doi/10.1145/3666086
Li XLi MHan XWang HYang YJiang C(2024)A Dynamic Duo of Finite Elements and Material PointsACM SIGGRAPH 2024 Conference Papers10.1145/3641519.3657449(1-11)Online publication date: 13-Jul-2024
https://dl.acm.org/doi/10.1145/3641519.3657449
Du TBrunvand E(2023)Deep Learning for Physics SimulationACM SIGGRAPH 2023 Courses10.1145/3587423.3595518(1-25)Online publication date: 24-Jul-2023
https://dl.acm.org/doi/10.1145/3587423.3595518
Li XLi MJiang C(2022)Energetically consistent inelasticity for optimization time integrationACM Transactions on Graphics10.1145/3528223.353007241:4(1-16)Online publication date: 22-Jul-2022
https://dl.acm.org/doi/10.1145/3528223.3530072
Gao RPeters J(2021)Improving Hexahedral-FEM-Based Plasticity in Surgery SimulationMedical Image Computing and Computer Assisted Intervention – MICCAI 202110.1007/978-3-030-87202-1_55(571-580)Online publication date: 27-Sep-2021
https://dl.acm.org/doi/10.1007/978-3-030-87202-1_55
Chen JBudninskiy MOwhadi HBao HHuang JDesbrun M(2019)Material-adapted refinable basis functions for elasticity simulationACM Transactions on Graphics10.1145/3355089.335656738:6(1-15)Online publication date: 8-Nov-2019
https://dl.acm.org/doi/10.1145/3355089.3356567
Pan ZManocha D(2018)Active Animations of Reduced Deformable Models with Environment InteractionsACM Transactions on Graphics10.1145/319756537:3(1-17)Online publication date: 7-Aug-2018
https://dl.acm.org/doi/10.1145/3197565
Chen JBao HWang TDesbrun MHuang J(2018)Numerical coarsening using discontinuous shape functionsACM Transactions on Graphics10.1145/3197517.320138637:4(1-12)Online publication date: 30-Jul-2018
https://dl.acm.org/doi/10.1145/3197517.3201386
Zhu FZhao JLi STang YWang G(2017)Dynamically Enriched MPM for Invertible ElasticityComputer Graphics Forum10.1111/cgf.1298736:6(381-392)Online publication date: 1-Sep-2017
https://dl.acm.org/doi/10.1111/cgf.12987
Kikuuwe R(2017)A time-integration method for stable simulation of extremely deformable hyperelastic objectsThe Visual Computer: International Journal of Computer Graphics10.1007/s00371-016-1225-033:10(1335-1346)Online publication date: 1-Oct-2017
https://dl.acm.org/doi/10.1007/s00371-016-1225-0
Show More Cited By

View Options

View options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

Media

Figures

Other

Tables

View Issue’s Table of Contents