Locking-Proof Tetrahedra

被引:8
作者
Francu, Mihai [1 ]
Asgeirsson, Arni [1 ]
Erleben, Kenny [1 ]
Ronnow, Mads J. L. [2 ]
机构
[1] Univ Copenhagen, Univ Pk 5, DK-2100 Copenhagen, Denmark
[2] Chalmers Univ Technol, Lindholmsplatsen 1, S-41756 Gothenburg, Sweden
来源
ACM TRANSACTIONS ON GRAPHICS | 2021年 / 40卷 / 02期
基金
欧盟地平线“2020”;
关键词
Finite element method (FEM); mixed FEM; incompressible; locking; nonlinear materials; constrained dynamics; FINITE-ELEMENT; ELASTICITY; FEM; SIMULATION; MODELS;
D O I
10.1145/3444949
中图分类号
TP31 [计算机软件];
学科分类号
081202 ; 0835 ;
摘要
The simulation of incompressible materials suffers from locking when using the standard finite element method (FEM) and coarse linear tetrahedral meshes. Locking increases as the Poisson ratio v gets close to 0.5 and often lower Poisson ratio values are used to reduce locking, affecting volume preservation. We propose a novel mixed FEM approach to simulating incompressible solids that alleviates the locking problem for tetrahedra. Our method uses linear shape functions for both displacements and pressure, and adds one scalar per node. It can accommodate nonlinear isotropic materials described by a Young's modulus and any Poisson ratio value by enforcing a volumetric constitutive law. The most realistic such material is Neo-Hookean, and we focus on adapting it to our method. For nu = 0.5, we can obtain full volume preservation up to any desired numerical accuracy. We show that standard Neo-Hookean simulations using tetrahedra are often locking, which, in turn, affects accuracy. We show that our method gives better results and that our Newton solver is more robust. As an alternative, we propose a dual ascent solver that is simple and has a good convergence rate. We validate these results using numerical experiments and quantitative analysis.
引用
收藏
页数:17
相关论文
共 102 条
  • [1] Ahrens J, 2005, VISUALIZATION HDB, V717
  • [2] Akhrass Dina Al, 2012, EUR C COMP METH APPL
  • [3] Geometric Stiffness for Real-time Constrained Multibody Dynamics
    Andrews, Sheldon
    Teichmann, Marek
    Kry, Paul G.
    [J]. COMPUTER GRAPHICS FORUM, 2017, 36 (02) : 235 - 246
  • [4] [Anonymous], 2017, EUROGRAPHICS 2017 TU
  • [5] [Anonymous], 1987, P 14 ANN C COMP GRAP, DOI DOI 10.1145/37402.37427
  • [6] Some First-Order Algorithms for Total Variation Based Image Restoration
    Aujol, Jean-Francois
    [J]. JOURNAL OF MATHEMATICAL IMAGING AND VISION, 2009, 34 (03) : 307 - 327
  • [7] LOCKING EFFECTS IN THE FINITE-ELEMENT APPROXIMATION OF ELASTICITY PROBLEMS
    BABUSKA, I
    SURI, M
    [J]. NUMERISCHE MATHEMATIK, 1992, 62 (04) : 439 - 463
  • [8] Baraff D., 1998, Computer Graphics. Proceedings. SIGGRAPH 98 Conference Proceedings, P43, DOI 10.1145/280814.280821
  • [9] Animation of Deformable Bodies with Quadratic Bezier Finite Elements
    Bargteil, Adam W.
    Cohen, Elaine
    [J]. ACM TRANSACTIONS ON GRAPHICS, 2014, 33 (03):
  • [10] Bathe K.J., 1996, Finite Element Procedures in Engineering Analysis