Enrichment textures for detailed cutting of shells

We present a method for simulating highly detailed cutting and fracturing of thin shells using low-resolution simulation meshes. Instead of refining or remeshing the underlying simulation domain to resolve complex cut paths, we adapt the extended finite element method (XFEM) and enrich our approximation by customdesigned basis functions, while keeping the simulation mesh unchanged. The enrichment functions are stored in enrichment textures, which allows for fracture and cutting discontinuities at a resolution much finer than the underlying mesh, similar to image textures for increased visual resolution. Furthermore, we propose harmonic enrichment functions to handle multiple, intersecting, arbitrarily shaped, progressive cuts per element in a simple and unified framework. Our underlying shell simulation is based on discontinuous Galerkin (DG) FEM, which relaxes the restrictive requirement of C1 continuous basis functions and thus allows for simpler, C0 continuous XFEM enrichment functions.

[1]  T. Belytschko,et al.  New crack‐tip elements for XFEM and applications to cohesive cracks , 2003 .

[2]  Ronald Fedkiw,et al.  Arbitrary cutting of deformable tetrahedralized objects , 2007, SCA '07.

[3]  Matthias Müller,et al.  Hierarchical Position Based Dynamics , 2008, VRIPHYS.

[4]  Eitan Grinspun,et al.  To appear in the ACM SIGGRAPH conference proceedings Efficient Simulation of Inextensible Cloth , 2007 .

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

[6]  Mario Botsch,et al.  Implementation of Discontinuous Galerkin Kirchhoff-Love Shells , 2009 .

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

[8]  Steven J. Gortler,et al.  Geometry images , 2002, SIGGRAPH.

[9]  Julien Réthoré,et al.  An energy‐conserving scheme for dynamic crack growth using the eXtended finite element method , 2005 .

[10]  Markus H. Gross,et al.  A Finite Element Method on Convex Polyhedra , 2007, Comput. Graph. Forum.

[11]  Gerald Wempner,et al.  Mechanics of Solids and Shells: Theories and Approximations , 2002 .

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

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

[14]  John Hart,et al.  ACM Transactions on Graphics , 2004, SIGGRAPH 2004.

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

[16]  Hervé Delingette,et al.  Removing tetrahedra from a manifold mesh , 2002, Proceedings of Computer Animation 2002 (CA 2002).

[17]  Samir Akkouche,et al.  Modeling cracks and fractures , 2005, The Visual Computer.

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

[19]  Eitan Grinspun,et al.  Sparse matrix solvers on the GPU: conjugate gradients and multigrid , 2003, SIGGRAPH Courses.

[20]  Robert Bridson,et al.  Animating developable surfaces using nonconforming elements , 2008, ACM Trans. Graph..

[21]  Eitan Grinspun,et al.  A Discrete Model for Inelastic Deformation of Thin Shells , 2004 .

[22]  Leonidas J. Guibas,et al.  Meshless animation of fracturing solids , 2005, ACM Trans. Graph..

[23]  Markus H. Gross,et al.  Polyhedral Finite Elements Using Harmonic Basis Functions , 2008, Comput. Graph. Forum.

[24]  Lenka Jerábková,et al.  Stable Cutting of Deformable Objects in Virtual Environments Using XFEM , 2009, IEEE Computer Graphics and Applications.

[25]  Wolfgang Straßer,et al.  A consistent bending model for cloth simulation with corotational subdivision finite elements , 2006 .

[26]  James A. Sethian,et al.  Level Set Methods and Fast Marching Methods , 1999 .

[27]  Ted Belytschko,et al.  An extended finite element method with higher-order elements for curved cracks , 2003 .

[28]  Yazid Abdelaziz,et al.  Review: A survey of the extended finite element , 2008 .

[29]  Eitan Grinspun,et al.  Enrichment textures for detailed cutting of shells , 2009, SIGGRAPH 2009.

[30]  Ludovic Noels,et al.  A discontinuous Galerkin formulation of non‐linear Kirchhoff–Love shells , 2009 .

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

[32]  Christian Laugier,et al.  Simulating 2D tearing phenomena for interactive medical surgery simulators , 2000, Proceedings Computer Animation 2000.

[33]  Bernardo Cockburn Discontinuous Galerkin methods , 2003 .

[34]  Jean-Herve Prevost,et al.  MODELING QUASI-STATIC CRACK GROWTH WITH THE EXTENDED FINITE ELEMENT METHOD PART II: NUMERICAL APPLICATIONS , 2003 .

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

[36]  R. Radovitzky,et al.  A new discontinuous Galerkin method for Kirchhoff–Love shells , 2008 .

[37]  Ted Belytschko,et al.  Elastic crack growth in finite elements with minimal remeshing , 1999 .

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

[39]  Ronald Fedkiw,et al.  Fracturing Rigid Materials , 2007, IEEE Transactions on Visualization and Computer Graphics.

[40]  Markus H. Gross,et al.  Interactive Cuts through 3‐Dimensional Soft Tissue , 1999, Comput. Graph. Forum.

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

[42]  I. Babuska,et al.  The partition of unity finite element method: Basic theory and applications , 1996 .

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

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

[45]  T. Belytschko,et al.  Blending in the extended finite element method by discontinuous Galerkin and assumed strain methods , 2008 .

[46]  Markus H. Gross,et al.  Eurographics/ Acm Siggraph Symposium on Computer Animation (2008) Flexible Simulation of Deformable Models Using Discontinuous Galerkin Fem , 2022 .

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

[48]  Douglas N. Arnold,et al.  Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems , 2001, SIAM J. Numer. Anal..

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

[50]  Ted Belytschko,et al.  A finite element method for crack growth without remeshing , 1999 .