]. K. Bat82 and . Bathe, Finite Element Procedures in Engineering Analysis, 1982.

[. Baba-ali, G. Damiand, X. Skapin, and D. Marcheix, Insertion and Expansion Operations for n-Dimensional Generalized Maps, Discrete Geometry and Computer Imagery, pp.141-152, 2008.
DOI : 10.1007/978-3-540-79126-3_14
URL : https://hal.archives-ouvertes.fr/hal-00305482

D. Bielser and M. H. Gross, Interactive simulation of surgical cuts, Proceedings the Eighth Pacific Conference on Computer Graphics and Applications, pp.116-125, 2000.
DOI : 10.1109/PCCGA.2000.883933

[. Bielser, P. Glardon, M. Teschner, and M. Gross, A state machine for real-time cutting of tetrahedral meshes, Pacific Graphics, pp.277-386, 2003.

]. E. Bri89 and . Brisson, Adaptive Resolution for Topology Modifications in Physically-based Animation Representing geometric structures in d dimensions: topology and order, Annual symposium on Computational geometry, pp.218-227, 1989.

H. [. Cotin, N. Delingette, and . Ayache, A hybrid elastic model allowing real-time cutting, deformation and force-feedback for surgery training and simulation. The Visual Computer, pp.437-452, 2000.

[. Chang, K. T. Mcdonnell, and H. Qin, A new solid subdivision scheme based on box splines, Proceedings of the seventh ACM symposium on Solid modeling and applications , SMA '02, pp.226-233, 2002.
DOI : 10.1145/566282.566316

M. [. Debunne, M. P. Desbrun, A. H. Cani, and . Barr, Dynamic real-time deformations using space & time adaptive sampling, Proceedings of the 28th annual conference on Computer graphics and interactive techniques , SIGGRAPH '01, 2001.
DOI : 10.1145/383259.383262
URL : https://hal.archives-ouvertes.fr/inria-00510045

J. [. Dick, R. Georgii, and . Westermann, A Hexahedral Multigrid Approach for Simulating Cuts in Deformable Objects, IEEE Transactions on Visualization and Computer Graphics, vol.17, issue.11, pp.1663-1675, 2011.
DOI : 10.1109/TVCG.2010.268

J. Dequidt, D. Marchal, and L. Grisoni, Time-critical animation of deformable solids, Computer Animation and Virtual Worlds, vol.23, issue.3-4, pp.3-4177, 2005.
DOI : 10.1002/cav.110

H. [. Forest, N. Delingette, and . Ayache, Cutting simulation in manifold volumetric meshes, Medical Image Computing and Computer Assisted Intervention, pp.235-244, 2002.

H. [. Forest, N. Delingette, and . Ayache, Removing tetrahedra from manifold tetrahedralisation: application to real-time surgical simulation, Medical Image Analysis, vol.9, issue.2, pp.113-122, 2005.
DOI : 10.1016/j.media.2004.11.003
URL : https://hal.archives-ouvertes.fr/inria-00615666

. [. Frisken-gibson, Using linked volumes to model object collisions, deformation, cutting, carving, and joining, IEEE Transactions on Visualization and Computer Graphics, vol.5, issue.4, pp.333-348, 1999.
DOI : 10.1109/2945.817350

]. E. Flé14 and . Fléchon, Définition d'un modèle unifié pour la simulation physique adaptative avec changements topologiques, 2014.

F. [. Fléchon, G. Zara, F. Damiand, and . Jaillet, A generic topological framework for physical simulation, International Conferences in Central Europe on Computer Graphics, Visualization and Computer Vision (WSCG), pp.104-113, 2013.

F. [. Fléchon, G. Zara, F. Damiand, and . Jaillet, A unified topological-physical model for adaptive refinement, Eurographics workshop on Virtual Reality Interactions and Physical Simulation, pp.39-48, 2014.

[. Ganovelli, P. Cignoni, C. Montani, and R. Scopigno, A Multiresolution Model for Soft Objects Supporting Interactive Cuts and Lacerations, Computer Graphics Forum, vol.19, issue.3, pp.271-281, 2000.
DOI : 10.1111/1467-8659.00419

D. Hutchinson, M. Preston, and T. Hewitt, Adaptive Refinement for Mass/Spring Simulations, Eurographics workshop on Computer animation and simulation, pp.31-45, 1996.
DOI : 10.1007/978-3-7091-7486-9_3
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.48.2438

P. Kraemer, D. Cazier, and D. Bechmann, Extension of half-edges for the representation of multiresolution subdivision surfaces. The Visual Computer, pp.149-163, 2009.
URL : https://hal.archives-ouvertes.fr/hal-01208558

[. Koschier, S. Lipponer, and J. Bender, Adaptive tetrahedral meshes for brittle fracture simulation, ACM SIG- GRAPH/Eurographics Symposium on Computer Animation, 2014.

]. P. Lie94 and . Lienhardt, N-dimensional generalized combinatorial maps and cellular quasimanifolds, Int. J. of Computational Geometry and Applications, vol.4, issue.3, pp.275-324, 1994.

]. A. Ljf-+-91, S. Luciani, J. L. Jimenez, C. Florens, O. Cadoz et al., Computational physics : a modeler simulator for animated physical objects, EUROGRAPHICS Workshop on Computer Animation and Simulation, pp.425-437, 1991.

]. C. Loo87 and . Loop, Smooth subdivision surfaces based on triangles, 1987.

Z. [. Molino, R. Bao, and . Fedkiw, A virtual node algorithm for changing mesh topology during simulation, ACM Transactions on Graphics, vol.23, issue.3, pp.385-392, 2004.
DOI : 10.1145/1015706.1015734

P. Meseure, E. Darles, and X. Skapin, Topology-based physical simulation, Eurographics workshop on Virtual Reality Interactions and Physical Simulation, pp.1-10, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00563396

M. Müller and M. Gross, Interactive virtual materials, Graphics Interface, pp.239-246, 2004.

T. [. Mor and . Kanade, Modifying Soft Tissue Models: Progressive Cutting with Minimal New Element Creation, Medical Image Computing and Computer Assisted InterventionNPF05] Matthieu Nesme, Yohan Payan, and François Faure. Efficient, physically plausible finite elements Eurographics, pp.598-607, 2000.
DOI : 10.1007/978-3-540-40899-4_61

]. A. Ntb-+-91, G. Norton, B. Turk, J. Bacon, P. Gerth et al., Animation of fracture by physical modeling, The Visual Computer, vol.7, pp.210-219, 1991.

F. James, A. W. O-'brien, J. K. Bargteil, and . Hodgins, Graphical modeling and animation of ductile fracture, Transaction on Graphics (SIGGRAPH), pp.291-294, 2002.

]. X. Pro95 and . Provot, Deformation constraints in a mass-spring model to describe rigid cloth behaviour, Graphics Interface, pp.147-154, 1995.

C. Paulus and L. Untereiner, Hadrien Courtecuisse, Stéphane Cotin, and David Cazier. Virtual cutting of deformable objects based on efficient topological operations, Visual Computer, pp.1-11, 2015.

K. [. Sifakis, R. Der, and . Fedkiw, Arbitrary cutting of deformable tetrahedralized objects, ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp.73-80, 2007.

[. Steinemann and M. Harders, Marlus Gross, and Gabor Szekely. Hybrid cutting of deformable solids, IEEE Conf. on Virtual Reality, 2006.

M. [. Serby, C. Harders, and . Székely, A New Approach to Cutting into Finite Element Models, Medical Image Computing and Computer Assisted Intervention, pp.425-433, 2001.
DOI : 10.1007/3-540-45468-3_51

M. [. Steinemann, M. Otaduy, and . Gross, Fast arbitrary splitting of deforming objects, ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp.63-72, 2006.

K. [. Terzopoulos and . Fleisher, Modeling inelastic deformation : Viscoelasticity, plasticity, fracture, Computer Graphics (Proceedings of ACM SIGGRAPH 88), pp.269-278, 1988.
DOI : 10.1145/54852.378522
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.133.5518

J. [. Terzopoulos, A. Platt, K. Barr, and . Fleisher, Elastically deformable models, Computer Graphics (Proceedings of ACM SIG- GRAPH, vol.87, issue.214, pp.205-214, 1987.
DOI : 10.1145/37401.37427
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.324.2890

]. J. Tssb-+-05, E. Teran, S. Sifakis, V. Salinas-blemker, C. Ng-thow-hing et al., Creating and simulating skeletal muscle from the visible human data set, IEEE Transactions on Visualization and Computer Graphics, vol.11, pp.317-328, 2005.

D. Untereiner, D. Cazier, and . Bechmann, n-Dimensional multiresolution representation of subdivision meshes with arbitrary topology, Graphical Models, vol.75, issue.5, pp.231-246, 2013.
DOI : 10.1016/j.gmod.2013.03.003
URL : https://hal.archives-ouvertes.fr/hal-01162101

P. Untereiner, D. Kraemer, D. Cazier, and . Bechmann, Cph: a compact representation for hierarchical meshes generated by primal refinement. to appear in Computer Graphics Forum, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01162098

J. Wu, R. Westermann, and C. Dick, Physicallybased simulation of cuts in deformable bodies: A survey, Eurographics STARs, pp.1-19, 2014.