300
A. Wittek et al.
35. Dolbow, J., Belytschko, T.: Numerical integration of the Galerkin weak form in meshfree
methods. Comput. Mech. 23, 219–230 (1999)
36. Beissel, S., Belytschko, T.: Nodal integration of the element-free Galerkin method. Comput.
Methods Appl. Mech. Eng. 139, 49–74 (1996)
37. Chen, J.-S., Wu, C.-T., Yoon, S., You, Y.: A stabilized conforming nodal integration for
Galerkin mesh-free methods. Int. J. Numer. Methods Eng. 50, 435–466 (2001)
38. Quak, W., van den Boogaard, A., González, D., Cueto, E.: A comparative study on the
performance of meshless approximations and their integration. Comput. Mech. 48, 121–137
(2011)
39. Wittek, A., Joldes, G., Miller, K.: Algorithms for computational biomechanics of the brain. In:
Miller, K. (ed.) Biomechanics of the Brain, pp. 189–219. Springer, New York (2011)
40. Mor, A.B., Kanade, T.: Modifying soft tissue models: progressive cutting with minimal
new element creation. In: Delp, S.L., DiGoia, A.M., Jaramaz, B. (eds.) Medical Image
Computing and Computer-Assisted Intervention – MICCAI 2000, pp. 598–607. Springer,
Berlin/Heidelberg (2000)
41. Bielser, D., Glardon, P., Teschner, M., Gross, M.: Interactive simulation of surgical cuts. Graph.
Model. 66, 116–125 (2004)
42. Courtecuisse, H., Jung, H., Allard, J., Duriez, C., Lee, D.Y., Cotin, S.: GPU-based real-time
soft tissue deformation with cutting and haptic feedback. Prog. Biophys. Mol. Biol. 103, 159–
168 (2010)
43. Courtecuisse, H., Allard, J., Kerfriden, P., Bordas, S., Cotin, S., Duriez, C.: Real-time
simulation of contact and cutting of heterogeneous soft-tissues. Med. Image Anal. 18, 394–
410 (2014)
44. Bui, H.P., Tomar, S., Courtecuisse, H., Cotin, S., Bordas, S.P.A.: Real-time error control for
surgical simulation. IEEE Trans. Biomed. Eng. 65, 596–607 (2018)
45. Cotin, S., Delingette, H., Ayache, N.: A hybrid elastic model for real-time cutting, deformations, and force feedback for surgery training and simulation. Vis. Comput. 16, 437–452 (2000)
46. Belytschko, T., Lu, Y.Y., Gu, L.: Element-free Galerkin methods. Int. J. Numer. Methods Eng.
37, 229–256 (1994)
47. Belytschko, T., Tabbara, M.: Dynamic fracture using element-free Galerkin methods. Int. J.
Numer. Methods Eng. 39, 923–938 (1996)
48. Belytschko, T., Organ, D., Gerlach, C.: Element-free Galerkin methods for dynamic fracture
in concrete. Comput. Methods Appl. Mech. Eng. 187, 385–399 (2000)
49. Rabczuk, T., Belytschko, T.: Adaptivity for structured meshfree particle methods in 2D and
3D. Int. J. Numer. Methods Eng. 63, 1559–1582 (2005)
50. Bordas, S., Rabczuk, T., Zi, G.: Three-dimensional crack initiation, propagation, branching
and junction in non-linear materials by an extended meshfree method without asymptotic
enrichment. Eng. Fract. Mech. 75, 943–960 (2008)
51. Ionescu, I., Weiss, J.A., Guilkey, J., Cole, M., Kirby, R.M., Berzins, M.: Ballistic injury
simulation using the material point method. Stud. Health Technol. Inform. 119, 228–233
(2006)
52. Rabczuk, T., Belytschko, T.: A three-dimensional large deformation meshfree method for
arbitrary evolving cracks. Comput. Methods Appl. Mech. Eng. 196, 2777–2799 (2007)
53. Belytschko, T., Krongauz, Y., Organ, D., Flaming, M., Krysl, P.: Meshless methods: an
overview and recent developments. Comput. Methods Appl. Mech. Eng. 139, 3–47 (1996)
54. Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: algorithms based
on Hamilton-Jacobi formulations. J. Comput. Phys. 79, 12–49 (1988)
55. Stolarska, M., Chopp, D.L., Moës, N., Belytschko, T.: Modelling crack growth by level sets in
the extended finite element method. Int. J. Numer. Methods Eng. 51, 943–960 (2001)
56. Jin, X., Lee, J.B., Leung, L.Y., Zhang, L., Yang, K.H., King, A.I.: Biomechanical response of
the bovine pia-arachnoid complex to tensile loading at varying strain-rates. Stapp Car Crash J.
50, 637–649 (2006)
57. Jin, X.: Biomechanical response and constitutive modeling of bovine pia-arachnoid complex,
p. 140. Wayne State University, Michigan (2009)
A. Wittek et al.
35. Dolbow, J., Belytschko, T.: Numerical integration of the Galerkin weak form in meshfree
methods. Comput. Mech. 23, 219–230 (1999)
36. Beissel, S., Belytschko, T.: Nodal integration of the element-free Galerkin method. Comput.
Methods Appl. Mech. Eng. 139, 49–74 (1996)
37. Chen, J.-S., Wu, C.-T., Yoon, S., You, Y.: A stabilized conforming nodal integration for
Galerkin mesh-free methods. Int. J. Numer. Methods Eng. 50, 435–466 (2001)
38. Quak, W., van den Boogaard, A., González, D., Cueto, E.: A comparative study on the
performance of meshless approximations and their integration. Comput. Mech. 48, 121–137
(2011)
39. Wittek, A., Joldes, G., Miller, K.: Algorithms for computational biomechanics of the brain. In:
Miller, K. (ed.) Biomechanics of the Brain, pp. 189–219. Springer, New York (2011)
40. Mor, A.B., Kanade, T.: Modifying soft tissue models: progressive cutting with minimal
new element creation. In: Delp, S.L., DiGoia, A.M., Jaramaz, B. (eds.) Medical Image
Computing and Computer-Assisted Intervention – MICCAI 2000, pp. 598–607. Springer,
Berlin/Heidelberg (2000)
41. Bielser, D., Glardon, P., Teschner, M., Gross, M.: Interactive simulation of surgical cuts. Graph.
Model. 66, 116–125 (2004)
42. Courtecuisse, H., Jung, H., Allard, J., Duriez, C., Lee, D.Y., Cotin, S.: GPU-based real-time
soft tissue deformation with cutting and haptic feedback. Prog. Biophys. Mol. Biol. 103, 159–
168 (2010)
43. Courtecuisse, H., Allard, J., Kerfriden, P., Bordas, S., Cotin, S., Duriez, C.: Real-time
simulation of contact and cutting of heterogeneous soft-tissues. Med. Image Anal. 18, 394–
410 (2014)
44. Bui, H.P., Tomar, S., Courtecuisse, H., Cotin, S., Bordas, S.P.A.: Real-time error control for
surgical simulation. IEEE Trans. Biomed. Eng. 65, 596–607 (2018)
45. Cotin, S., Delingette, H., Ayache, N.: A hybrid elastic model for real-time cutting, deformations, and force feedback for surgery training and simulation. Vis. Comput. 16, 437–452 (2000)
46. Belytschko, T., Lu, Y.Y., Gu, L.: Element-free Galerkin methods. Int. J. Numer. Methods Eng.
37, 229–256 (1994)
47. Belytschko, T., Tabbara, M.: Dynamic fracture using element-free Galerkin methods. Int. J.
Numer. Methods Eng. 39, 923–938 (1996)
48. Belytschko, T., Organ, D., Gerlach, C.: Element-free Galerkin methods for dynamic fracture
in concrete. Comput. Methods Appl. Mech. Eng. 187, 385–399 (2000)
49. Rabczuk, T., Belytschko, T.: Adaptivity for structured meshfree particle methods in 2D and
3D. Int. J. Numer. Methods Eng. 63, 1559–1582 (2005)
50. Bordas, S., Rabczuk, T., Zi, G.: Three-dimensional crack initiation, propagation, branching
and junction in non-linear materials by an extended meshfree method without asymptotic
enrichment. Eng. Fract. Mech. 75, 943–960 (2008)
51. Ionescu, I., Weiss, J.A., Guilkey, J., Cole, M., Kirby, R.M., Berzins, M.: Ballistic injury
simulation using the material point method. Stud. Health Technol. Inform. 119, 228–233
(2006)
52. Rabczuk, T., Belytschko, T.: A three-dimensional large deformation meshfree method for
arbitrary evolving cracks. Comput. Methods Appl. Mech. Eng. 196, 2777–2799 (2007)
53. Belytschko, T., Krongauz, Y., Organ, D., Flaming, M., Krysl, P.: Meshless methods: an
overview and recent developments. Comput. Methods Appl. Mech. Eng. 139, 3–47 (1996)
54. Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: algorithms based
on Hamilton-Jacobi formulations. J. Comput. Phys. 79, 12–49 (1988)
55. Stolarska, M., Chopp, D.L., Moës, N., Belytschko, T.: Modelling crack growth by level sets in
the extended finite element method. Int. J. Numer. Methods Eng. 51, 943–960 (2001)
56. Jin, X., Lee, J.B., Leung, L.Y., Zhang, L., Yang, K.H., King, A.I.: Biomechanical response of
the bovine pia-arachnoid complex to tensile loading at varying strain-rates. Stapp Car Crash J.
50, 637–649 (2006)
57. Jin, X.: Biomechanical response and constitutive modeling of bovine pia-arachnoid complex,
p. 140. Wayne State University, Michigan (2009)