10 Finite Element Algorithms for Computational Biomechanics of the Brain
271
37. Miller, K., Joldes, G., Lance, D., Wittek, A.: Total Lagrangian explicit dynamics finite element
algorithm for computing soft tissue deformation. Commun. Numer. Methods Eng. 23, 121–134
(2007)
38. Joldes, G.R., Wittek, A., Miller, K.: Non-locking tetrahedral finite element for surgical
simulation. Commun. Numer. Methods Eng. 25, 827–836 (2008)
39. Underwood, P.: Dynamic relaxation. In: Belytschko, T., Hughes, T.J.R. (eds.) Computational
Methods for Transient Analysis, vol. 1, pp. 245–265. New-Holland, Amsterdam (1983)
40. Joldes, G.R., Wittek, A., Miller, K.: Computation of intra-operative brain shift using dynamic
relaxation. Comput. Methods Appl. Mech. Eng. 198, 3313–3320 (2009)
41. Isaacson, E.: Analysis of Numerical Methods. Wiley, New York (1966)
42. Joldes, G.R., Wittek, A., Miller, K.: An adaptive dynamic relaxation method for solving
nonlinear finite element problems. Application to brain shift estimation. Int. J. Numer. Method.
Biomed. Eng. 27, 173–185 (2011)
43. Miller, K.: Biomechanics of the Brain for Computer Integrated Surgery. Publishing House of
Warsaw University of Technology, Warsaw (2002)
44. Miller, K., Chinzei, K.: Mechanical properties of brain tissue in tension. J. Biomech. 35, 483–
490 (2002)
45. Miller, K., Chinzei, K., Orssengo, G., Bednarz, P.: Mechanical properties of brain tissue invivo: experiment and computer simulation. J. Biomech. 33, 1369–1376 (2000)
46. Miller, K.: Constitutive modelling of abdominal organs. J. Biomech. 33, 367–373 (2000)
47. Miller, K., Chinzei, K.: Constitutive modelling of brain tissue; Experiment and Theory. J.
Biomech. 30, 1115–1121 (1997)
48. Bilston, L.E., Liu, Z., Phan-Tien, N.: Linear viscoelastic properties of bovine brain tissue in
shear. Biorheology. 34, 377–385 (1997)
49. Margulies, S.S., Thibault, L.E., Gennarelli, T.A.: Physical model simulations of brain injury in
the primate. J. Biomech. 23, 823–836 (1990)
50. Bonet, J., Burton, A.J.: A simple averaged nodal pressure tetrahedral element for incompressible and nearly incompressible dynamic explicit applications. Commun. Numer. Methods Eng.
14, 437–449 (1998)
51. Bonet, J., Marriott, H., Hassan, O.: An averaged nodal deformation gradient linear tetrahedral
element for large strain explicit dynamic applications. Commun. Numer. Methods Eng. 17,
551–561 (2001)
52. Zienkiewicz, O.C., Rojek, J., Taylor, R.L., Pastor, M.: Triangles and tetrahedra in explicit
dynamic codes for solids. Int. J. Numer. Methods Eng. 43, 565–583 (1998)
53. Dohrmann, C.R., Heinstein, M.W., Jung, J., Key, S.W., Witkowski, W.R.: Node-based uniform
strain elements for three-node triangular and four-node tetrahedral meshes. Int. J. Numer.
Methods Eng. 47, 1549–1568 (2000)
54. Joldes, G.R., Wittek, A., Miller, K.: Non-locking tetrahedral finite element for surgical
simulation. Commun. Numer. Methods Eng. 25, 827–836 (2009)
55. Joldes, G.R., Wittek, A., Miller, K.: An efficient hourglass control implementation for the
uniform strain hexahedron using the Total Lagrangian formulation. Commun. Numer. Methods
Eng. 23, 315–323 (2008)
56. Hallquist, J.O., Goudreau, G.L., Benson, D.J.: Sliding interfaces with contact-impact in largescale Lagrangian computations. Comput. Methods Appl. Mech. Eng. 51, 107–137 (1985)
57. Doghri, I., Muller, A., Taylor, R.L.: A general three-dimensional contact procedure for implicit
finite element codes. Eng. Comput. 15, 233–259 (1998)
58. Stewart, J.R., Gullerud, A.S., Heinstein, M.W.: Solution verification for explicit transient
dynamics problems in the presence of hourglass and contact forces. Comput. Methods Appl.
Mech. Eng. 195, 1499–1516 (2006)
59. Sauvé, R.G., Morandin, G.D.: Simulation of contact in finite deformation problems – algorithm. Int. J. Mech. Mater. Des. 1, 287–316 (2004)
60. Dassault Systèmes Simulia Corporation: ABAQUS Theory Guide: Version 6.14 (2014)
271
37. Miller, K., Joldes, G., Lance, D., Wittek, A.: Total Lagrangian explicit dynamics finite element
algorithm for computing soft tissue deformation. Commun. Numer. Methods Eng. 23, 121–134
(2007)
38. Joldes, G.R., Wittek, A., Miller, K.: Non-locking tetrahedral finite element for surgical
simulation. Commun. Numer. Methods Eng. 25, 827–836 (2008)
39. Underwood, P.: Dynamic relaxation. In: Belytschko, T., Hughes, T.J.R. (eds.) Computational
Methods for Transient Analysis, vol. 1, pp. 245–265. New-Holland, Amsterdam (1983)
40. Joldes, G.R., Wittek, A., Miller, K.: Computation of intra-operative brain shift using dynamic
relaxation. Comput. Methods Appl. Mech. Eng. 198, 3313–3320 (2009)
41. Isaacson, E.: Analysis of Numerical Methods. Wiley, New York (1966)
42. Joldes, G.R., Wittek, A., Miller, K.: An adaptive dynamic relaxation method for solving
nonlinear finite element problems. Application to brain shift estimation. Int. J. Numer. Method.
Biomed. Eng. 27, 173–185 (2011)
43. Miller, K.: Biomechanics of the Brain for Computer Integrated Surgery. Publishing House of
Warsaw University of Technology, Warsaw (2002)
44. Miller, K., Chinzei, K.: Mechanical properties of brain tissue in tension. J. Biomech. 35, 483–
490 (2002)
45. Miller, K., Chinzei, K., Orssengo, G., Bednarz, P.: Mechanical properties of brain tissue invivo: experiment and computer simulation. J. Biomech. 33, 1369–1376 (2000)
46. Miller, K.: Constitutive modelling of abdominal organs. J. Biomech. 33, 367–373 (2000)
47. Miller, K., Chinzei, K.: Constitutive modelling of brain tissue; Experiment and Theory. J.
Biomech. 30, 1115–1121 (1997)
48. Bilston, L.E., Liu, Z., Phan-Tien, N.: Linear viscoelastic properties of bovine brain tissue in
shear. Biorheology. 34, 377–385 (1997)
49. Margulies, S.S., Thibault, L.E., Gennarelli, T.A.: Physical model simulations of brain injury in
the primate. J. Biomech. 23, 823–836 (1990)
50. Bonet, J., Burton, A.J.: A simple averaged nodal pressure tetrahedral element for incompressible and nearly incompressible dynamic explicit applications. Commun. Numer. Methods Eng.
14, 437–449 (1998)
51. Bonet, J., Marriott, H., Hassan, O.: An averaged nodal deformation gradient linear tetrahedral
element for large strain explicit dynamic applications. Commun. Numer. Methods Eng. 17,
551–561 (2001)
52. Zienkiewicz, O.C., Rojek, J., Taylor, R.L., Pastor, M.: Triangles and tetrahedra in explicit
dynamic codes for solids. Int. J. Numer. Methods Eng. 43, 565–583 (1998)
53. Dohrmann, C.R., Heinstein, M.W., Jung, J., Key, S.W., Witkowski, W.R.: Node-based uniform
strain elements for three-node triangular and four-node tetrahedral meshes. Int. J. Numer.
Methods Eng. 47, 1549–1568 (2000)
54. Joldes, G.R., Wittek, A., Miller, K.: Non-locking tetrahedral finite element for surgical
simulation. Commun. Numer. Methods Eng. 25, 827–836 (2009)
55. Joldes, G.R., Wittek, A., Miller, K.: An efficient hourglass control implementation for the
uniform strain hexahedron using the Total Lagrangian formulation. Commun. Numer. Methods
Eng. 23, 315–323 (2008)
56. Hallquist, J.O., Goudreau, G.L., Benson, D.J.: Sliding interfaces with contact-impact in largescale Lagrangian computations. Comput. Methods Appl. Mech. Eng. 51, 107–137 (1985)
57. Doghri, I., Muller, A., Taylor, R.L.: A general three-dimensional contact procedure for implicit
finite element codes. Eng. Comput. 15, 233–259 (1998)
58. Stewart, J.R., Gullerud, A.S., Heinstein, M.W.: Solution verification for explicit transient
dynamics problems in the presence of hourglass and contact forces. Comput. Methods Appl.
Mech. Eng. 195, 1499–1516 (2006)
59. Sauvé, R.G., Morandin, G.D.: Simulation of contact in finite deformation problems – algorithm. Int. J. Mech. Mater. Des. 1, 287–316 (2004)
60. Dassault Systèmes Simulia Corporation: ABAQUS Theory Guide: Version 6.14 (2014)