11 Meshless Algorithms for Computational Biomechanics of the Brain
301
58. Jin, X., Zhang, G., Joldes, G.R., Yang, K.-H., Rohan, P.-Y., Miller, K., Wittek, A.: 2D Meshless algorithm for modelling of soft tissue undergoing fragmentation and large
deformation: Verification and performance evaluation. In: Proceedings of the 10th International
Symposium on Computer Methods in Biomechanics and Biomedical Engineering, pp. 327–
332. Arup (2012)
59. Jin, X., Joldes, G.R., Miller, K., Wittek, A.: 3D Algorithm for simulation of soft tissue cutting.
In: Wittek, A., Miller, K., Nielsen, P.M.F. (eds.) Computational Biomechanics for Medicine:
Models, Algorithms and Implementation, pp. 49–62. Springer, New York, ISBN 978-146146350-4 (2013)
60. Gültekin, O., Dal, H., Holzapfel, G.A.: A phase-field approach to model fracture of arterial
walls: theory and finite element analysis. Comput. Methods Appl. Mech. Eng. 312, 542–566
(2016)
61. Belytschko, T., Liu, W.K., Moran, B.: Nonlinear Finite Elements for Continua and Structures.
Wiley, Chichester (2006)
62. Isaacson, E.: Analysis of Numerical Methods. Wiley, New York (1966)
63. Cook, R.D., Malkus, D.S., Plesha, M.E.: Finite elements in dynamics and vibrations. In:
Concepts and Applications of Finite Element Analysis, pp. 367–428. Wiley, New York (1989)
64. Joldes, G.R., Wittek, A., Miller, K.: Stable time step estimates for mesh-free particle methods.
Int. J. Numer. Methods Eng. 91, 450–456 (2012)
65. Bathe, K.-J.: Finite Element Procedures. Prentice-Hall, Englewood Cliffs (1996)
66. Puso, M.A., Chen, J.S., Zywicz, E., Elmer, W.: Meshfree and finite element nodal integration
methods. Int. J. Numer. Methods Eng. 74, 416–446 (2008)
67. Waldron, K.J., Kinzel, G.L.: Kinematics, Dynamics, and Design of Machinery. Wiley, New
York (1999)
68. Wittek, A., Bourantas, G., Joldes, G.R., Khau, A., Mountris, K., Singh, S., Miller, K.: Meshless
method for simulation of needle insertion into soft tissues: preliminary results. In: Nash, M.,
Nielsen, P.M.F., Wittek, A., Miller, K., Joldes, G.R. (eds.) Computational Biomechanics for
Medicine, p. 15. Springer (2018). Accepted for publication
69. Bucholz, R., MacNeil, W., McDurmont, L.: The operating room of the future. Clin. Neurosurg.
51, 228–237 (2004)
70. Rivlin, R.S., Sawyers, K.N.: The strain-energy function for elastomers. Trans. Soc. Rheol. 20,
545–557 (1976)
301
58. Jin, X., Zhang, G., Joldes, G.R., Yang, K.-H., Rohan, P.-Y., Miller, K., Wittek, A.: 2D Meshless algorithm for modelling of soft tissue undergoing fragmentation and large
deformation: Verification and performance evaluation. In: Proceedings of the 10th International
Symposium on Computer Methods in Biomechanics and Biomedical Engineering, pp. 327–
332. Arup (2012)
59. Jin, X., Joldes, G.R., Miller, K., Wittek, A.: 3D Algorithm for simulation of soft tissue cutting.
In: Wittek, A., Miller, K., Nielsen, P.M.F. (eds.) Computational Biomechanics for Medicine:
Models, Algorithms and Implementation, pp. 49–62. Springer, New York, ISBN 978-146146350-4 (2013)
60. Gültekin, O., Dal, H., Holzapfel, G.A.: A phase-field approach to model fracture of arterial
walls: theory and finite element analysis. Comput. Methods Appl. Mech. Eng. 312, 542–566
(2016)
61. Belytschko, T., Liu, W.K., Moran, B.: Nonlinear Finite Elements for Continua and Structures.
Wiley, Chichester (2006)
62. Isaacson, E.: Analysis of Numerical Methods. Wiley, New York (1966)
63. Cook, R.D., Malkus, D.S., Plesha, M.E.: Finite elements in dynamics and vibrations. In:
Concepts and Applications of Finite Element Analysis, pp. 367–428. Wiley, New York (1989)
64. Joldes, G.R., Wittek, A., Miller, K.: Stable time step estimates for mesh-free particle methods.
Int. J. Numer. Methods Eng. 91, 450–456 (2012)
65. Bathe, K.-J.: Finite Element Procedures. Prentice-Hall, Englewood Cliffs (1996)
66. Puso, M.A., Chen, J.S., Zywicz, E., Elmer, W.: Meshfree and finite element nodal integration
methods. Int. J. Numer. Methods Eng. 74, 416–446 (2008)
67. Waldron, K.J., Kinzel, G.L.: Kinematics, Dynamics, and Design of Machinery. Wiley, New
York (1999)
68. Wittek, A., Bourantas, G., Joldes, G.R., Khau, A., Mountris, K., Singh, S., Miller, K.: Meshless
method for simulation of needle insertion into soft tissues: preliminary results. In: Nash, M.,
Nielsen, P.M.F., Wittek, A., Miller, K., Joldes, G.R. (eds.) Computational Biomechanics for
Medicine, p. 15. Springer (2018). Accepted for publication
69. Bucholz, R., MacNeil, W., McDurmont, L.: The operating room of the future. Clin. Neurosurg.
51, 228–237 (2004)
70. Rivlin, R.S., Sawyers, K.N.: The strain-energy function for elastomers. Trans. Soc. Rheol. 20,
545–557 (1976)