104
P. Kumar et al.
66. R. Radojcic, M. Nowak, M. Nakamoto, TechTuning: stress management for 3D through-siliconvia stacking technologies. AIP Conf. Proc. 1378, 5–20 (2011)
67. F. Roters, Advanced material models for the crystal plasticity finite element method: development of a general CPFEM framework. Habilitation Thesis, RWTH Aachen University
(2011)
68. G.I. Taylor, The mechanism of plastic deformation of crystals. Part I. Theor. Proc. R. Soc.
Lond. A 145, 362–387 (1934)
69. G.I. Taylor, The mechanism of plastic deformation of crystals. Part II. Comparison with
observations. Proc. R. Soc. Lond. A 145, 388–404 (1934)
70. D. Peirce, R.J. Asaro, A. Needleman, An analysis of nonuniform and localized deformation in
ductile single crystals. Acta Metall. 30, 1087–1119 (1982)
71. S.V. Harren, H.E. Deve, R.J. Asaro (1988) Shear band formation in plane strain compression.
Acta Metall. 36, 2435–2480 (1988)
72. S.V. Harren, R.J. Asaro, Nonuniform deformations in polycrystals and aspects of the validity
of the Taylor model. J. Mech. Phys. Solids 37, 191–232 (1989)
73. R. Becker, J.F. Butler, H. Hu, L.A. Lalli, Analysis of an aluminum single crystal with unstable
initial orientation (001) [110] in channel die compression. Metall. Trans. A 22, 45–48 (1991)
74. W.D. Nix, J.R. Greer, G. Feng, E.T. Lilleodden, Deformation at the nanometer and micrometer
length scales: effects of strain gradients and dislocation starvation. Thin Solid Films 515,
3152–3157 (2007)
75. S.R. Kalidindi, Incorporation of deformation twinning in crystal plasticity models. J. Mech.
Phys. Solids 46, 267–290 (1998)
76. D. Raabe, D. Ma, F. Roters, Effects of initial orientation, sample geometry and friction
on anisotropy and crystallographic orientation changes in single crystal microcompression
deformation: a crystal plasticity finite element study. Acta Mater. 55, 4567–4583 (2007)
77. F. Roters, P. Eisenlohr, C. Kords, D.D. Tjahjanto, M. Diehl, D. Raabe, DAMASK: the Du¨sseldorf advanced material simulation kit for studying crystal plasticity using an FE based or a
spectral numerical solver. Procedia IUTAM 3, 3–10 (2012)
78. D. Cereceda, M. Diehl, F. Roters, D. Raabe, J.M. Perlado, J. Marian, Unraveling the temperature
dependence of the yield strength in single-crystal tungsten using atomistically-informed crystal
plasticity calculations. Int. J. Plasticity 78, 242–265 (2016)
79. L.Q. Chen, Phase-field models for microstructure evolution. Ann. Rev. Mater. Res. 32, 113–140
(2002)
80. N. Provatas, K. Elder, Phase-Field Methods in Material Science and Engineering (Wiley-VCH,
Weinheim, 2010)
81. K.R. Elder, M. Katakowski, M. Haataja, M. Grant, Modeling elasticity in crystal growth. Phys.
Rev. Lett. 88, 245701 (2002)
82. M. Seymour, N. Provatas, Structural phase field crystal approach for modeling graphene and
other two-dimensional structures. Phys Rev B 93, 035447 (2016)
83. L. Granasy, F. Podmaniczky, G.I. Toth, G. Tegze, T. Pusztai, Heterogeneous nucleation of/on
nanoparticles: a density functional study using the phase-field crystal model. Chem. Soc. Rev.
43, 2159–2173 (2014)
84. K.R. Elder, N. Provatas, J. Berry, P. Stefanovic, M. Grant, Phase-field crystal modeling and
classical density functional theory of freezing. Phys. Rev. B 75, 064107 (2007)
85. N. Ofori-Opoku, V. Fallah, M. Greenwood, S. Esmaeili, N. Provatas, Multicomponent phasefield crystal model for structural transformations in metal alloys. Phys. Rev. B 87, 134105
(2013)
86. J. Berry, N. Provatas, J. Rottler, C.W. Sinclair, Defect stability in phase-field crystal models:
Stacking faults and partial dislocations. Phys. Rev. B 86, 224112 (2012)
87. J. Berry, N. Provatas, J. Rottler, C.W. Sinclair, Phase field crystal modeling as a unified atomistic
approach to defect dynamics. Phys. Rev. B 89, 214117 (2014)
88. J. Berry, J. Rottler, C.W. Sinclair, N. Provatas, Atomistic study of diffusion-mediated plasticity
and creep using phase field crystal methods. Phys. Rev. B 92, 134103 (2015)
P. Kumar et al.
66. R. Radojcic, M. Nowak, M. Nakamoto, TechTuning: stress management for 3D through-siliconvia stacking technologies. AIP Conf. Proc. 1378, 5–20 (2011)
67. F. Roters, Advanced material models for the crystal plasticity finite element method: development of a general CPFEM framework. Habilitation Thesis, RWTH Aachen University
(2011)
68. G.I. Taylor, The mechanism of plastic deformation of crystals. Part I. Theor. Proc. R. Soc.
Lond. A 145, 362–387 (1934)
69. G.I. Taylor, The mechanism of plastic deformation of crystals. Part II. Comparison with
observations. Proc. R. Soc. Lond. A 145, 388–404 (1934)
70. D. Peirce, R.J. Asaro, A. Needleman, An analysis of nonuniform and localized deformation in
ductile single crystals. Acta Metall. 30, 1087–1119 (1982)
71. S.V. Harren, H.E. Deve, R.J. Asaro (1988) Shear band formation in plane strain compression.
Acta Metall. 36, 2435–2480 (1988)
72. S.V. Harren, R.J. Asaro, Nonuniform deformations in polycrystals and aspects of the validity
of the Taylor model. J. Mech. Phys. Solids 37, 191–232 (1989)
73. R. Becker, J.F. Butler, H. Hu, L.A. Lalli, Analysis of an aluminum single crystal with unstable
initial orientation (001) [110] in channel die compression. Metall. Trans. A 22, 45–48 (1991)
74. W.D. Nix, J.R. Greer, G. Feng, E.T. Lilleodden, Deformation at the nanometer and micrometer
length scales: effects of strain gradients and dislocation starvation. Thin Solid Films 515,
3152–3157 (2007)
75. S.R. Kalidindi, Incorporation of deformation twinning in crystal plasticity models. J. Mech.
Phys. Solids 46, 267–290 (1998)
76. D. Raabe, D. Ma, F. Roters, Effects of initial orientation, sample geometry and friction
on anisotropy and crystallographic orientation changes in single crystal microcompression
deformation: a crystal plasticity finite element study. Acta Mater. 55, 4567–4583 (2007)
77. F. Roters, P. Eisenlohr, C. Kords, D.D. Tjahjanto, M. Diehl, D. Raabe, DAMASK: the Du¨sseldorf advanced material simulation kit for studying crystal plasticity using an FE based or a
spectral numerical solver. Procedia IUTAM 3, 3–10 (2012)
78. D. Cereceda, M. Diehl, F. Roters, D. Raabe, J.M. Perlado, J. Marian, Unraveling the temperature
dependence of the yield strength in single-crystal tungsten using atomistically-informed crystal
plasticity calculations. Int. J. Plasticity 78, 242–265 (2016)
79. L.Q. Chen, Phase-field models for microstructure evolution. Ann. Rev. Mater. Res. 32, 113–140
(2002)
80. N. Provatas, K. Elder, Phase-Field Methods in Material Science and Engineering (Wiley-VCH,
Weinheim, 2010)
81. K.R. Elder, M. Katakowski, M. Haataja, M. Grant, Modeling elasticity in crystal growth. Phys.
Rev. Lett. 88, 245701 (2002)
82. M. Seymour, N. Provatas, Structural phase field crystal approach for modeling graphene and
other two-dimensional structures. Phys Rev B 93, 035447 (2016)
83. L. Granasy, F. Podmaniczky, G.I. Toth, G. Tegze, T. Pusztai, Heterogeneous nucleation of/on
nanoparticles: a density functional study using the phase-field crystal model. Chem. Soc. Rev.
43, 2159–2173 (2014)
84. K.R. Elder, N. Provatas, J. Berry, P. Stefanovic, M. Grant, Phase-field crystal modeling and
classical density functional theory of freezing. Phys. Rev. B 75, 064107 (2007)
85. N. Ofori-Opoku, V. Fallah, M. Greenwood, S. Esmaeili, N. Provatas, Multicomponent phasefield crystal model for structural transformations in metal alloys. Phys. Rev. B 87, 134105
(2013)
86. J. Berry, N. Provatas, J. Rottler, C.W. Sinclair, Defect stability in phase-field crystal models:
Stacking faults and partial dislocations. Phys. Rev. B 86, 224112 (2012)
87. J. Berry, N. Provatas, J. Rottler, C.W. Sinclair, Phase field crystal modeling as a unified atomistic
approach to defect dynamics. Phys. Rev. B 89, 214117 (2014)
88. J. Berry, J. Rottler, C.W. Sinclair, N. Provatas, Atomistic study of diffusion-mediated plasticity
and creep using phase field crystal methods. Phys. Rev. B 92, 134103 (2015)