Reference
1. Besson J. Continuum models of ductile fracture: A review.International Journal of Damage Mechanics . 2010;19(1):3–52.
2. Griffith AA. The Phenomena of Rupture and Flow in Solids.Philosophical Transactions of the Royal Society A: Mathematical,
Physical and Engineering Sciences . 1921;221(582–593):163–98.
3. Kuhn C, Müller R. A continuum phase field model for fracture.Engineering Fracture Mechanics . 2010;77(18):3625–34.
4. Hakim V, Karma A. Laws of crack motion and phase-field models of
fracture. Journal of the Mechanics and Physics of Solids .
2009;57(2):342–68.
5. Francfort GA, Marigo JJ. Revisiting brittle fracture as an energy
minimization problem. Journal of the Mechanics and Physics of
Solids . 1998;46(8):1319–42.
6. Mumford D, Shah J. Optimal approximations by piecewise smooth
functions and associated variational problems. Communications on
Pure and Applied Mathematics . 1989;42(5):577–685.
7. Bourdin B, Francfort GA, Marigo JJ. Numerical experiments in
revisited brittle fracture. Journal of the Mechanics and Physics
of Solids . 2000;48(4):797–826.
8. Miehe C, Hofacker M, Welschinger F. A phase field model for
rate-independent crack propagation: Robust algorithmic implementation
based on operator splits. Computer Methods in Applied Mechanics
and Engineering . 2010;199(45–48):2765–78.
9. Miehe C, Welschinger F, Hofacker M. Thermodynamically consistent
phase-field models of fracture: Variational principles and multi-field
FE implementations. International Journal for Numerical Methods in
Engineering . 2010;83(10):1273–311.
10. Larsen CJ. Models for dynamic fracture based on Griffith’s
criterion. IUTAM Bookseries . 2010;21:131–40.
11. LARSEN CJ, ORTNER C, SÜLI E. Existence of Solutions To a Regularized
Model of Dynamic Fracture. Mathematical Models and Methods in
Applied Sciences . 2010;20(07):1021–48.
12. Bourdin B, Larsen CJ, Richardson CL. A time-discrete model for
dynamic fracture based on crack regularization. International
Journal of Fracture . 2011;168(2):133–43.
13. Borden MJ, Verhoosel C V., Scott MA, Hughes TJR, Landis CM. A
phase-field description of dynamic brittle fracture. Computer
Methods in Applied Mechanics and Engineering . 2012;217–220:77–95.
14. Hofacker M, Miehe C. A phase field model of dynamic fracture: Robust
field updates for the analysis of complex crack patterns.International Journal for Numerical Methods in Engineering .
2013;93(3):276–301.
15. Ambati M, Gerasimov T, De Lorenzis L. Phase-field modeling of
ductile fracture. Computational Mechanics . 2015;55(5):1017–40.
16. Ambati M, Kruse R, De Lorenzis L. A phase-field model for ductile
fracture at finite strains and its experimental verification.Computational Mechanics . 2016;57(1):149–67.
17. Miehe C, Hofacker M, Schänzel L-M, Aldakheel F. ScienceDirect Phase
field modeling of fracture in multi-physics problems. Part II. Coupled
brittle-to-ductile failure criteria and crack propagation in
thermo-elastic–plastic solids. Comput Methods Appl Mech Engrg .
2014;
18. Miehe C, Aldakheel F, Raina A. Phase field modeling of ductile
fracture at finite strains: A variational gradient-extended
plasticity-damage theory. International Journal of Plasticity .
2016;84:1–32.
19. Broka SM, Dubois PE, Joucken KL. A structural deficiency of TCI
syringes [6]. Anesthesia and Analgesia . 2000;90(4):1002–3.
20. Hofacker M, Miehe C. A Phase Field Model for Ductile to Brittle
Failure Mode Transition. Pamm . 2012;12(1):173–4.
21. Miehe C, Teichtmeister S, Aldakheel F. Phase-field modelling of
ductile fracture: A variational gradient-extended plasticity-damage
theory and its micromorphic regularization. Philosophical
Transactions of the Royal Society A: Mathematical, Physical and
Engineering Sciences . 2016;374(2066).
22. Duda FP, Ciarbonetti A, Sánchez PJ, Huespe AE. A
phase-field/gradient damage model for brittle fracture in
elastic-plastic solids. International Journal of Plasticity .
2014;65:269–96.
23. Gerasimov T, De Lorenzis L. On penalization in variational
phase-field models of brittle fracture. Computer Methods in
Applied Mechanics and Engineering . 2019;354:990–1026.
24. Brach S, Tanné E, Bourdin B, Bhattacharya K. Phase-field study of
crack nucleation and propagation in elastic–perfectly plastic bodies.Computer Methods in Applied Mechanics and Engineering .
2019;353:44–65.
25. Sargado JM, Keilegavlen E, Berre I, Nordbotten JM. High-accuracy
phase-field models for brittle fracture based on a new family of
degradation functions. Journal of the Mechanics and Physics of
Solids . 2018;111:458–89.
26. Bourdin B, Francfort GA, Marigo JJ. The variational approach to
fracture. The Variational Approach to Fracture . 2008;1–164.
27. Borden MJ, Hughes TJR, Landis CM, Anvari A, Lee IJ. Corrigendum to
“A phase-field formulation for fracture in ductile materials: Finite
deformation balance law derivation, plastic degradation, and stress
triaxiality effects” [Comput. Methods Appl. Mech. Engrg. 312 (2016)
130–166](S0045782516311069)(10.1016. Computer Methods in
Applied Mechanics and Engineering . 2017;324:712–3.
28. Amor H, Marigo JJ, Maurini C. Regularized formulation of the
variational brittle fracture with unilateral contact: Numerical
experiments. Journal of the Mechanics and Physics of Solids .
2009;57(8):1209–29.
29. Contrafatto L, Cuomo M. A framework of elastic-plastic damaging
model for concrete under multiaxial stress states. International
Journal of Plasticity . 2006;22(12):2272–300.
30. Comi C, Perego U. Fracture energy based bi-dissipative damage model
for concrete. International Journal of Solids and Structures .
2001;38(36–37):6427–54.
31. Faria R, Oliver J, Cervera M. A strain-based plastic viscous-damage
model for massive concrete structures. International Journal of
Solids and Structures . 1998;35(14):1533–58.
32. Ambati M, Gerasimov T, De Lorenzis L. A review on phase-field models
of brittle fracture and a new fast hybrid formulation.Computational Mechanics . 2014;55(2):383–405.
33. Larsen, CJ; O, C; S, E. Existence of Solutions To a Regularized
Model of Dynamic Fracture. Mathematical Models & Methods in
Applied Sciences . 2010;20(7):1021–48.
34. Schlüter A, Willenbücher A, Kuhn C, Müller R. Phase field
approximation of dynamic brittle fracture. Computational
Mechanics . 2014;54(5):1141–61.
35. Ambati M, Gerasimov T, De Lorenzis L. Phase-field modeling of
ductile fracture. Computational Mechanics . 2015;55(5):1017–40.
36. Computational inelasticity. Vol. 37, Computers & Mathematics with
Applications. 2003. 134 p.
37. Ambrosio L, Tortorelli VM. Approximation of functional depending on
jumps by elliptic functional via t‐convergence. Communications on
Pure and Applied Mathematics . 1990;43(8):999–1036.
38. Development of Eight Node Isoparametric Quadrilateral (QUAD8)
Elements in Java.
39. Function S. 18 18–1. :1–15.
40. Msekh MA, Sargado JM, Jamshidian M, Areias PM, Rabczuk T. Abaqus
implementation of phase-field model for brittle fracture.Computational Materials Science . 2015;96(PB):472–84.
41. Eduardo A. de Souza Neto, Djordje Peric DRJO. Computational Methods
for Plasticity: Theory and Applications.
42. PETRINIC FDAN. Introduction to Computational Plasticity.
43. Simo, J.C., Hughes TJR. Computational Inelasticity.
44. Simo J ~C. Topics on the numerical analysis and
simulation of plasticity. Handbook of Numerical Analysis .
1999;III.
45. Auricchio F, Taylor RL. Two material models for cyclic plasticity:
Nonlinear kinematic hardening and generalized plasticity.International Journal of Plasticity . 1995;11(1):65–98.
46. Borden MJ, Hughes TJR, Landis CM, Anvari A, Lee IJ. A phase-field
formulation for fracture in ductile materials: Finite deformation
balance law derivation, plastic degradation, and stress triaxiality
effects. Computer Methods in Applied Mechanics and Engineering .
2016;312:130–66.
47. Xue L, Xue Liang. Ductile fracture modeling: theory, experimental
investigation and numerical verification. PhD Thesis . 2007;251.
48. Mediavilla J, Peerlings RHJ, Geers MGD. Discrete crack modelling of
ductile fracture driven by non-local softening plasticity.International Journal for Numerical Methods in Engineering .
2006;66(4):661–88.
49. Mediavilla J, Peerlings RHJ, Geers MGD. A robust and consistent
remeshing-transfer operator for ductile fracture simulations.Computers and Structures . 2006;84(8–9):604–23.
50. Amstutz BE, Sutton MA, Dawicke DS, Bonne M l. Effects of Mixed Mode
I/II Loading and Grain Orientation on Crack Initiation and Stable
Tearing in 2024-T3 Aluminum. Fatigue and Fracture Mechanics .
1997;27:105–25.
51. Hashin Z, Voloshin A. A Method to Produce Uniform Plane-stress
States with Applications to Fiber-reinforced Materials. :141–6.
52. Tvergaard V, Needleman A. Analysis of the cup-cone fracture in a
round tensile bar. Acta Metallurgica . 1984;32(1):157–69.
53. Rodriguez P, Ulloa J, Samaniego C, Samaniego E. A variational
approach to the phase field modeling of brittle and ductile fracture.International Journal of Mechanical Sciences . 2018;144:502–17.
54. Mediavilla J, Peerlings RHJ, Geers MGD. A robust and consistent
remeshing-transfer operator for ductile fracture simulations.Computers and Structures . 2006;84(8–9):604–23.
55. Mahmoud S, Lease K. The effect of specimen thickness on the
experimental characterization of critical crack-tip-opening angle in
2024-T351 aluminum alloy. Engineering Fracture Mechanics .
2003;70(3–4):443–56.
56. Introduction to the finite element method. Studies in
Mathematics and its Applications . 1978;4(C):36–109.
57. Molnár G, Gravouil A. 2D and 3D Abaqus implementation of a robust
staggered phase-field solution for modeling brittle fracture.Finite Elements in Analysis and Design . 2017;130:27–38.