A mixed finite element implementation of a gradient-enhanced coupled damage-plasticity model

International Journal of Damage Mechanics

Volumn 15, Issue 3, 2006, Pages 201-235

  Dorgan, Robert J ^a   Voyiadjis, George Z ^a  

^a LOUISIANA STATE UNIVERSITY   (United States)

Author keywords

Coupled damage plasticity; Enhanced continuum; Gradient theory; Localization; Mixed finite elements

Indexed keywords

ANISOTROPY; DEGREES OF FREEDOM (MECHANICS); FINITE ELEMENT METHOD; FREE ENERGY; GRADIENT METHODS; HARDENING; MATHEMATICAL MODELS; PLASTICITY;

COUPLED DAMAGE-PLASTICITY MODEL; DAMAGE TENSOR; PLASTIC STRAINS;

CONTINUUM MECHANICS;

EID: 33745292436     PISSN: 10567895     EISSN: 15307921     Source Type: Journal    
DOI: 10.1177/1056789506060740     Document Type: Article

References (55)

1. Aifantis, E.C. (1984a). Remarks on Media with Microstructures, International Journal of Engineering Science, 22 (8-10): 961-968.
2. Aifantis, E.C. (1984b). On the Microstructural Origin of Certain Inelastic Models, Journal of Engineering Materials and Technology, 106 (4): 326-330.
3. Aifantis, E.C. and Hirth, J.P. (1985). The Mechanics of Dislocations, ASM, Metals Park.
4. Aifantis, E.C. (1987). The Physics of Plastic Deformation, International Journal of Plasticity, 3 (3): 211-247.
5. Bammann, D.J. and Aifantis, E.C. (1981). On the Perfect Lattice-Dislocated State Interaction, In: Proceedings, International Symposium on the Mechanical Behaviour of Structured Media, Ottawa, Canada, May 18-21, pp. 79-91.
6. Bammann, D.J. and Aifantis, E.C. (1982). On a Proposal for a Continuum with Microstructure, Acta Mechanica, 45 (1-2): 91-121.
7. Bammann, D.J., Mosher, D., Hughes, D.A., Moody, N.R. and Dawson, P.R. (1999). Using Spatial Gradients to Model Localization Phenomena, Sandia National Laboratories Report SAND 99-8588.
8. Bažant, Z.P. and Pijaudier-Cabot, G. (1988). Nonlocal Continuum Damage, Localization Instability and Convergence, Journal of Applied Mechanics, 55: 287- 293.
9. Bažant, Z.P. (1984). Imbricate Continuum and its Variational Derivation, Journal of Engineering Mechanics, ASCE, 110 (12): 1693-1711.
10. Bažant, Z.P. and Chang, T.-P. (1984). Instability of Nonlocal Continuum and Strain Averaging, Journal of Engineering Mechanics, ASCE, 110 (10): 1441-1450.
11. Bažant, Z.P., Belytschko, T. and Chang, T.-P. (1984). Continuum Theory for Strain Softening, Journal of Engineering Mechanics, ASCE, 110 (12): 1666-1692.
12. Bažant, Z.P. and Pijaudier-Cabot, G. (1988). Nonlocal Continuum Damage, Localization Instability and Convergence, Journal of Applied Mechanics, 55: 287-293.
13. Belytschko, T., Liu, W.K. and Moran, B. (2000). Nonlinear Finite Elements for Continua and Structures, Wiley & Sons Ltd, New York.
14. Coussy, O. (1995). Mechanics of Porous Continua, Wiley and Sons Ltd, New York.
15. de Borst, R. and Mühlhaus, H.-B. (1992). Gradient-Dependent Plasticity Formulation and Algorithmic Aspects, International Journal of Numerical Methods in Engineering, 35 (3): 521-539.
16. de Borst, R., Pamin, J. and Sluys, L.J. (1995). Computational Issues in Gradient Plasticity, In: Muhlhaus, H.-B. (ed.), Continuum Models for Materials with Microstructure, pp. 159-200, John Wiley & Sons Ltd, New York.
17. de Borst, R. and Pamin, J. (1996) Some Novel Developments in Finite Element Procedures for Gradient-Dependent Plasticity, International Journal for Numerical Methods in Engineering, 39 (14): 2477-2505.
18. Doghri, I. (1993). Fully Implicit Integration and Consistent Tangent Modulus in Elasto-Plasticity, International Journal for Numerical Methods in Engineering, 36: 3915-3932.
19. Dorgan, R.J. and Voyiadjis, G.Z. (2003). Nonlocal Dislocation Based Plasticity Incorporating Gradients of Hardening, Mechanics of Materials, 35 (8): 721-732.
20. Eringen, A.C. and Edelen, D.G.B. (1972). On Nonlocal Elasticity, International Journal for Engineering Science, 10: 233-248.
21. Fleck, N.A. and Hutchinson, J.W. (1993). A Phenomenological Theory for Strain Gradient Effects in Plasticity, Journal of the Mechanics and Physics of Solids, 41 (12): 1825-1857.
22. Fleck, N.A., Muller, G.M., Ashby, M.F. and Hutchinson, J.W. (1994). Strain Gradient Plasticity: Theory and Experiment, Acta Metallurgica Et Materialia, 42 (2): 475-487.
23. Kachanov, L.M. (1958). On the Creep Fracture Time, Izvestiya Akademii Nauk USSR Otd. Tech., 8: 26-31 (in Russian).
24. Kröner, E. (1967). Elasticity Theory of Materials with Long Range Cohesive Forces, International Journal of Solid and Structures, 3: 731-742.
25. Kunin, I.A. (1968). The Theory of Elastic Media with Microstructure and the Theory of Dislocations, In: Kroner, E. (ed.), Mechanics of Generalized Continua, pp. 298-311, Springer-Verlag, Heidelberg, Germany.
26. Kuhl, E., Ramm, E. and de Borst, R. (2000). An Anisotropic Gradient Damage Model for Quasi-Brittle Materials, Computer Methods in Applied Mechanics and Engineering, 183 (1-2): 87- 103.
27. Kuhn, H. and Tucker, A. (1951). Nonlinear Programming, In: Proceedings, 2nd Berkeley Symposium on Mathematical Statistics and Probabilistics, University of California Press, pp. 481-492.
28. Lee, H., Peng, K. and Wang, J. (1985). An Anisotropic Damage Criterion for Deformation Instability and its Application to Forming Limit Analysis of Metal Plates, Engineering Fracture Mechanics, 21 (5): 1031-1054.
29. Malvern, L.E. (1969). Introduction to the Mechanics of a Continuous Medium, Prentice-Hall, New Jersey.
30. Mühlhaus, H.B. and Aifantis, E.C. (1991). A Variational Principle for Gradient Plasticity, International Journal of Solids and Structures, 28 (7): 845-857.
31. Pamin, J. (1994). Gradient-Dependent Plasticity in Numerical Simulation of Localization Phenomena, Dissertation, Delft University of Technology.
32. Pamin, J. and de Borst, R. (1999). Stiffness Degradation in Gradient-Dependent Coupled Damage-Plasticity, Archives of Mechanics, 51 (3-4): 419-446.
33. Peerlings, R.H.J., de Borst, R., Brekelmans, W.A.M. and de Vree, J.H.P. (1996). Gradient Enhanced Damage for Quasi-Brittle Materials, International Journal for Numerical Methods in Engineering, 39: 3391-3403.
34. Pijaudier-Cabot, G. and Bazant, Z.P. (1987). Nonlocal Damage Theory, Journal of Engineering Mechanics, 113 (10): 1512-1533.
35. Ramaswamy, S. and Aravas, N. (1998). Finite-Element Implementation Of Gradient Plasticity Models: Part I: Gradient-Dependent Yield Functions, Computer Methods in Applied Mechanics and Engineering, 163 (1-4): 11-532.
36. Simo, J.C. and Hughes, T.J.R. (1998). Computational Inelasticity, Springer-Verlag, New York.
37. Stolken, J.S. and Evans, A.G. (1998). A Microbend Test Method for Measuring the Plasticity Length-Scale, Acta Metallurgica Et Materialia, 46 (14): 5109-5115.
38. Vardoulakis, I. and Aifantis, E.C. (1989). Gradient - Dependent Dilatancy and its Implications in Shear Banding and Liquefaction, Ingenieur - Archive, 59 (3): 197-208.
39. Voyiadjis, G.Z. and Kattan, P.I. (1992). A Plasticity-Damage Theory for Large Deformation of Solids, Part I: Theoretical Formulation, International Journal of Engineering Science, 30 (9): 1089-1108.
40. Voyiadjis, G.Z. and Kattan, P.I. (1993). Damage of Fiber-Reinforced Composite Materials with Micromechanical Characterization, International Journal of Solids and Structures, 30 (20): 2757- 2778.
41. Voyiadjis, G.Z. and Kattan, P.I. (1999). Advances in Damage Mechanics: Metals and Metals Matrix Composites, Elsvier, Oxford.
42. Voyiadjis, G.Z. and Deliktas, B. (2000). A Coupled Anisotropic Damage Model for the Inelastic Response of Composite Materials-, Computer Methods in Applied Mechanics and Engineering, 183 (3-4): 159-199.
43. Voyiadjis, G.Z. and Dorgan, R.J. (2001). Gradient Formulation in Coupled Damage-Plasticity, Archives of Mechanics, 53 (4-5): 565-597.
44. Voyiadjis, G.Z., Deliktas, B. and Aifantis, E.C. (2001a). Multi-scale Analysis of Multiple Damage Mechanisms Coupled with Inelastic Behavior of Composite Materials, Journal of Engineering Mechanics, ASCE, 127 (7): 636-645.
45. Voyiadjis, G.Z. Dorgan, R.J. and Dorroh, J.R. (2001b). Bridging Length Scales Between Macroscopic Response and Microstructure Through Gradient Anisotropic Damage for MMCs, In: Proceedings, 2001 Energy Sources Technology Conference & Exhibition, February 2001, ASME Publishing Company, Houston, Texas.
46. Voyiadjis, G.Z. and Dorgan, R.J. (2002). Gradient Formulation in Coupled Damage-Plasticity, In: Khan, A.S. and Lopez-Pamies, O. (eds), Symposium on Plasticity, Damage and Fracture at Macro, Micro and Nano Scales, The Ninth International Symposium on Plasticity and its Applications, January 3-9, NEAT Press, Aruba.
47. Voyiadjis, G.Z. and Dorgan, R.J. (2004a). Bridging of Length Scales through Gradient Theory and Diffusion Equations of Dislocations, In: Liu, W.K. et al. (eds), Computer Methods in Applied Mechanics and Engineering, Special Issue on Multiple Scale Methods for Nanoscale Mechanics and Materials, 193 (17-20): 1671-1692.
48. Voyiadjis, G.Z. and Dorgan, R.J. (2004b). Formulation of a Gradient Enhanced Plasticity Model, In: Proceedings, 17th ASCE Engineering Mechanics Conference, June 13-16, 2004, University of Delaware, 8 pages.
49. Voyiadjis, G.Z., Abu Al-Rub, R.K., Palazotto, A.N. (2004). Thermodynamic Framework for Coupling of Non-Local Viscoplasticity and Non-Local Anisotropic Viscodamage for Dynamic Localization Problems using Gradient Theory, International Journal of Plasticity, 20 (6): 981-1038.
50. Voyiadjis, G.Z. and Dorgan, R.J. (2004). A Gradient Enhanced, Generalized Plasticity/Damage Model: Rigorous Mathematical Formulation and Finite Element Implementation, Journal of Mechanical Behavior of Materials, 15 (4-5): 309-340.
51. Voyiadjis, G.Z., Alsaleh, M.A. and Alshibli, K.A. (2005). Evolving Internal Length Scales in Plastic Strain Localization for Granular Materials, International Journal of Plasticity, 21 (10): 2000-2024.
52. Voyiadjis, G.Z. and Abu Al-Rub, R.K. (2005). Gradient Plasticity Theory with a Variable Length Scale Parameter, International Journal of Solids and Structures, 42 (14): 3998-4029.
53. Walgraef, D. and Aifantis, E.C. (1988). Plastic Instabilities, Dislocation Patterns and Nonequilibrium Phenomena, Res Mechanica, 23: 161-195.
54. Walgraef, D. and Aifantis, E.C. (1995). Dislocation Patterning in Fatigued Metals as a Result of Dynamical Instabilities, Journal of Applied Physics, 58 (2-3): 668-691.
55. Zbib, H.M. and Aifantis, E.C. (1988). On the Localization and Post-Localization Behavior of Plastic Deformation - I, II, III, Res Mechanica, 23: 261-305.