A coupled damage-plasticity model for concrete based on thermodynamic principles: Part II: Non-local regularization and numerical implementation

International Journal for Numerical and Analytical Methods in Geomechanics

Volumn 32, Issue 4, 2008, Pages 391-413

  Nguyen, Giang D ^a   Houlsby, Guy T ^b  

^a UNIVERSITY OF NEW MEXICO   (United States)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Concrete; Damage; Non local; Numerical implementation; Plasticity

Indexed keywords

CONSTITUTIVE MODELS; DAMAGE DETECTION; FINITE ELEMENT METHOD; INTEGRAL EQUATIONS; NONLINEAR ANALYSIS; PLASTICITY; STRESS CONCENTRATION; THERMODYNAMICS;

DAMAGE-PLASTICITY MODEL; NON-LOCAL REGULARIZATION; SOFTENING MATERIALS;

CONCRETES;

CONCRETES; CONSTITUTIVE MODELS; DAMAGE DETECTION; FINITE ELEMENT METHOD; INTEGRAL EQUATIONS; NONLINEAR ANALYSIS; PLASTICITY; STRESS CONCENTRATION; THERMODYNAMICS;

CONCRETE; CONSTITUTIVE EQUATION; DAMAGE; MODELING; PLASTICITY; THERMODYNAMICS;

EID: 40849115115     PISSN: 03639061     EISSN: 10969853     Source Type: Journal    
DOI: 10.1002/nag.649     Document Type: Article

References (44)

1. Nguyen GD, Houlsby GT. A coupled damage-plasticity model for concrete based on thermodynamic principles: Part I: model formulation and parameter identification. International Journal for Numerical and Analytical Methods in Geomechanics 2007; DOI: 10.1002/nag.627.
2. Pijaudier-Cabot G, Bazant ZP. Non-local damage theory. Journal of Engineering Mechanics (ASCE) 1987; 113(10):1512-1533.
3. Bazant ZP, Jirásek M. Non-local integral formulation of plasticity and damage: survey of progress. Journal of Engineering Mechanics (ASCE) 2002; 128(11):1119-1149.
4. Jirásek M, Marfia S. Non-local damage model based on displacement averaging. International Journal for Numerical Methods in Engineering 2005; 63(1):77-102.
5. Grassl P, Jirásek M. Plastic model with non-local damage applied to concrete. International Journal for Numerical and Analytical Methods in Geomechanics 2006; 30:71-90.
6. Jirásek M, Bazant ZP. Inelastic Analysis of Structures. Wiley: New York, 2002.
7. Nguyen GD, Houlsby GT. Nonlocal damage modelling of concrete: a procedure for the determination of parameters. International Journal for Numerical and Analytical Methods in Geomechanics 2007; 31:867-891.
8. Crisfield MA. Non-linear Finite Element Analysis of Solids and Structures, vols. 1 and 2. Wiley: New York, 1997.
9. May IM, Duan Y. A local arc-length procedure for strain softening. Computers and Structures 1997; 64(1-4): 297-303.
10. Nguyen GD. A thermodynamic approach to constitutive modelling of concrete using damage mechanics and plasticity theory. D.Phil. Dissertation, Department of Engineering Science, University of Oxford, August 2005.
11. Houlsby GT, Puzrin AM. A thermomechanical framework for constitutive models for rate-independent dissipative materials. International Journal of Plasticity 2000; 16:1017-1047.
12. Collins IF, Houlsby GT. Application of thermomechanical principles to the modelling of geotechnical materials. Proceedings of the Royal Society of London, Series A 1997; 453:1975-2001.
13. Ladeveze P. Sur une theorie de l'endommagement anisotrope. Rapport interne No. 34, LMT Cachan, France, 1983.
14. Ortiz M. A constitutive theory for the inelastic behaviour of concrete. Mechanics of Materials 1985; 4:67-93.
15. Bazant ZP, Oh BH. Crack band theory for fracture of concrete. Materials and Structures (RILEM, Paris) 1983; 16:155-177.
16. Jirásek M, Patzák B. Models for quasibrittle failure: theoretical and computational aspects. ECCM-2001 European Conference on Computational Mechanics, Cracow, Poland, 26-29 June 2001.
17. Jirásek M. Nonlocal models for damage and fracture: comparison of approaches. International Journal of Solids and Structures 1998; 35(31-32):4133-4145.
18. Bazant ZP. Why continuum damage is non-local: micromechanics arguments. Journal of Engineering Mechanics (ASCE) 1991; 117(5):1070-1087.
19. Bazant ZP. Non-local damage theory based on micromechanics of crack interactions. Journal of Engineering Mechanics (ASCE) 1994; 120(3):593-617.
20. Nguyen GD. A thermodynamic approach to non-local damage modelling of concrete. International Journal of Solids and Structures 2007, submitted.
21. Gitman IM, Askes H, Aifantis EC. The representative volume size in static and dynamic micro-macro transitions. International Journal of Fracture 2005; 135:L3-L9.
22. Rots JG, Nauta P, Kusters GMA, Blaauwendraad J. Smeared crack approach and fracture localization in concrete. Heron 30(1), Stevin Laboratory, Delft University of Technology, Delft, The Netherlands, 1985.
23. De Borst R, Muhlhaus H-B. Gradient-dependent plasticity: formulation and algorithmic aspects. International Journal for Numerical Methods in Engineering 1992; 35:521-539.
24. Meftah F, Reynouard JM. A multilayered mixed beam element in gradient plasticity for the analysis of localized failure modes. Mechanics of Cohesive-frictional Materials 1998; 3:305-322.
25. Zhao J, Sheng D, Zhou W. Shear banding analysis of geomaterials by strain gradient enhanced damage model. International Journal of Solids and Structures 2005; 42(20):5335-5355.
26. Bazant ZP, Pijaudier-Cabot G. Measurement of characteristic length of nonlocal continuum. Journal of Engineering Mechanics (ASCE) 1989; 115(4):755-767.
27. Carmeliet J. Optimal estimation of gradient damage parameters from localization phenomena in quasi-brittle materials. Mechanics of Cohesive-frictional Materials 1999; 4:1-16.
28. Le Bellego C, Dube JF, Pijaudier-Cabot G, Gerard B. Calibration of non-local damage model from size effect tests. European Journal of Mechanics - A/Solids 2003; 22:33-46.
29. De Borst R. Nonlinear analysis of frictional materials. Ph.D. Dissertation, Delft University of Technology, Delft, The Netherlands, 1986.
30. Peerlings RHJ, de Borst R, Brekelmans WAM, Geers MGD. Gradient enhanced damage modelling of concrete fracture. Mechanics of Cohesive-frictional Materials 1998; 3:323-342.
31. Peerlings RHJ. Enhanced damage modelling for fracture and fatigue. Ph.D. Dissertation, Eindhoven University of Technology, Eindhoven, The Netherlands, 1999.
32. Jirásek M, Patzák B. Consistent tangent stiffness for non-local damage models. Computers and Structures 2002; 80:1279-1293.
33. Jirásek M, Rolshoven S, Grassl P. Size effect on fracture energy induced by non-locality. International Journal for Numerical and Analytical Methods in Geomechanics 2004; 28:653-670.
34. Shi C, van Dam AG, van Mier JGM, Sluys LJ. Crack interaction in concrete. In Materials for Buildings and Structures EUROMAT, Wittmann FH (ed.), vol. 6. Wiley-VCH: Weinheim, Germany, 2000; 125-131.
35. Petersson PE. Crack growth and development of fracture zones in plain concrete and similar materials. Report TVBM-1006, Division of Building Materials, Lund Institute of Technology, Lund, Sweden, 1981.
36. Hordijk DA. Local approach to fatigue of concrete. Ph.D. Dissertation, Delft University of Technology, Delft, The Netherlands, 1991.
37. Arrea M, Ingraffea A. Mixed mode crack propagation in mortar and concrete. Report 81-13, Department of Structural Engineering, Cornell University, Ithaca, NY, U.S.A., 1982.
38. Alfaiate J, Pires EB, Martins JAC. A finite element model for the study of crack propagation in concrete. Proceedings of 2nd International Conference on Computer Aided Assessment and Control (Localized Damage 92), vol. 1: Fatigue and Fracture Mechanics, Southampton, U.K., 1992; 261-280.
39. Jefferson AD. Craft - a plastic-damage-contact model for concrete. II. Model implementation with implicit return-mapping algorithm and consistent tangent matrix. International Journal of Solids and Structures 2003; 40: 6001-6022.
40. Rocco C, Guinea GV, Planas J, Elices M. The effect of the boundary conditions on the cylinder splitting strength. In Fracture Mechanics of Concrete Structures, Wittmann FH (ed.); Proceedings of the FRAMCOS-2. AEDIFICATIO Publishers: Freiburg, 1995.
41. Rocco C, Guinea GV, Planas J, Elices M. Review of splitting-test standards from a fracture mechanics point of view. Cement and Concrete Research 2001; 31:73-82.
42. CEB-FIB Model Code 1990: Design Code/Comité Euro-International du Béton. Thomas Telford Publishing: London, England, 1993.
43. Comi C, Perego U. Fracture energy based bi-dissipative damage model for concrete. International Journal of Solids and Structures 2001; 38:6427-6454.
44. Feenstra PH, de Borst R. A composite plasticity model for concrete. International Journal of Solids and Structures 1996; 33(5):707-730.