Non-local damage modelling of concrete: A procedure for the determination of model parameters

International Journal for Numerical and Analytical Methods in Geomechanics

Volumn 31, Issue 7, 2007, Pages 867-891

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

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Characteristic length; Length parameter; Non local damage; Parameter identification

Indexed keywords

COMPUTATIONAL MECHANICS; DAMAGE DETECTION; FRACTURE; MATHEMATICAL MODELS;

DAMAGE MODELLING; LENGTH PARAMETER; NON-LOCAL DAMAGE;

CONCRETES;

COMPUTATIONAL MECHANICS; CONCRETES; DAMAGE DETECTION; FRACTURE; MATHEMATICAL MODELS;

CORRELATION; DAMAGE MECHANICS; FRACTURE ZONE; IDENTIFICATION METHOD; NUMERICAL MODEL; PARAMETERIZATION;

EID: 34248230822     PISSN: 03639061     EISSN: 10969853     Source Type: Journal    
DOI: 10.1002/nag.563     Document Type: Article

References (47)

1. Pijaudier-Cabot G, Bazant ZP. Non-local damage theory. Journal of Engineering Mechanics 1987; 113(10): 1512-1533.
2. De Borst R, Muhlhaus HB. Gradient-dependent plasticity: formulation and algorithmic aspects. International Journal for Numerical Methods in Engineering 1992; 35:521-539.
3. Peerlings RHJ, de Borst R, Brekelmans WAM, de Vree JHP. Gradient enhanced damage for quasi-brittle materials. International Journal for Numerical Methods in Engineering 1996; 39:3391-3403.
4. Peerlings RHJ. Enhanced damage modelling for fracture and fatigue. Ph.D. Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 1999.
5. Jirásek M, Bazant ZP. Inelastic Analysis of Structures. Wiley: New York, 2002.
6. Le Bellego C, Dube JF, Pijaudier-Cabot G, Gerard B. Calibration of nonlocal damage model from size effect tests. European Journal of Mechanics - A/Solids 2003; 22:33-46.
7. Bazant ZP, Pijaudier-Cabot G. Measurement of characteristic length of nonlocal continuum. Journal of Engineering Mechanics 1989; 115(4):755-767.
8. Jirásek M. Comparison of nonlocal models for damage and fracture. LSC Internal Report 98/02, Department of Civil Engineering, Swiss Federal Institutive of Technology (EPFL), Lausanne, Switzerland, 1998.
9. Carmeliet J. Optimal estimation of gradient damage parameters from localization phenomena in quasi-brittle materials. Mechanics of Cohesive-frictional Materials 1999; 4:1-16.
10. Mahnken R, Kuhl E. Parameter identification of gradient enhanced damage models with the finite element method. European Journal of Mechanics - A/Solids 1999; 18:819-835.
11. Ferrara L, Di Prisco M. Mode I fracture behaviour in concrete: non-local damage modelling. Journal of Engineering Mechanics 2001; 127(7):678-692.
12. 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.
13. Mazars J, Pijaudier-Cabot G. From damage to fracture mechanics and conversely: a combined approach. International Journal of Solids and Structures 1996; 33(20-22):3327-3342.
14. Bazant ZP. Concrete fracture models: testing and practice. Engineering Fracture Mechanics 2002; 69:165-205.
15. Elices M, Guinea GV, Gomez J, Planas J. The cohesive zone model: advantages, limitations and challenges. Engineering Fracture Mechanics 2002; 69:137-163.
16. De Borst R, Pamin J. Gradient plasticity in numerical simulation of concrete cracking. European Journal of Mechanics - A/Solids 1996; 15(2):295-320.
17. Di Prisco M, Ferrara L, Meftah F, Pamin J, De Borst R, Mazars J, Reynouard JM. Mixed mode fracture in plain and reinforced concrete: some results on benchmark tests. International Journal of Fracture 2000; 103:127-148.
18. 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.
19. 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.
20. 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.
21. Bazant ZP. Analysis of work-of-fracture method for measuring fracture energy of concrete. Journal of Engineering Mechanics 1996; 122(2):138-144.
22. Tin-loi F, Que NS. Parameter identification of quasibrittle materials as a mathematical program with equilibrium constraints. Computer Methods in Applied Mechanics and Engineering 2001; 190:5819-5836.
23. Que NS, Tin-loi F. An optimization approach for indirect identification of cohesive crack properties. Computers and Structures 2002; 80:1383-1392.
24. Bazant ZP, Oh BH. Crack band theory for fracture of concrete. Materials and Structures (RILEM Paris) 1983; 16:155-177.
25. Bazant ZP, Jirásek M. Non-local integral formulation of plasticity and damage: survey of progress. Journal of Engineering Mechanics 2002; 128(11):1119-1149.
26. Karihaloo BL, Abdalla HM, Imjai T. A simple method for determining the true specific fracture energy of concrete. Magazine of Concrete Research 2003; 55(5):471-481.
27. Hu X, Duan K. Influence of fracture process zone height on fracture energy of concrete. Cement and Concrete Research 2004; 34(8):1321-1330.
28. Vardoulakis I. 2nd gradient constitutive models. In Constitutive Modelling of Granular Materials, Kolymbas D (ed.). Springer: Berlin, 1999; 225-248.
29. 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.
30. Nguyen GD. A thermodynamic approach to constitutive modelling of concrete using damage mechanics and plasticity theory. D.Phil. Thesis, Department of Engineering Science, Oxford University, 2005.
31. Houlsby GT, Puzrin AM. A thermomechanical framework for constitutive models for rate-independent dissipative materials. International Journal of Plasticity 2000; 16:1017-1047.
32. Ortiz M. A constitutive theory for the inelastic behavior of concrete. Mechanics of Materials 1985; 4:67-93.
33. Kupfer HB, Gerstle KH. Behavior of concrete under biaxial stresses. Journal of Engineering Mechanics 1973; 99(EM4):853-866.
34. Bazant ZP. Why continuum damage is non-local: micromechanics arguments. Journal of Engineering Mechanics 1991; 117(5):1070-1087.
35. Bazant ZP, Becq-Giraudon E. Statistical prediction of fracture parameters of concrete and implications for choice of testing standard. Cement and Concrete Research 2002; 32:529-556.
36. Planas J, Elices M. Fracture criteria for concrete: mathematical approximation and experimental validation. Engineering Fracture Mechanics 1990; 35:87-94.
37. Bazant ZP, Yu Q, Zi G. Choice of standard fracture test for concrete and its statistical evaluation. International Journal of Fracture 2002; 118:303-337.
38. Rots JG. Computational modelling of concrete fracture. Ph.D. Thesis, Delft University of Technology, 1988.
39. Feenstra PH, de Borst R. Constitutive model for reinforced concrete. Journal of Engineering Mechanics 1995; 121(5):587-595.
40. Bazant ZP, Cedolin L. Stability of Structures: Elastic, Inelastic, Fracture and Damage Theories. Oxford University Press: Oxford, 1991.
41. Perdikaris PC, Romeo A. Size effect on fracture energy of concrete and stability issues in three-point bending fracture toughness testing. ACI Materials Journal 1995; 92(5):483-496.
42. Shi C, van Dam AG, van Mier JGM, Stuys LJ. Crack interaction in concrete. In Materials for Buildings and Structures EUROMAT, vol. 6, Wittmann FH (ed.). Wiley-VCH Verlag: Weinheim, Germany, 2000; 125-131.
43. Arrea M, Ingraffea A. Mixed mode crack propagation in mortar and concrete. Report 81-13, Department of Structural Engineering, Cornell University, Ithaca, NY, 1982.
44. CEB-FIP model code 1990: design code. Comité Euro-International du Béton. Thomas Telford Publisher: London, 1993.
45. Galvez JC, Cervenka J, Cendon DA, Sauma V. A discrete crack approach to normal/shear cracking of concrete. Cement and Concrete Research 2002; 32:1567-1585.
46. 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; 291-280.
47. 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.