Continuum damage mechanics for hysteresis and fatigue of quasi-brittle materials and structures

International Journal for Numerical and Analytical Methods in Geomechanics

Volumn 31, Issue 2, 2007, Pages 307-329

  Desmorat, R ^a   Ragueneau, F ^a   Pham, H ^a  

^a SORBONNE UNIVERSITÉ   (France)

Author keywords

Concrete; Damage; Fatigue; Hysteresis; Unilateral conditions

Indexed keywords

BRITTLENESS; COMPRESSIVE STRESS; FATIGUE OF MATERIALS; HYSTERESIS; INTERNAL FRICTION; MATHEMATICAL MODELS; STIFFNESS; TENSILE STRESS;

DAMAGE; STIFFNESS RECOVERY;

CONTINUUM MECHANICS;

BRITTLENESS; COMPRESSIVE STRESS; CONTINUUM MECHANICS; FATIGUE OF MATERIALS; HYSTERESIS; INTERNAL FRICTION; MATHEMATICAL MODELS; STIFFNESS; TENSILE STRESS;

CONCRETE; CONTINUUM DAMAGE MECHANICS; FATIGUE; HYSTERESIS; NUMERICAL MODEL;

EID: 33846944039     PISSN: 03639061     EISSN: 10969853     Source Type: Journal    
DOI: 10.1002/nag.532     Document Type: Article

References (62)

1. Chen ES, Buyukozturk O. Constitutive model for concrete in cyclic compression. Journal of Engineering Mechanics 1985; 111(6):797-814.
2. Laborderie C, Berthaud Y, Pijaudier-Cabot G. Crack closure effect in continuum damage mechanics: numerical implementation. Proceedings of the 2nd International Conference on Computer Aided Analysis and Design of Concrete Structures. Zell am See, Austria, 4-6 April, 1990; 975-986.
3. Yazdani S, Schreyer L. Combined plasticity and damage Mechanics model for plain concrete. Journal of Engineering Mechanics 1990; 116(7):1435-1451.
4. Papa E. A damage model for concrete subject to fatigue loading. European Journal of Mechanics - A/Solids 1993; 12(3):429-440.
5. Dragon A, Halm D. An anisotropic model of damage and frictional sliding for brittle materials. European Journal of Mechanics - A/Solids 1998; 17:439-460.
6. Meschke G, Lackner R, Mang HA. An anisotropic elastoplastic-damage model for plain concrete. International Journal for Numerical Methods in Engineering 1998; 42:703-727.
7. Al-Gadhib AH, Baluch MH, Shaalan A, Khan AR. Damage model for monotonic and fatigue response of high strength concrete. International Journal of Damage Mechanics 2000; 9(1):57-78.
8. Ragueneau F, La Borderie C, Mazars J. Damage model for concrete like materials coupling cracking and friction, contribution towards structural damping: first uniaxial application. Mechanics Cohesive Frictional Materials 2000; 5:607-625.
9. Manson SS, Hirschberg MH. Fatigue: An Interdisciplinary Approach. Syracuse University Press: Syracuse, NY, 1964.
10. Aas-Jackobsen K, Lenshow R. Behavior of reinforced columns subjected to fatigue loading. ACI Journal 1973; 70(3):199-206.
11. Tepfers R, Kutti T. Fatigue strength of plain, ordinary and light weight concrete. ACI Journal 1979; 76(5):635-652.
12. Ramakrishnan V, Bremner TW, Malhotra VM. Fatigue strength and endurance limit of lightweight concrete. In Proceedings of the American Concrete Institute Symposium on Performance of Lightweight Concrete, Holm TA, Vaysburd AM (eds). Dallas, TX, 14 November, 1992; 397-420.
13. Lemaitre J, Plumtree A. Application of damage concepts to predict creep-fatigue failures. Journal of Engineering Materials and Technology 1979; 101:284-292.
14. Hua CT, Socie DF. Fatigue damage in 1045 steel under constant amplitude biaxial loading. Fatigue of Engineering Materials and Structures 1984; 7:165-179.
15. Chaboche JL, Lesne PM. A non-linear continuous fatigue damage model. Fatigue and Fracture of Engineering Materials and Structures 1998; 11:1-17.
16. Lemaitre J, Chaboche JL. Mécanique des Matériaux Solides (Dunod 1985), Mechanics of Solid Materials. Oxford University Press: Oxford, 1987 (English translation).
17. Paas MH. Continuum damage mechanics with an application to fatigue. Ph.D. Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 1990.
18. Lemaitre J. A Course on Damage Mechanics. Springer: Berlin, 1992.
19. Paas MH, Schreurs PJG, Brekelmans WAM. A continuum approach to brittle and fatigue damage: theory and numerical procedures. International Journal of Solids and Structures 1993; 30:579-599.
20. Peerlings RHJ. Continuum damage modelling of fatigue crack initiation. Internal Report MT 97.037, Faculty of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands, 1997.
21. Bodin D, Chabot A, de La Roche C, Pijaudier-Cabot G. A continuum damage approach of asphalt concrete fatigue tests. 15th ASCE Engineering Mechanics Conference, Columbia University, New York, U.S.A., 2-5 June, 2002.
22. Lemaitre J, Desmorat R. Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures. Springer: Berlin, 2005.
23. Bazant ZP, Prat PC. Microplane model for brittle plastic material: 1. Theory. Journal of Engineering Mechanics (ASCE) 1988; 114:1672-1688.
24. Hild F, Buff A, Leckie FA. Matrix cracking and debonding of ceramic-matrix composites. International Journal of Solids and Structures 1996; 33(8):1209-1220.
25. Pensée V, Kondo D, Dormieux L. Micromechanical analysis of anisotropic damage in brittle materials. Journal of Engineering Mechanics (ASCE) 2002; 128(8):889-897.
26. Desmorat R, Cantournet S. Thermodynamics modelling of internal friction and hysteresis of elastomers. Second European Conference on Constitutive Models for Rubber, Vienna, Autriche, September 2001.
27. Kachanov M. A microcrack model of rock inelasticity, Part I: Frictional sliding on microcracks. Mechanics of Materials 1982; 1:19-27.
28. Kachanov M. Elastic solids with many cracks and related problems. In Advances in Applied Mechanics, Hutchinson J, Wu T (eds), vol. 1, Academic Press: New York, 1993; 260-445.
29. Horii H, Nemat-Nasser S. Overall moduli of solids with microcracks: load induced anisotropy. Journal of the Mechanics and Physics of Solids 1983; 31:155-171.
30. Nemat-Nasser S, Obata M. A microcrack model of dilatancy in brittle materials. Journal of Applied Mechanics 1988; 55:24-35.
31. Andrieux S, Bamberger Y, Marigo JJ. Un modèle de matériau microfissuré pour les bétons et les roches. Journal de Mécanique Théorique et Appliquée 1986; 5(3):471-513.
32. Lauterbach B, Gross D. Crack growth in brittle solids under compression. Mechanics of Materials 1998; 29: 81-92.
33. Leckie FA, Onat ET. Tensorial nature of damage measuring internal variables. In Physical Non-Linearities in Structural Analysis, Hult J, Lemaitre J (eds). Springer: Berlin, 1981; 140-155.
34. Ragueneau F, Dominguez N, Ibrahimbegovic A. Thermodynamic-based constitutive model for concrete-steel bond modelling. Computer Methods in Applied Mechanics in Engineering 2005, in press.
35. Cordebois JP, Sidoroff F. Endommagement anisotrope en élasticité et plasticité. Journal de Mécanique Théorique et Appliquée (JMTA, Numéro spécial) 1982; 45-60.
36. Ladevèze P. On an anisotropic damage theory. In Proceedings of CNRS International College, 351, Villars-de-Lans, Failure criteria of structured media, Boehler JP (ed.), 1983; 355-363.
37. Chow CL, Wang J. An anisotropic theory for continuum damage mechanics. International Journal of Fracture 1987; 33:3-16.
38. Lemaitre J, Desmorat R, Sauzay M. Anisotropic damage law of evolution. European Journal of Mechanics - A/Solids 2000; 19:187-208.
39. Lemaitre J, Doghri I. Damage 90: a post-processor for crack initiation. Computer Methods in Applied Mechanics and Engineering 1994; 115:197-232.
40. Desmorat R, Lemaitre J. Two scale damage model for quasi-brittle and fatigue damage. Handbook of Materials Behavior Models (chapter Continuous Damage, Section 6.15), Lemaitre J (ed.). Academic Press: New York, 2001; 525-535.
41. Sermage JP, Lemaitre J, Desmorat R. Multiaxial creep fatigue under anisothermal conditions. Fatigue and Fracture of Engineering Materials & Structures 2000; 23(3):241-252.
42. Ladevèze P, Lemaitre J. Damage effective stress in quasi unilateral conditions. 16th International Congress of Theoretical and Applied Mechanics, Lyngby, Denmark, 1984.
43. Cantournet S, Desmorat R. Modélisation thermodynamique du frottement interne et de l'hystérésis des élastomères. Thermodynamics modelling of internal friction and hysteresis of elastomers. C. R. Mécanique 2003; 331:265-270.
44. Desmorat R. Phenomenological constitutive damage models. In Local Approach to Fracture, Chapter VII, Besson J (ed.). Presses de l'Ecole des Mines de Paris: Paris, 2004; 193-220.
45. Rabotnov YN. Creep Problems in Structural Members. North-Holland: Amsterdam, 1969.
46. Grzybowski M, Meyer C. Damage accumulation in concrete with and without fibre reinforcement. ACI Materials Journal 1993; 90(6):594-604.
47. Paskova T, Meyer C. Low cycle fatigue of plain and fibre-reinforced concrete. ACI Materials Journal 1997; 94(4):273-285.
48. Lemaitre J, Sermage JP, Desmorat R. A two scale damage concept applied to fatigue. International Journal of Fracture 1999; 97:67-81.
49. Bazant ZP, Pan J-Y, Pijaudier-Cabot G. Softening in reinforced concrete beams and frames. Journal of Structural Engineering (ASCE) 1987; 113(12):2333-2347.
50. Laborderie C, Phénomènes unilatéraux dans un matériau endommageable. Ph.D. Thesis, University Paris 6, 1991.
51. Guedes J, Pegon P, Pinto AV. A fibre/Timoshenko beam element in CASTEM 2000. Special Publication Nr.1.94.31, Joint Research Center, Ispra, Italy, 1994.
52. Ortiz M. A constitutive theory for the inelastic behaviour of concrete. Mechanics of Materials 1985; 4:67-93.
53. Voyiadjis GZ, Abu-Lebdeh TM. Plasticity model for concrete using the bounding surface model. International Journal of Plasticity 1994; 10:1-21.
54. Mazars J. Application de la mécanique de l'endommagement au comportement non linéaire et à la rupture du béton de structure. Thèse d'état, University Paris 6, 1984.
55. Herrmann G, Kestin J. On the thermodynamics foundation of a damage theory in elastic solids. In Cracking and Damage, Mazars J, Bazant ZP (eds). Elsevier: Amsterdam, 1988; 228-232.
56. Chaboche JL. Development of continuum damage mechanics for elastic solids sustaining anisotropic and unilateral damage. International Journal of Damage Mechanics 1993; 2:311-329.
57. Dragon A, Halm D, Désoyer T. Anisotropic damage in quasi-brittle solids: modelling, computational issues and applications. Computer Methods in Applied Mechanics and Engineering 2000; 183:331-352.
58. Geers M, de Borst R, Peerlings FHJ. Damage and crack modelling in single-edge and double-edge notched concrete beams. Engineering Fracture Mechanics 2000; 65:247-261.
59. Mazars J, Berthaud Y, Ramtani S. The unilateral behaviour of damaged concrete. Engineering Fracture Mechanics 1990; 35(4/5):629-635.
60. Papa E, Talierco A. Anisotropic damage model for the multi-axial static and fatigue behaviour of plain concrete. Engineering Fracture Mechanics 1996; 55(2):163-179.
61. Fichant S, Laborderie C, Pijaudier-Cabot G. Isotropic and anisotropic descriptions of damage in concrete structures. International Journal of Mechanics of Cohesive Frictional Materials 1999; 4:339-359.
62. Desmorat R. Local and nonlocal anisotropic damage models for quasi-brittle materials. ALERT Geomaterials, Aussois, France, 14-16 October, 2004.