Continuum damage model for orthotropic materials: Application to masonry

Computer Methods in Applied Mechanics and Engineering

Volumn 200, Issue 9-12, 2011, Pages 917-930

  Pelà, Luca ^a   Cervera, Miguel ^b   Roca, Pere ^b  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b INTERNATIONAL CENTER FOR NUMERICAL METHODS IN ENGINEERING CIMNE   (Spain)

Author keywords

Continuum damage mechanics; Damage surface; Mapping; Masonry; Orthotropy; Transformation tensor

Indexed keywords

AUXILIARY MODELS; CONTINUUM DAMAGE MODEL; DAMAGE CRITERIA; DAMAGE SURFACE; FAILURE MECHANISM; INDUCED DAMAGE; LOCAL DAMAGE; MASONRY; MECHANICAL BEHAVIOUR; ONE-TO-ONE MAPPINGS; ORTHOTROPIC MATERIALS; ORTHOTROPY; PLANE STRESS CONDITION; STRESS TENSORS; STRESS TRANSFORMATION; TENSION AND COMPRESSION; TRANSFORMATION TENSOR; UNILATERAL EFFECT;

BEHAVIORAL RESEARCH; COMPUTER SIMULATION; CONTINUUM DAMAGE MECHANICS; MAPPING; MECHANICS; TENSORS;

MASONRY MATERIALS;

EID: 78650625481     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2010.11.010     Document Type: Article

References (76)

1. Hendry A.W. Structural Masonry 1990, Macmillan Education, London.
2. Drysdale R.G., Hamid A.A., Baker L.R. Masonry Structures: Behavior and Design 1994, Prentice-Hall, Englewood Cliffs, New Jersey.
3. Roca P., Cervera M., Gariup G., Pelà L. Structural analysis of masonry historical constructions. Classical and advanced approaches. Arch. Comput. Methods Engrg. 2010, 17:299-325.
4. Page A.W. Finite element model for masonry. J. Struct. Div. 1978, 104:1267-1285.
5. Samarasinghe W., Page A.W., Hendry A.W. Behaviour of masonry shear walls. Struct. Engrg. 1981, 59:42-48.
6. Pande G.N., Liang J.X., Middleton J. Equivalent elastic moduli for brick masonry. Comput. Geotech. 1989, 8:243-265.
7. Pietruszczak S., Niu X. A mathematical description of macroscopic behaviour of brick masonry. Int. J. Solids Struct. 1992, 29:531-546.
8. Anthoine A. Derivation of the in-plane elastic characteristics of masonry through homogenization theory. Int. J. Solids Struct. 1995, 32:137-163.
9. Zucchini A., Lourenço P.B. A micro-mechanical model for the homogenisation of masonry. Int. J. Solids Struct. 2002, 39:3233-3255.
10. Cecchi A., Sab K. A multi-parameter homogenization study for modeling elastic masonry. Eur. J. Mech. A/Solids 2002, 21:249-268.
11. Yokel F.Y., Fattal S.G. Failure hypothesis for masonry shear walls. J. Struct. Div. 1976, 102:515-532.
12. Mann W., Müller H. Failure of shear-stressed masonry - an enlarged theory, tests and application to shear walls. Proc. Brit. Ceram. Soc. 1982, 30:223-235.
13. Page A.W. The biaxial compressive strength of brick masonry. Proc. Inst. Civil Engrg. 1981, 71:893-906.
14. Page A.W. The strength of brick masonry under biaxial tension-compression. Int. J. Masonry Constr. 1983, 3:26-31.
15. Dhanasekar M., Page A.W., Kleeman P.W. The failure of brick masonry under biaxial stresses. Proc. Inst. Civil Engrg. 1985, 79:295-313.
16. H.R. Ganz, B. Thürlimann, Strength of brick walls under normal force and shear, in: Proc. 8th International Symposium on Load Bearing Brickwork, London, 1983.
17. Tsai S.W., Wu E.M. A general theory of strength for anisotropic materials. J. Compos. Mater. 1971, 5:58-80.
18. Syrmakezis C.A., Asteris P.G. Masonry failure criterion under biaxial stress state. J. Mater. Civil. Engrg. 2001, 13:58-64.
19. Berto L., Saetta A., Scotta R., Vitaliani R. An orthotropic damage model for masonry structures. Int. J. Numer. Methods Engrg. 2002, 55:127-157.
20. Hoffman O. The brittle strength of orthotropic materials. J. Compos. Mater. 1967, 1:200-206.
21. Lourenço P.B. Computational Strategy for Masonry Structures 1996, Delft University Press.
22. Feenstra P.H., De Borst R. A composite plasticity model for concrete. Int. J. Solids Struct. 1996, 33:707-730.
23. Drucker D.C., Prager W. Solid mechanics and plastic analysis for limit design. Quart. Appl. Math. 1952, 10:157-165.
24. Lourenço P.B., De Borst R., Rots J.G. Plane stress softening plasticity model for orthotropic materials. Int. J. Numer. Methods Engrg. 1997, 40:4033-4057.
25. Alpa G., Monetto I. Microstructural model for dry block masonry walls with inplane loading. J. Mech. Phys. Solids 1994, 42:1159-1175.
26. Gambarotta L., Lagomarsino S. A microcrack damage model for brittle materials. Int. J. Solids Struct. 1993, 30:177-198.
27. Gambarotta L., Lagomarsino S. Damage models for the seismic response of brick masonry shear walls. Part I: The mortar joint model and its applications. Earthq. Engrg. Struct. D 1997, 26:423-439.
28. Gambarotta L., Lagomarsino S. Damage models for the seismic response of brick masonry shear walls. Part II: The continuum model and its applications. Earthq. Engrg. Struct. D 1997, 26:441-462.
29. Papa E. A unilateral damage model for masonry based on a homogenisation procedure. Mech. Cohes.-Frict. Mater. 1996, 1:349-366.
30. Massart T.J., Peerlings R.H.J., Geers M.G.D. Mesoscopic modeling of failure and damage-induced anisotropy in brick masonry. Eur. J. Mech. A/Solids 2004, 23:719-735.
31. Milani G., Lourenço P.B., Tralli A. Homogenised limit analysis of masonry walls. Part I: Failure Surfaces. Comput. Struct. 2006, 84:166-180.
32. Milani G., Lourenço P.B., Tralli A. Homogenised limit analysis of masonry walls. Part II: Structural Examples. Comput. Struct. 2006, 84:181-195.
33. Lourenço P.B., Milani G., Tralli A., Zucchini A. Analysis of masonry structures: review and recent trends of homogenisation techniques. Can. J. Civil Engrg. 2007, 34:1443-1457.
34. Sacco E. A nonlinear homogenization procedure for periodic masonry. Eur. J. Mech. A/Solids 2009, 28:209-222.
35. Uva G., Salerno G. Towards a multiscale analysis of periodic masonry brickwork: a FEM algorithm with damage and friction. Int. J. Solids Struct. 2006, 43:3739-3769.
36. Brasile S., Casciaro R., Formica G. Multilevel approach for brick masonry walls. Part I: A numerical strategy for the nonlinear analysis. Comput. Methods Appl. Mech. Engrg. 2007, 196:4934-4951.
37. Massart T.J., Peerlings R.H.J., Geers M.G.D. Structural damage analysis of masonry walls using computational homogenisation. Int. J. Damage Mech. 2007, 16:199-226.
38. Massart T.J., Peerlings R.H.J., Geers M.G.D. An enhanced multi-scale approach for masonry wall computations with localization of damage. Int. J. Numer. Methods Engrg. 2007, 69:1022-1059.
39. Mercatoris B.C.N., Massart T.J. Assessment of periodic homogenization-based multiscale computational schemes for quasi-brittle structural failure. Int. J. Multiscale Comput. Engrg. 2009, 7:153-170.
40. Mihai L.A., Ainsworth M. An adaptive multi-scale computational modelling of Clare College Bridge. Comput. Methods Appl. Mech. Engrg. 2009, 198:1839-1847.
41. Betten J. Creep Theory of Anisotropic Solids. J. Rheol. 1981, 25:565-581.
42. Betten J. Applications of tensor functions to the formulation of yield criteria for anisotropic materials. Int. J. Plasticity 1988, 4:29-46.
43. Oller S., Botello S., Miquel J., Oñate E. An anisotropic elastoplastic model based on an isotropic formulation. Engrg. Comput. 1995, 12:245-262.
44. Oller S., Oñate E., Miquel J. Mixing anisotropic formulation for analysis of composites. Commun. Numer. Methods Engrg. 1996, 12:471-482.
45. Oller S., Car E., Lubliner J. Definition of a general implicit orthotropic yield criterion. Comput. Methods Appl. Mech. Engrg. 2003, 192:895-912.
46. L. Pelà, Continuum Damage Model for Nonlinear Analysis of Masonry Structures, Ph.D. Thesis, Technical University of Catalonia, University of Ferrara, 2009.
47. R. Faria, J. Oliver, A Rate Dependent Plastic-Damage Constitutive Model for Large Scale Computations in Concrete Structures, CIMNE Monograph 17, Technical University of Catalonia, 1993.
48. Faria R., Oliver J., Cervera M. A strain-based plastic viscous-damage model for massive concrete structures. Int. J. Solids Struct. 1998, 35:1533-1558.
49. R. Faria, J. Oliver, M. Cervera, On Isotropic Scalar Damage Models for the Numerical Analysis of Concrete Structures, CIMNE Monograph PI198, Technical University of Catalonia, 2000.
50. Faria R., Oliver J., Cervera M. Modeling material failure in concrete structures under cyclic actions. J. Struct. Engrg. 2004, 130:1997-2005.
51. Cervera M., Oliver J., Faria R. Seismic evaluation of concrete dams via continuum damage models. Earthq. Engrg. Struct. D 1995, 24:1225-1245.
52. Cervera M., Oliver J., Manzoli O. A rate-dependent isotropic damage model for the seismic analysis of concrete dams. Earthq. Engrg. Struct. D 1996, 25:987-1010.
53. Cervera M., Oliver J., Prato T. Thermo-chemo-mechanical model for concrete. II: Damage and creep. J. Engrg. Mech. 1999, 125:1028-1039.
54. M. Cervera, Viscoelasticity and Rate-Dependent Continuum Damage Models, CIMNE, Monograph No. 79, Technical University of Catalonia, 2003.
55. Pegon P., Anthoine A. Numerical strategies for solving continuum damage problems with softening: application to the homogenization of masonry. Comput. Struct. 1997, 64:623-642.
56. Lemaitre J., Chaboche J.L. Aspects phénoménologiques de la rupture par endommagement. J. Méc. Appl. 1978, 2:317-365.
57. Wu J.Y., Li J. On the mathematical and thermodynamical descriptions of strain equivalence based anisotropic damage model. Mech. Mater. 2008, 40:377-400.
58. Simó J.C., Ju J.W. Strain- and stress-based continuum damage models - I. Formulation. Int. J. Solids Struct. 1987, 23:821-840.
59. Cervera M., Pelà L., Clemente R., Roca P. A crack-tracking technique for localized damage in quasi-brittle materials. Engrg. Fract. Mech. 2010, 77:2431-2450.
60. Bazant Z.P., Oh B.H. Crack band theory for fracture of concrete. Mater. Struct. 1983, 16:155-177.
61. E. Car, S. Oller, E. Oñate, Algorithmic tangent matrices in the elastoplastic problem (in Spanish), in: Proceedings of the XVIII Spanish American Congress on Computational Methods in Engineering (CILAMCE), vol. IV, Brasilia, 1997, pp. 2039-2051.
62. Pérez-Foguet A., Rodríguez-Ferran A., Huerta A. Numerical differentiation for local and global tangent operators in computational plasticity. Comput. Methods Appl. Mech. Engrg. 2000, 189:277-296.
63. Lourenço P.B., Rots J.G., Blaauwendraad J. Continuum model for masonry: parameter estimation and validation. J. Struct. Engrg. 1998, 124:642-652.
64. Dhanasekar M., Haider W. Explicit finite element analysis of lightly reinforced masonry shear walls. Comput. Struct. 2008, 86:15-26.
65. Trovalusci P., Masiani R. Non-linear micropolar and classical continua for anisotropic discontinuous materials. Int. J. Solids Struct. 2003, 40:1281-1297.
66. Pijaudier-Cabot G., Bazant Z.P. Nonlocal damage theory. J. Engrg. Mech. 1987, 113:1512-1533.
67. Peerlings R.H.J., De Borst R., Brekelmans W.A.M., De Vree J.H.P. Gradient enhanced damage for quasi-brittle materials. Int. J. Numer. Methods Engrg. 1996, 39:3391-3403.
68. Cervera M., Chiumenti M., Valverde Q., Agelet de Saracibar C. Mixed linear/linear simplicial elements for incompressible elasticity and plasticity. Comput. Methods Appl. Mech. Engrg. 2003, 192:5249-5263.
69. Cervera M., Chiumenti M., Agelet de Saracibar C. Softening, localization and stabilization: capture of discontinuous solutions in J2 plasticity. Int. J. Numer. Anal. Methods Geomech. 2004, 28:373-393.
70. Cervera M., Chiumenti M., Agelet de Saracibar C. Shear band localization via local J2 continuum damage mechanics. Comput. Methods Appl. Mech. Engrg. 2004, 193:849-880.
71. Cervera M., Chiumenti M. Size effect and localization in J2 plasticity. Int. J. Solids Struct. 2009, 46:3301-3312.
72. Cervera M., Chiumenti M., Codina R. Mixed stabilized finite element methods in nonlinear solid mechanics. Part I: Formulation. Comput. Methods Appl. Mech. Engrg. 2010, 199:2559-2570.
73. Cervera M., Chiumenti M., Codina R. Mixed stabilized finite element methods in nonlinear solid mechanics. Part II: Strain localization. Comput. Methods Appl. Mech. Engrg. 2010, 199:2571-2589.
74. Lourenço P.B., Rots J.G., Feenstra P.H. A " tensile" Rankine-type orthotropic model for masonry. Computer Methods in Structural Masonry 1995, vol. 3. Books & Journals International, Swansea.
75. H.R. Ganz, B. Thürlimann, Tests on the biaxial strength of masonry (in German), Report No. 7502-3, Institute of Structural Engineering, ETH Zurich, 1982.
76. F. Lurati, H. Graf, B. Thürlimann, Experimental determination of the strength parameters of concrete masonry (in German), Report No. 8401-2, Institute of Structural Engineering, ETH Zurich, 1990.