Modelling of size effects in concrete using elasto-plasticity with non-local softening

Archives of Civil Engineering

Volumn 52, Issue 1, 2006, Pages

  Bobinski J ^a   Tejchman, J ^a  

^a GDANSK UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Concrete; Elasto plasticity; FEM; Localization of deformation; Non locality; Size effect; Softening

Indexed keywords

COMPUTER SIMULATION; ELASTOPLASTICITY; FINITE ELEMENT METHOD; HARDENING; MICROSTRUCTURE; NUMERICAL ANALYSIS;

LOCALIZATION OF DEFORMATION; NON-LOCALITY; SIZE EFFECT;

CONCRETES;

EID: 33845642530     PISSN: 12302945     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (64)

1. Abaqus, Theory Manual, Version 5.8, Hibbit, Karlsson & Sorensen Inc., 1998.
2. J. AKKERMANN, Rotationsverhalten von Stahlbeton-Rahmenecken, Dissertation, Universität Fridericiana zu Karlsruhe, Karlsruhe 2000.
3. H. ASKES, L. J. SLUYS, A classification of higher-order strain gradient models in damage mechanics, Arch. Appl. Mech., 53 (5-6), 448-465, 2003.
4. Z. P. BAZANT, Size effect in blunt fracture: concrete, rock, metal., J. Engng. Mech. ASCE, 110, 518-535, 1984.
5. Z. P. BAZANT, F. LIN, Non-local yield limit degradation. Int. J. Num. Meth. Engng., 35, 1805-1823, 1988.
6. Z. P. BAZANT, J. PLANAS, Fracture and size effect in concrete and other quasi-brittle materials, CRC Press, Boca Raton 1998.
7. Z. BAZANT, M. JIRASEK, Nonlocal integral formulations of plasticity arid damage: survey of progress, J. Engng. Mech., 128, 11, 1119-1149, 2002.
8. Z. P. BAZANT, Scaling of Structural Strength, Hermes-Penton, London 2003.
9. Z. P. BAZANT, A. YAVARI, Is the cause of size effect on structural strength fractal or energetic-statistical?, Engineering Fracture Mechanics, 72, 1-31, 2005.
10. C. LE BELLEGO, J. F. DUBE, G. PIJAUDIER-CABOT, B. GERARD, Calibration of nonlocal damage model from size effect tests, E. J. Mechanics A/Solids, 22, 33-46, 2003.
11. A. BENALLAL, R. BILLARDON, G. GEYMONAT, Localization phenomena at the boundaries and interfaces of solids.[In:] C. S. Desai et al., [Eds.] Proc. of the 3rd Int. Conf. Constitutive Laws for Engineering Materials: Theory and Applications, 387-390, Tucson, Arizona 1987.
12. J. BOBIŃSKI, J. TEJCHMAN, Numerical simulations of localization of deformation in quasi-brittle materials within non-local softening plasticity, Computers and Concrete, 4, 433-453, 2004.
13. J. BOBÍNSKI, J. TEJCHMAN, Modelling of concrete behaviour with a non-local continuum damage approach, Archives of Hydro-Engineering and Environmental Mechanics, 52, 2, 85-105, 2005.
14. th International Conference On Nonlinear Engineering Computations, 239-260, 1991.
15. DE R. BORST, H.-B. MÜHLHAUS, J. PAMIN, L. SLUYS, Computational modelling of localization of deformation [In:] D. R. J. Owen, H. Onate, E. Hinton [Eds.], Proc. of the 3rd Int. Conf. Comp. Plasticity, 483-508, Pineridge Press, Swansea 1992.
16. R. B. BRINKGREVE, Geomaterial models and numerical analysis of softening, PhD Thesis, Delft University of Technology, Delft 1994.
17. J. CHEN, H. YUAN, D. KALKHOF, A nonlocal damage model for elastoplastic materials based on gradient plasticity theory, Report Nr.01-13, Paul Scherrer Institut, 1-130, 2001.
18. W. EHLERS, T. GRAF, Adaptive computation of localization phenomena in geotechnical applications [In:] Bifurcations and Instabilities in Geomechanics [Eds. J. Labuz and A. Drescher], Swets and Zeitlinger, 247-262, 2003.
19. M. GEERS, T. PEIJS, W. BREKELMANS, DE R. BORST, Experimental monitoring of strain localization and failure behaviour of composite materials, Compos. Sci. Technol., 56, 1283-1290, 1996.
20. A. E. GROEN, Three-dimensional elasto-plastic analysis of soils, PhD Thesis, Delft University, 1-114, 1997.
21. G. GUDEHUS, K. NÜBEL, Evolution of shear bands in sand, Geotechnique, 54, 3, 187-201, 2004.
22. M. A. GUTIERREZ, DE R. BORST, Deterministic and stochastic analysis of size effects and damage evaluation in quasi-brittle materials, Archives of Applied Mechanics, 69, 655-676, 1999.
23. M. A. GUTIERREZ, DE R. BORST, Simulation of size-effect behaviour through sensitivity analysis, Engineering Fracture Mechanics, 70, 2269-2279, 2003.
24. U. HÄUSSLER-COMBE, Size effects for plain and reinforced concrete structures, Proc. WCCM V Fifth World Congress on Computational Mechanics, Vienna 2002.
25. T. J. R. HUGHES, J. WINGET, Finite rotation effects in numerical integration of rate constitutive equations arising in large deformation analysis, International Journal for Numerical Methods in Engineering, 15, 1862-1867, 1980.
26. M. JIRASEK, S. ROLSHOVEN, Comparison of integral-type nonlocal plasticity models for strain-softening materials, Int. J. Engineering Science, 41, 1553-1602, 2003.
27. M. JIRASEK, S. ROLSHOVEN, P. GRASSL, Size effect on fracture energy induced by non-locality, International Journal for Numerical and Analytical Methods in Geomechanics, 28, 653-670, 2004.
28. T. ŁODYGOWSKI, P. PERZYNA, Numerical modelling of localized fracture of inelastic solids in dynamic loading process. Int. J. Num. Meth. Eng., 40, 22, 4137-4158, 1997.
29. B. LORET B. J. H. PREVOST, Dynamic strain localisation in elasto-visco-plastic solids, Part 1. General formulation and one-dimensional examples, Comp. Appl. Mech. Eng., 83, 247-273, 1990.
30. T. MAIER, Numerische Modellierung der Entfestigung im Rahmen der Hypoplastizität, PhD Thesis, University of Dortmund, 2002.
31. R. MAHNKEN, E. KUHL, Parameter identification of gradient enhanced damage models, Eur. J. Mech. A/Solids, 18, 819-835, 1999.
32. T. MARCHER, P. A. VERMEER, Macro-modelling of softening in non-cohesive soils, [In:] P. A. Vermeer et al. [Eds.], Continuous and discontinuous modelling of cohesive-frictional materials, Springer-Verlag, 89-110, 2001.
33. F. MEFTAH, J. M. REYNOUARD, A multilayered mixed beam element on gradient plasticity for the analysis of localized failure modes, Mechanics of Cohesive-Frictional Materials, 3, 305-322, 1998.
34. P. MENETREY, K. J. WILLAM, Triaxial failure criterion for concrete and its generalization, ACI Structural Journal, 311-318, 1995.
35. H.-B. MÜHLHAUS, Scherfugenanalyse bei Granularen Material im Rahmen der Cosserat-Theorie, Ingen. Archiv, 56, 389-399, 1986.
36. H.-B. MÜHLHAUS, E. C. AIFANTIS, A variational principle for gradient plasticity, Int. J. Solids Structures, 28, 845-858, 1991.
37. A. NEEDLEMAN, Material rate dependence and mesh sensitivity in localization problems, Comp. Meths. Appl. Mech. Eng., 67, 69-85, 1988.
38. M. ORTIZ, I. C. SIMO, An analysis of a new class of integration algorithms foe elastoplastic constitutive relation, Int. I, Num. Methods in Engrg., 23, 353-366, 1986.
39. J. OZBOLT, Maßstabseffekt und Duktilität von Beton- und Stahlbetonkonstruktionen, Habilitation, Universität Stuttgart, 1995.
40. J. PAMIN, DE R. BORST, Simulation of crack spacing using a reinforced concrete model with an internal length parameter, Arch. App. Mech., 68(9), 613-625, 1998.
41. J. PAMIN, DE R. BORST, Stiffness degradation in gradient-dependent coupled damage-plasticity. Arch. Mech., 51, 3-4, 419-146, 1999.
42. J. PAMIN, Gradient-enchanced continuum models: formulation, discretization and applications, Habilitation Monograph, Cracow University of Technology, Krakow, 2004.
43. R. H. J. PEERLINGS, DE R. BORST, W. A. M. BREKELMANS, M. G. D. GEERS, Gradient enhanced damage modelling of concrete fracture, Mech. Cohes.-Friction. Mater., 3, 323-342, 1998.
44. G. PIJAUDIER-CABOT, Z. P. BAZANT, Nonlocal damage theory, ASCE J. Eng. Mech., 113, 1512-1533, 1987.
45. G. PIJAUDIER-CABOT, K. HAIDAR, J. F. DUBE, Non-local damage model with evolving internal length, Int. J. Num. and Anal. Meths. in Geomech, 28, 633-652, 2004.
46. G. PIJAUDIER-CABOT, K. HAIDAR, A. LOUKILI, M. OMAR, Ageing and durability of concrete structures, Degradation and instabilities in geomaterials ([Eds.] F. Darve, I. Vardoulakis), Springer Verlag, 2004.
47. C. POLIZZOTTO, G. BORINO, P. FUSCHI, A thermodynamic consistent formulation of nonlocal and gradient plasticity, Mech. Res. Commun., 25, 75-82, 1998.
48. C. DI PRISCO, S. IMPOSIMATO, E. C. AIFANTIS, A visco-plastic constitutive model for granular soils modified according to non-local and gradient approaches, Int. J. Numer. Anal. Meth. Geomech., 26, 121-138, 2002.
49. R. A. REGUEIRO, R. I. BORJA, Plane strain finite element analysis of pressure sensitive plasticity with strong discontinuity, Int. J. Solids and Structures, 38, 21, 3647-3672, 2001.
50. A. SIMONE, L. SLUYS, Continous-discontinous modeling of mode-I and mode-II failure, Modelling of cohesive-frictional materials [Eds.] P. A. Vermeer, W. Ehlers, H. J. Hermann and E. Ramm, Balkema, 323-337, 2004.
51. L. SLUYS, Wave propagation, localisation and dispersion in softening solids, PhD Thesis, Delft University of Technology, 1992.
52. L. J. SLUYS, DE R. BORST, Dispersive properties of gradient and rate-dependent media, Mech. Mater., 183, 131-149, 1994.
53. L. STRÖMBERG, M. RISTINMAA, FE-formulation of nonlocal plasticity theory, Comput. Methods Appl. Mech. Engrg., 136, 127-144, 1996.
54. J. TEJCHMAN, W. WU, Numerical study on patterning of shear bands in a Cosserat continuum, Acta Mechanica, 99, 61-74, 1993.
55. J. TEJCHMAN, I. HERLE, J. WEHR, FE-studies on the influence of initial void ratio, pressure level and mean grain diameter on shear localisation, Int. J. Num. Anal. Meth. Geomech., 23, 2045-2074, 1999.
56. J. TEJCHMAN, G. GUDEHUS, Shearing of a narrow granular strip with polar quantities, J. Num. and Anal. Methods in Geomechanics, 25, 1-28, 2001.
57. J. TEJCHMAN, Influence of a characteristic length on shear zone formation in hypoplasticity with different enhancements, Computers and Geotechnics, 31, 8, 595-611, 2004.
58. W. WEIBULL, The phenomenon of rupture in solids, Proc. R. Swed. Inst. Engng. Res., 153, 1-55, 1939.
59. F. H. WITTMANN, H. MIHASHI, N. NOMURA, Size effect on fracture energy using three-point bend tests, Materials and Structures, 25, 327-334, 1992.
60. P. A. VERMEER, U. VOGLER, E. G. SEPTANIKA, O. STELZER, A strong discontinuity method without locking. Modelling of cohesive-frictional materials [Eds.] P. A. Vermeer, W. Ehlers, H. J. Herrmann and E. Ramm, Balkema, 381-394, 2004.
61. M. R. A. VAN VLIET, J. G. M. VAN MIER, Experimental investigation of concrete fracture under uniaxial compression, Mechanics of cohesive-frictional materials, 1, 115-127, 1996.
62. J. H. P. DE VREE, W. A. M. BREKELMANS, M. A. J. VAN GILS, Comparison of nonlocal approaches in continuum damage mechanics, Comput. Struct., 55, 581-588, 1995.
63. H. M. ZBIB, C. E. AIFANTIS, A gradient dependent flow theory of plasticity: application to metal and soil instabilities, Appl. Mech. Reviews, 42(11), 295-304, 1989.
64. W. ZHOU, J. ZHAO, Y. LIU, Q. YANG, Simulation of localization failure with strain-gradient-enhanced damage mechnics, Int. J. Numer. Anal. Meth. Geomech., 26, 793-813, 2002.