Fe analysis of strain localization in concrete in elasto-plasticity and damage mechanics with non-local softening

• Autorzy: Bobiński J.
• Języki publikacji: EN

Abstrakty

EN

Results of Finite Element Method (FEM) simulations of a strain localization in concrete specimens are presented. Two different continuum approaches have been used to model to behaviour of concrete: (i) an elasto-plastic constitutive law with the Drucker-Prager criterion in the compression regime and the Rankine criterion in the tensile regime, with isotropic hardening and softening and (ii) an isotropic continuum damage model with the equivalent strain corresponding to the Rankine failure criterion and modified Huber-Mises criterion in terms of strains, with exponential softening. Both constitutive models were enriched by non-local terms to describe strain localization properly, ensure mesh-independence in the softening regime and capture the deterministic size effect. The constitutive models were used to simulate strain localization in concrete in two boundary value problems under plane strain conditions, viz. uniaxial tension and three-point bending. The effect of the characteristic length on load-displacement curves and widths of strain localization is discussed.

Słowa kluczowe

EN

characteristic length; concrete; damage mechanics; elasto-plasticity; FEM; non-local model; strain localization

• Wydawca: Politechnika Gdańska
• Czasopismo: TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
• Rocznik: 2006
• Tom: Vol. 10, No 4
• Strony: 353--375
• Opis fizyczny: Bibliogr. 70 poz., rys.

Twórcy

autor

Bobiński J.

• Gdansk University of Technology, Faculty of Civil and Environmental Engineering, 80-952 Gdansk, Narutowicza 11/12, Poland,

Bibliografia

• [1] Bazant Z P 1984 Size effect in blunt fracture: concrete, rock, metal, J. Eng. Mech. ASCE 110 518
• [2] Bazant Z P 2003 Scaling of Structural Strength, Hermes-Penton, London
• [3] Wittmann F H, Mihashi Hand Nomura N 1992 Size effect on fracture energy using three-point bend tests, Mater. Struct. 25 327
• [4] van Vliet M R A and van Mier J G M 1996 Experimental investigation of concrete fracture under uniaxial compression, Mech. Cohesive-Frictional Mater. 1 115
• [5] Chen J, Yuan H and Kalkhof D 2001 A nonlocal damage model for elastoplastic materials based on gradient plasticity theory, Report Nr. 01-13, Paul Scherrer Institut, pp. 1-130
• [6] Palaniswamy R and Shah S P 1974 Fracture and stress-strain relationship of concrete under triaxial compression, J. Struct. Div. ASCE 100 901
• [7] Bazant Z P and Cedolin L 1979 Blunt crackband propagation in finite element analysis, J. Eng. Mech. Div. ASCE 105 (2) 297
• [8] Hilleborg A 1985 The theoretical basis of a method to determine the fracture energy of concrete, Mater. Struct. 18 291
• [9] Bazant Z P and Bhat P D 1976 Endochronic theory of inelasticity and failure of concrete, Eng. Mech. Div. ASCE 102 701
• [10] Bazant Z P and Shieh C L 1978 Endochronic model for nonlinear triaxial behaviour of concrete, Nucl. Eng. Des. 47305
• [11] Bazant Z P and Ozbolt J 1990 Non-local microplane model for fracture, damage and size effect in structures, J. Eng. Mech. ASCE 116 2485
• [12] Jirasek M 1999 Comments on microplane theory, Mechanics of quasi-brittle materials and structures (Pijaudier-Cabot G, Bittnar Z and Gerard B, Eds), Hermes Science Publications, pp. 55-77
• [13] Willam K J and Warlike E P 1975 Constitutive model for the triaxial behaviour of concrete, IABSE Seminar on concrete structures subjected to triaxial stress, Bergamo, Italy, pp. 1-31
• [14] Pietruszczak S, Jiang J and Mirza F A 1988 An elastoplastic constitutive model for concrete, Int. J. Solid Struct. 24 (7) 705
• [15] Menetrey P and Willam K J 1995 Triaxial failure criterion for concrete and its generalization, ACI Struct. J. 92 311
• [16] Bobiński J and Tejchman J 2004 Numerical simulations of localization of deformation in quasi-brittle materials within non-local softening plasticity, Comp. Concr. 4 433
• [17] Dragon A and Mroz Z 1979 A continuum model for plastic-brittle behaviour of rock and concrete, Int. J. Eng. Sci. 17 121
• [18] Peerlings R H J, de Borst R, Brekelmans W A M and Geers M G D 1998 Gradient enhanced damage modelling of concrete fracture, Mech. Coh.-Frict. Mater. 3 323
• [19] Chen E 1999 Non-local effects on dynamic damage accumulation in brittle solids, Int. J. Num. Anal. Meth. Geomech. 23 1
• [20] Bobiński J and Tejchman J 2005 Modelling of concrete behaviour with a non-local continuum damage approach, Arch. Hydro-Eng. Env. Mech. 52 (3) 243
• [21] Lemaitre J 1985 Coupled elasto-plasticity and damage constitutive equations, Comp. Meth. Appl. Mech. Eng. 51 31
• [22] de Borst R, Pamin J and Geers M G D 1999 On coupled gradient-dependent plasticity and damage theories with a view to localization analysis, Eur. J. Mech. A/Solids 18 (6) 939
• [23] Ibrahimbegovic A, Markovic D and Gatuing F 2003 Constitutive model of coupled damage plasticity and its finite element implementation, Eur. J. Finite Elem. 12 (4) 381
• [24] Salari M R, Saeb S, Willam K J, Patchet S J and Carrasco R C 2004 A coupled elastoplastic damage model for geomaterials, Comp. Meth. Appl. Mech. Eng. 193 2625
• [25] Herrmann H J, Hansen A and Roux S 1989 Fracture of disordered elastic lattices in two dimensions, Phys. Rev. B 39 637
• [26] Vervuurt A, van Mier J G M and Schlangen E 1994 Lattice model for analyzing steel-concrete interactions, Comp. Meth. Adv. Geomech. (Siriwardane and Zaman, Eds), Balkema, Rotterdam, pp. 713-718
• [27] Schlangen E and Garboczi 1997 Fracture simulations of concrete using lattice models: computational aspects, Eng. Fracture Mech. 57 319
• [28] Kozicki J and Tejchman J 2006 2D lattice model for fracture in brittle materials, Arch. Hydro-Eng. Env. Mech., Polish Academy of Sciences (under press)
• [29] Cusatis G, Bazant Z and Cedolin 12003 Confinement shear lattice model for concrete damage in tension and compression, J. Eng. Mech. ASCE 129 (12) 1439
• [30] Sakaguchi H and Mühlhaus H-B 1997 Mesh free modelling of failure and localisation in brittle materials (Asaoka A, Adachi T and aka F, Eds), Deformation and Progressive Failure in Geomechanics, Pergamon, pp. 15-21
• [31] D'Addetta G A, Kun F and Ramm E 2002 In the application of a discrete model to the fracture process of cohesive granular materials, Granular Matter 477
• [32] Donze F V, Magnier S A, Daudeville L, Mariotti C and Davenne L 1999 Numerical study of compressive behaviour of concrete at high strain rates, J. Eng. Mech. 125 1154
• [33] de Borst R, Mühlhaus H-B, Pamin J and Sluys L 1992 Computational modelling of localization of deformation (Owen D R J, Onate Hand Hinton E, Eds.), Proc. of the 3rd Int. Conf. Comp. Plasticity, Swansea, Pineridge Press, pp. 483 - 508
• [34] Pamin J and de Borst R 1998 Simulation of crack spacing using a reinforced concrete model with an internal length parameter, Arch. Appl. Mech. 68 (9) 613
• [35] Akkermann J 2000 Rotationsverhalten von Stahlbeton-Rahmenecken. Dissertation, Universitat Fridericiana zu Karlsruhe, Karlsruhe
• [36] Pijaudier-Cabot G and Bazant Z P 1987 Nonlocal damage theory, ASCE J. Eng. Mech. 113 1512
• [37] Sluys L J 1992 Wave propagation, localisation and dispersion in softening solids, PhD Thesis, Delft University of Technology
• [38] Sluys L J and de Borst R 1994 Dispersive properties of gradient and rate-dependent media, Mech. Mater. 183 131
• [39] Abaqus Theory Manual. Version 5.8, Hibbit, Karlsson & Sorensen Inc. 1998 [40] Lemaitre J and Chaboche J L 1990 Mechanics of Solid Materials, Cambridge University Press, Cambridge, UK
• [41] Bobiński J and Tejchman J 2006 Modelling of size effects in concrete using elasto-plasticity with non-local softening, Arch. Civ. Eng. LII 1 7
• [42] Kaczanov L M 1986 Introduction to Continuum Damage Mechanics, Martimus Nijhoff, Dordrecht
• [43] Simo J C and Ju J W 1987 Strain- and stress-based continuum damage models - I. Formulation, Int. J. Solid Struct. 23 (7) 821
• [44] Jirasek M and Marfia S 2005 Non-local damage model based on displacement averaging, Int. J. Num. Meth. Eng. 63 77
• [45] Simone A and Sluys L 2004 Continous-discontinous mode ling of mode-I and mode-II failure. Modelling of Cohesive-Frictional Materials (Vermeer P A, Ehlers W, Herrmann H J and Ramm E, Eds.), Balkema, pp. 323-337
• [46] Bazant Z P and Jirasek M 2002 Nonlocal integral formulations of plasticity and damage: survey of progress, J. Eng. Mech. 128 (11) 1119
• [47] Bazant Z P and Lin F B 1987 Non-local yield limit degradation, J. Eng. Mech. ASCE 113 1512
• [48] Brinkgreve R B J 1994 Geomaterial models and numerical analysis of softening, PhD Thesis, Delft University of Technology
• [49] Bazant Z P and Oh B H 1983 Crack band theory for fracture of concrete, Mater. Struct., RILEM 16 155
• [50] Geers M, Peijs T, Brekelmans W and de Borst R 1996 Experimental monitoring of strain localization and failure behaviour of composite materials, Compos. Sci. Technol. 56 1283
• [51] Mahnken R and Kuhl E 1999 Parameter identification of gradient enhanced damage models, Eur. J. Mech. A/Solids 18 819
• [52] Le Bellego C, Dube J F, Pijaudier-Cabot G and Gerard B 2003 Calibration of nonlocal damage model from size effect tests, Eur. J. Mech. A/Solids 22 33
• [53] Pijaudier-Cabot G, Haidar K and Dube J F 2004 Non-local damage model with evolving internal length, Int. J. Num. Anal. Meths. Geomech. 28633
• [54] Ferrara I and di Prisco M 2001 Mode I fracture behaviour in concrete: nonlocal damage modeling, ASGE J. Eng. Mech. 127 (7) 678
• [55] Bhandari A R and Inoue J 2005 Experimental study of strain rates effects on strain localization characteristics of soft rocks, Soils and Foundations 45 (1) 125
• [56] Bobiński J and Tejchman J 2006 Modelling of strain localization in quasi-brittle materials with non-local continuum models, Comp. Model. Concr. Struct., EURO-C (Meschke G, de Borst R, Mang H and Bicanic N, Eds.), Taylor and Francis, pp. 301-307
• [57] Grassl P and Jirasek M 2006 Plastic model with non-local damage applied to concrete, Int. J. Num. Anal. Meth. Geomech. 30 71
• [58] Ortiz M and Simo I C 1986 An analysis of a new class of integration algorithms foe elastoplastic constitutive relation, Int. J. Num. Meth. Eng. 23 353
• [59] Hughes T J R and Winget J 1980 Finite rotation effects in numerical integration of rate constitutive equations arising in large deformation analysis, Int. J. Num. Meth. Eng. 15 1862
• [60] Hordijk D A 1991 Local approach to fatigue of concrete, PhD Thesis, Delft University of Technology
• [61] Jirasek M and Rolshoven S 2003 Comparison of integral-type nonlocal plasticity models for strain-softening materials, Int. J. Eng. Sci. 41 1553
• [62] Malecki T, Marzec I, Bobiński J and Tejchman J 2006 FE-analysis of crack spacing in a reinforced concrete bar under tension using elasto-plasticity with non-local softening, Arch. Civ. Eng. (submitted)
• [63] Gutierrez M A and de Borst R 2003 Simulation of size-effect behaviour through sensitivity analysis, Eng. Fracture Mech. 70 2269
• [64] Pamin J 2004 Gradient-enchanced continuum models: formulation, discretization and applications. Habilitation Monography, Cracow University of Technology, Cracow
• [65] Rodriguez-Ferran A, Morata I and Huerta A 2002 Numerical modelling of notched specimens, Proc. WGGM V, Vienna, Austria (CD edition)
• [66] Pamin J 2005 Gradient plasticity and damage models: a short comparison, Comp. Mater. Sci. 32 472
• [67] Zhou W, Zhao J, Liu Y and Yang Q 2002 Simulation of localization failure with strain gradient-enhanced damage mechanics, Int. J. Num. Anal. Meth. Geomech. 26 793
• [68] Walukiewicz H, Bielewicz E and Gorski J 1997 Simulation of nonhomegeneous random fields for structural applications, Comp. Struct. 64 (1-4) 491
• [69] Tejchman J 2006 Effect of fluctuation of current void ratio on the shear zone formation in granular bodies within micro-polar hypoplasticity, Comp. Geotech. (under press)
• [70] Kozicki J and Tejchman J 2006 Measurements of the displacement field in concrete notched beams using a digital image correlation (DIG) technique, Lect., Int. Conf. EURO-C, Mayrhofen