Browse > Article
http://dx.doi.org/10.12989/cac.2012.9.1.035

Determination of representative volume element in concrete under tensile deformation  

Skarzyski, L. (Faculty of Civil and Environmental Engineering, Gdansk University of Technology)
Tejchman, J. (Faculty of Civil and Environmental Engineering, Gdansk University of Technology)
Publication Information
Computers and Concrete / v.9, no.1, 2012 , pp. 35-50 More about this Journal
Abstract
The 2D representative volume element (RVE) for softening quasi-brittle materials like concrete is determined. Two alternative methods are presented to determine a size of RVE in concrete subjected to uniaxial tension by taking into account strain localization. Concrete is described as a heterogeneous three-phase material composed of aggregate, cement matrix and bond. The plane strain FE calculations of strain localization at meso-scale are carried out with an isotropic damage model with non-local softening.
Keywords
characteristic length; concrete; heterogeneous material; representative volume element (RVE); damage mechanics; softening; strain localization;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
Times Cited By SCOPUS : 2
연도 인용수 순위
1 Bazant, Z. and Planas, J. (1998), Fracture and size effect in concrete and other quasi-brittle materials, CRC Press LLC, Boca Raton.
2 Bazant, Z.P. and Jirasek, M. (2002), "Nonlocal integral formulations of plasticity and damage: survey of progress", J. Eng. Mech. - ASCE, 128(11), 1119-1149.   DOI   ScienceOn
3 Bazant, Z.P. and Novak, D. (2003), "Stochastic models for deformation and failure of quasibrittle structures: recent advances and new directions", Computational Modelling of Concrete Structures EURO-C (eds.: N. Bicani$\ae$, R. de Borst, H. Mang and G. Meschke), 583-598.
4 Bobinski, J. and Tejchman, J. (2004), "Numerical simulations of localization of deformation in quasi-brittle materials with non-local softening plasticity", Comput. Concrete, 1(4), 433-455.   DOI
5 Bobinki, J. and Tejchman, J. (2010), Continuous and discontinuous modeling of cracks in concrete elements, Modelling of Concrete Structures (eds. N. Bicanic, R. de Borst, H. Mang, G. Meschke), Taylor and Francis Group, London, 263-270.
6 Drugan, W.J and Willis, J.R. (1996), "A micromechanics-based nonlocal constitutive equations and estimates of representative volume element size for elastic composites", J. Mech. Phys. Solids, 44(4), 497-524.   DOI   ScienceOn
7 Evesque, P. (2000), "Fluctuations, correlations and representative elementary volume (REV) in granular materials", Powders Grains, 11, 6-17.
8 Gitman, I.M., Askes, H. and Sluys, L.J. (2007), "Representative volume: existence and size determination", Eng. Fract. Mech., 74(16), 2518-2534.   DOI   ScienceOn
9 Gitman, I.M., Askes, H. and Sluys, L.J. (2008), "Coupled-volume multi-scale modelling of quasi-brittle material", Eur. J. Mech. A - Solid, 27(3), 302-327.   DOI   ScienceOn
10 He, H. (2010), "Computational modeling of particle packing in concrete", PhD thesis, Delft University of Technology.
11 Hill, R. (1963), "Elastic properties of reinforced solids: some theoretical principles", J. Mech. Phys. Solids, 11(5), 357-372.   DOI   ScienceOn
12 Jirasek, M. and Marfia, S. (2005), "Non-local damage model based on displacement averaging", Int. J. Numer. Meth. Eng., 63(1), 77-102.   DOI   ScienceOn
13 Kanit, T., Forest, S., Galliet, I., Mounoury, V. and Jeulin, D. (2003), "Determination of the size of the representative volume element for random composites: statistical and numerical approach", Int. J. Solids Struct., 40, 3647-3679.   DOI   ScienceOn
14 Kouznetsova, V.G., Geers, M.G.D. and Brekelmans, W.A.M. (2004), "Size of representative volume element in a second-order computational homogenization framework", Int. J. Multiscale Comput. Eng., 2(4), 575-598.   DOI
15 Katchanov, L.M. (1986), Introduction to continuum damage mechanics, Dordrecht: Martimus Publishers.
16 Kozicki, J. and Tejchman, J. (2008), "Modeling of fracture processes in concrete using a novel lattice model", Granular Matter, 10(5), 377-288.   DOI   ScienceOn
17 Le Bellego, C., Dube, J.F., Pijauder-Cabot, G. and Gerard, B. (2003), "Calibration of nonlocal damage model from size effect tests", Eur. J. Mech. A - Solid, 22(1), 33-46.   DOI   ScienceOn
18 Lilliu, G. and van Mier, J.G.M. (2003), "3D lattice type fracture model for concrete", Eng. Fract. Mech., 70(7-8), 927-941.   DOI   ScienceOn
19 Marzec, I., Bobinski, J. and Tejchman, J. (2007), "Simulations of crack spacing in reinforced concrete beams using elastic-plastic and damage with non-local softening", Comput. Concrete, 4(4), 377-403.   DOI
20 Nguyen, V.P., Lloberas Valls, O., Stroeven, M. and Sluys, L.J. (2010), "On the existence of representative volumes for softening quasi-brittle materials", Comput. Method. Appl. M., 199, 3028-3038.   DOI   ScienceOn
21 Nielsen, A.U., Montiero, P.J.M. and Gjorv, O.E. (1995), "Estimation of the elastic moduli of lightweight aggregate", Cement Concrete Res., 25(2), 276-280.   DOI   ScienceOn
22 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. Cohesive-Frictional Mat., 3(4), 323-342.   DOI   ScienceOn
23 Skarzynski, L . and Tejchman, J. (2009), "Mesoscopic modelling of strain localization in concrete", Arch. Civil Eng. LV, 4.
24 Bazant, Z.P. and Pijauder-Cabot, G. (1989), "Measurement of characteristic length of non-local continuum", J. Eng. Mech. - ASCE, 115(4), 755-767.   DOI
25 Pijauder-Cabot, G. and Bazant, Z.P. (1987), "Nonlocal damage theory", J. Eng. Mech. - ASCE, 113(10), 1512- 1533.   DOI   ScienceOn
26 Sengul, O., Tasdemir, C. and Tasdemir, M.A. (2002), "Influence of aggregate type on mechanical behaviour of normal- and high-strength concretes", ACI Mater. J., 99(6), 528-533.
27 Simo, J.C. and Ju, J.W. (1987), "Strain- and stress-based continuum damage models - I. Formulation", Int. J. Solids Struct., 23(7), 821-840.   DOI   ScienceOn
28 Simone, A. and Sluys, L. (2004), "The use of displacement discontinuities in a rate-dependent medium", Comput. Method. Appl. M., 193(27-29), 3015-3033.   DOI   ScienceOn
29 Skarzynski, L ., Syroka, E. and Tejchman, J. (2009), "Measurements and calculations of the width of the fracture process zones on the surface of notched concrete beams", Strain, doi: 10.1111/j.1475- 1305.2008.00605.x.
30 Skarzynski, L . and Tejchman, J. (2010), "Calculations of fracture process zones on meso-scale in notched concrete beams subjected to three-point bending", Eur. J. Mech. A - Solid, 29, 746-760.   DOI   ScienceOn
31 van Mier, J.G.M. (2000), "Microstructural effects on fracture scaling in concrete, rock and ice", IUTAM Symposium on Scaling Laws in Ice Mechanics and Ice Dynamics (eds.: J.P. Dempsey and H.H. Shen), Kluwer Academic Publishers, 171-182.
32 Verhoosel, C.V., Remmers, J.J.C. and Gutierrez, M.A. (2010a), "A partition of unity-based multiscale approach for modelling fracture in piezoelectric ceramics", Int. J. Numer. Meth. Eng., 82(8), 966-994.
33 Verhoosel, C.V., Remmers, J.J.C., Gutieerrez, M.A. and de Borst, R. (2010b), "Computational homogenization for adhesive and cohesive failure in quasi-brittle solids", Int. J. Numer. Meth. Eng., 83, 1155-1179.   DOI   ScienceOn