Skip to main content
SpringerLink
Log in

Mesoscopic Modelling of Strain Localization in Plain Concrete

  • Chapter
Continuous and Discontinuous Modelling of Fracture in Concrete Using FEM

Part of the book series: Springer Series in Geomechanics and Geoengineering ((SSGG))

  • 2746 Accesses

Abstract

The Chapter deals with modelling of strain localization in concrete at meso-scale. Concrete was considered as a composite material by distinguishing three phases: cement matrix, aggregate and interfacial transition zones. For FE calculations, an isotropic damage model with non-local softening was used. The simulations were carried out with concrete specimens under uniaxial tension and bending. The effect of aggregate density, aggregate size, aggregate distribution, aggregate shape, aggregate stiffness, aggregate size distribution, characteristic length and specimen size was investigated. The representative volume element was also determined.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Bažant, Z.P., Novak, D.: Stochastic models for deformation and failure of quasibrittle structures: recent advances and new directions. In: Bicanić, N., de Borst, R., Mang, H., Meschke, G. (eds.) Computational Modelling of Concrete Structures, pp. 583–598 (2003)

    Google Scholar 

  • Bažant, Z.P., Oh, B.H.: Crack band theory for fracture of concrete. Materials and Structures RILEM 16(93), 155–177 (1983)

    Google Scholar 

  • Bažant, Z.P., Pijauder-Cabot, G.: Measurement of characteristic length of non-local continuum. ASCE Journal of Engineering Mechanics 115(4), 755–767 (1989)

    Article  Google Scholar 

  • Bažant, Z., Planas, J.: Fracture and size effect in concrete and other quasi-brittle materials. CRC Press LLC (1998)

    Google Scholar 

  • Belytschko, T., Moes, N., Usui, S., Parimi, C.: Arbitrary discontinuities in finite elements. International Journal for Numerical Methods in Engineering 50(4), 993–1013 (2001)

    Article  MATH  Google Scholar 

  • Belytschko, T., Gracie, R., Ventura, G.: A review of extended/generalized finite element methods for material modeling. Modelling and Simulation in Material Science and Engineering 17(4), 1–24 (2009)

    Article  MathSciNet  Google Scholar 

  • Bobiński, J., Tejchman, J.: Numerical simulations of localization of deformation in quasi-brittle materials with non-local softening plasticity. Computers and Concrete 1(4), 433–455 (2004)

    Google Scholar 

  • Carol, I., López, C.M., Roa, O.: Micromechanical analysis of quasi-brittle materials using fracture-based interface elements. International Journal for Numerical Methods in Engineering 52(12), 193–215 (2001)

    Article  Google Scholar 

  • Donze, F.V., Magnier, S.A., Daudeville, L., Mariotti, C.: Numerical study of compressive behaviour of concrete at high strain rates. Journal for Engineering Mechanics 125(10), 1154–1163 (1999)

    Article  Google Scholar 

  • Drugan, W.J., Willis, J.R.: A micromechanics-based nonlocal constitutive equations and estimates of representative volume element size for elastic composites. Journal of the Mechanics and Physics of Solids 44(4), 497–524 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  • Du, C.B., Sun, L.G.: Numerical simulation of aggregate shapes of two dimensional concrete and its application. Journal of Aerospace Engineering 20(3), 172–178 (2007)

    Article  MathSciNet  Google Scholar 

  • Eckardt, S., Konke, C.: Simulation of damage in concrete structures using multi-scale models. In: Bicanić, N., de Borst, R., Mang, H., Meschke, G. (eds.) Computational Modelling of Concrete Structures, EURO-C, pp. 77–89. Taylor and Francis (2006)

    Google Scholar 

  • Evesque, P.: Fluctuations, correlations and representative elementary volume (REV) in granular materials. Poudres et Grains 11(1), 6–17 (2000)

    Google Scholar 

  • Geers, M.G.D., Kouznetsova, V.G., Brekelmans, W.A.M.: Multi-scale computational homogenization: trends and challenges. Journal of Computational and Applied Mathematics 234(7), 2175–2182 (2010)

    Article  MATH  Google Scholar 

  • Gitman, I.M.: Representative Volumes and multi-scale modelling of quasi-brittle materials, PhD Thesis. Delft University of Technology (2006)

    Google Scholar 

  • Gitman, I.M., Askes, H., Sluys, L.J.: Representative volume: existence and size determination. Engineering Fracture Mechanics 74(16), 2518–2534 (2007)

    Article  Google Scholar 

  • Gitman, I.M., Askes, H., Sluys, L.J.: Coupled-volume multi-scale modelling of quasi-brittle material. European Journal of Mechanics A/Solids 27(3), 302–327 (2008)

    Article  MATH  Google Scholar 

  • He, H., Guo, Z., Stroeven, P., Stroeven, M., Sluys, L.J.: Influence of particle packing on elastic properties of concrete. In: Proc. First International Conference on Computational Technologies in Concrete Structures (CTCS 2009), Jeju, Korea, pp. 1177–1197 (2009)

    Google Scholar 

  • He, H.: Computational modeling of particle packing in concrete. PhD Thesis. Delft University of Technology (2010)

    Google Scholar 

  • Hill, R.: Elastic properties of reinforced solids: some theoretical principles. Journal of the Mechanics and Physics of Solids 11(5), 357–372 (1963)

    Article  MATH  Google Scholar 

  • Kaczmarczyk, L., Pearce, C.J., Bicanic, N., de Souza Neto, E.: Numerical multiscale solution strategy for fracturing heterogeneous materials. Computer Merhods in Applied Mechanics and Engineering 199(17-20), 1100–1113 (2010)

    Article  MATH  Google Scholar 

  • Kanit, T., Forest, S., Galliet, I., Mounoury, V., Jeulin, D.: Determination of the size of the representative volume element for random composites: statistical and numerical approach. International Journal of Solids and Structures 40(13-14), 3647–3679 (2003)

    Article  MATH  Google Scholar 

  • Kim, S.M., Abu Al-Rub, R.K.: Meso-scale computational modelling of the plastic-damage response of cementitious composites. Cement and Concrete Research 41(3), 339–358 (2011)

    Article  Google Scholar 

  • Kouznetsova, V.G., Geers, M.G.D., Brekelmans, W.A.M.: Size of Representative Volume Element in a second-order computational homogenization framework. International Journal for Multiscale Computational Engineering 2(4), 575–598 (2004)

    Article  Google Scholar 

  • Kozicki, J., Tejchman, J.: Modeling of fracture processes in concrete using a novel lattice model. Granular Matter 10(5), 377–388 (2008)

    Article  Google Scholar 

  • Le Bellěgo, C., Dube, J.F., Pijaudier-Cabot, G., Gerard, B.: Calibration of nonlocal damage model from size effect tests. European Journal of Mechanics A/Solids 22(1), 33–46 (2003)

    Article  MATH  Google Scholar 

  • Lilliu, G., van Mier, J.G.M.: 3D lattice type fracture model for concrete. Engineering Fracture Mechanics 70(7-8), 927–941 (2003)

    Article  Google Scholar 

  • Marzec, I., Bobiński, J., Tejchman, J.: Simulations of crack spacing in reinforced concrete beams using elastic-plastic and damage with non-local softening. Computers and Concrete 4(5), 377–403 (2007)

    Google Scholar 

  • Mihashi, H., Nomura, N.: Correlation between characteristics of fracture process zone and tension softening properties of concrete. Nuclear Engineering and Design 165(3), 359–376 (1996)

    Article  Google Scholar 

  • Nguyen, V.P., Lloberas Valls, O., Stroeven, M., Sluys, L.J.: On the existence of representative volumes for softening quasi-brittle materials. Computer Methods in Applied Mechanics and Engineering 199(45-48), 3028–3038 (2010)

    Article  MATH  Google Scholar 

  • Nielsen, A.U., Montiero, P.J.M., Gjorv, O.E.: Estimation of the elastic moduli of lightweight aggregate. Cement and Concrete Research 25(2), 276–280 (1995)

    Article  Google Scholar 

  • Pijaudier-Cabot, G., Bazant, Z.P.: Nonlocal damage theory. Journal of Engineering Mechanics ASCE 113(10), 1512–1533 (1987)

    Article  Google Scholar 

  • Sengul, O., Tasdemir, C., Tasdemir, M.A.: Influence of aggregate type on mechanical behaviour of normal- and high-strength concretes. ACI Materials Journal 99(6), 528–533 (2002)

    Google Scholar 

  • Shahbeyk, S., Hosseini, M., Yaghoobi, M.: Mesoscale finite element prediction of concrete failure. Computational Materials Science 50(7), 1973–1990 (2011)

    Article  Google Scholar 

  • Skarżyński, L., Tejchman, J.: Mescopic modeling of strain localization in concrete. Archives of Civil Engineering LV(4), 521–540 (2009)

    Google Scholar 

  • Skarżyński, L., Tejchman, J.: Calculations of fracture process zones on meso-scale in notched. concrete beams subjected to three-point bending. European Journal of Mechanics A/Solids 29(4), 746–760 (2010)

    Article  Google Scholar 

  • Skarżynski, L., Syroka, E., Tejchman, J.: Measurements and calculations of the width of the fracture process zones on the surface of notched concrete beams. Strain 47(s1), 319–322 (2011)

    Article  Google Scholar 

  • Skarżyński, L., Tejchman, J.: Determination of representative volume element in concrete under tensile deformation. Computers and Concrete 1(9), 35–50 (2012)

    Google Scholar 

  • Syroka, E., Tejchman, J.: Experimental investigations of size effect in reinforced concrete beams without shear reinforcement. Internal Report. Gdańsk University of Technology (2011)

    Google Scholar 

  • van der Sluis, O.: Homogenisation of structured elastoviscoplastic solids. PhD Thesis. Technical University Eindhoven (2001)

    Google Scholar 

  • van Mier, J.G.M., Schlangen, E., Vervuurt, A.: Latice type fracture models for concrete. In: Mühlhaus, H.-B. (ed.) Continuum Models for Material and Microstructure, pp. 341–377. John Wiley & Sons (1995)

    Google Scholar 

  • van Mier, J.G.M.: Microstructural effects on fracture scaling in concrete, rock and ice. In: Dempsey, J.P., Shen, H.H. (eds.) IUTAM Symposium on Scaling Laws in Ice Mechanics and Ice Dynamics, pp. 171–182. Kluwer Academic Publishers (2000)

    Google Scholar 

  • Verhoosel, C.V., Remmers, J.J.C., Gutierrez, M.A.: A partition of unity-based multiscale approach for modelling fracture in piezoelectric ceramics. International Journal for Numerical Methods in Engineering 82(8), 966–994 (2010a)

    Article  MATH  Google Scholar 

  • Verhoosel, C.V., Remmers, J.J.C., Gutieerrez, M.A., de Borst, R.: Computational homogenization for adhesive and cohesive failure in quasi-brittle solids. International Journal for Numerical Methods in Engineering 83(8-9), 1155–1179 (2010b)

    Article  MATH  Google Scholar 

  • White, D.J., Take, W.A., Bolton, M.D.: Soil deformation measurement using particle image velocimetry (PIV) and photogrammetry. Geotechnique 53(7), 619–631 (2003)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Civil and Environmental Engineering, Gdansk University of Technology, Narutowicza 11/12, Gdansk-Wrzeszcz, Poland

    Jacek Tejchman

  2. Faculty of Civil and Environmental Engineering, Gdansk University of Technology, Narutowicza 11/12, 80-233, Gdansk-Wrzeszcz, Poland

    Jerzy Bobiński

Authors
  1. Jacek Tejchman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jerzy Bobiński
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jacek Tejchman .

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag GmbH Berlin Heidelberg

About this chapter

Cite this chapter

Tejchman, J., Bobiński, J. (2013). Mesoscopic Modelling of Strain Localization in Plain Concrete. In: Continuous and Discontinuous Modelling of Fracture in Concrete Using FEM. Springer Series in Geomechanics and Geoengineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28463-2_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-28463-2_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28462-5

  • Online ISBN: 978-3-642-28463-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation