Skip to main content
SpringerLink
Log in

Introduction

  • Chapter
Shear Localization in Granular Bodies with Micro-Polar Hypoplasticity

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

Abstract

This chapter describes shortly the phenomenon of shear localization in dry and cohesionless granular materials. It presents the main problems in granular bodies related to this phenomenon. In addition, it summarizes different continuum approaches capable to properly describe shear localization using a finite element method and enhanced constitutive models. A micro-polar hypoplastic constitutive model is briefly described to numerically investigate shear localization in dry and cohesionless granular materials during mainly monotonic deformation paths. The differences between hypoplastic and conventional elasto-plastic continuum models are stressed. The outline of the book is given.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
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

  • Al Hattamleh, O., Muhunthan, B., Zbib, H.M.: Stress distribution in granular heaps using multi-slip formulation. Int. J. Numer. Analyt. Meth. Geomech. 29, 713–727 (2005)

    Article  MATH  Google Scholar 

  • Alonso-Marroquin, F., Herrmann, H.J., Vardoulakis, I.: Micromechanical aspects of soil plasticity; an investigation using a discrete model of polygonal particles. In: Vermeer, P.A., Ehlers, W., Herrmann, H.J., Ramm, E. (eds.) Modelling of Cohesive-Frictional Materials, Balkema, pp. 45–69 (2004)

    Google Scholar 

  • Alshibli, K.A., Sture, S.: Shear band formation in plane strain experiments of sand. J. Geotech. Geoenviron. Engng. ASCE 126(6), 495–503 (2000)

    Article  Google Scholar 

  • Arslan, H., Sture, S., Willam, K.: Finite element simulation of localization in granular material by micro-polar continuum approach. Comp. Geotech. (in press, 2008)

    Google Scholar 

  • Bauer, E.: Calibration of a comprehensive hypoplastic model for granular materials. Soils Found. 36(1), 13–26 (1996)

    Google Scholar 

  • Bauer, E.: Conditions of embedding Casagrande’s critical states into hypoplasticity. Mech. Coh.-Frict. Mater. 5, 125–148 (2000)

    Article  Google Scholar 

  • Bazant, Z., Lin, F., Pijaudier-Cabot, G.: Yield limit degradation: non-local continuum model with local strain. In: Owen, R., et al. (eds.) Proc. Int. Conf. Computational Plasticity, Barcelona, pp. 1757–1780 (1987)

    Google Scholar 

  • Becker, M., Lippmann, H.: Plane plastic flow of granular model material. Arch. Mech. 29, 829–846 (1977)

    Google Scholar 

  • Belytschko, T., Chiang, H., Plaskacz, E.: High resolution two dimensional shear band computations: imperfections and mesh dependence. Com. Meth. Appl. Mech. Engng. 119, 1–15 (1994)

    Article  MATH  Google Scholar 

  • Beltyschko, T., Krongauz, Y., Organ, D., Fleming, M., Krysl, P.: Meshless methods: an overview and recent developments. Comp. Meth. Appl. Mech. Engrg. 139, 3–47 (1996)

    Article  Google Scholar 

  • Benallal, A., Billardon, R., Geymonat, G.: Localization phenomena at the boundaries and interfaces of solids. In: Desai, C.S., et al. (eds.) Proc. of the 3rd Int. Conf. Constitutive Laws for Engineering Materials: Theory and Applications, Tucson, Arizona, pp. 387–390 (1987)

    Google Scholar 

  • Bogdanova-Bontscheva, N., Lippmann, H.: Rotations symmetrisches ebenes Fliessen eines granularen Modellmaterials. Acta Mech. 21, 93–113 (1975)

    Article  Google Scholar 

  • de Borst, R.: Simulation of strain localization: a reappraisal of the Cosserat continuum. Engng. Comput. 8, 317–332 (1991)

    Article  Google Scholar 

  • de Borst, R., Mühlhaus, H.B., Pamin, J., Sluys, L.Y.: Computational modelling of localization of deformation. In: Owen, D.R.J., Onate, E., Hinton, E. (eds.) Proc. of the 3rd Int. Conf. Comp. Plasticity, pp. 483–508. Pineridge Press, Swansea (1992)

    Google Scholar 

  • de Borst, R., Mühlhaus, H.B.: Gradient dependent plasticity: formulation and algorithmic aspects. Int. J. Numer. Methods Engng. 35, 521–539 (1992)

    Article  MATH  Google Scholar 

  • Brinkgreve, R.: Geomaterial models and numerical analysis of softening. PhD thesis, Delft University, 1-153 (1994)

    Google Scholar 

  • Chambon, R., Matsushima, T., Caillerie, D.: Plastic continuum with microstructure, local second gradient theories for geomaterials: localisation studies. Int. J. Solids Structures 38, 8503–8527 (2001)

    Article  MATH  Google Scholar 

  • Darve, F., Flavigny, E., Megachou, M.: Yield surfaces and principle of superposition revisited by incrementally non-linear constitutive relations. Int. J. Plasticity 11(8), 927–948 (1995)

    Article  MATH  Google Scholar 

  • David, C.T., Garcia-Rojo, R., Herrmann, H.J., Luding, S.: Powder Flow Testing with 2D and 3D biaxial and triaxial simulations. J. Particle and Particle System Charact. 24(1), 29–33 (2007)

    Article  Google Scholar 

  • Desrues, J., Hammad, W.: Shear banding dependency on mean pressure level in sand. In: Dembicki, E., et al. (eds.) Proc. Int. Workshop on Numerical Methods for Localization and Bifurcation of Granular Bodies, Gdansk, Poland, pp. 57–67 (1989)

    Google Scholar 

  • Desrues, J., Chambon, R., Mokni, M., Mazerolle, F.: Void ratio evolution inside shear bands in triaxial sand specimens studied by computed tomography. Géotechnique 46(3), 529–546 (1996)

    Google Scholar 

  • Desreues, J., Viggiani, G.: Strain localization in sand: overview of the experiments in Grenoble using stereo photogrammetry. Int. J. Numer. Anal. Meth. Geomech. 28(4), 279–321 (2004)

    Article  Google Scholar 

  • Ehlers, W., Volk, W.: On theoretical and numerical methods in the theory of porous media based on polar and non-polar elasto-plastic solid materials. Int. J. Solids Structures 35, 4597–4616 (1998)

    Article  MATH  Google Scholar 

  • Ehlers, W., Ellsiepen, P., Ammann, M.: Time- and space-adaptive computations of localization phenomena in standard and micropolar frictional porous materials. In: Mühlhaus, H.B., Dyskin, A., Pasternak, E. (eds.) Bifurcation Localisation Theory in Geomechanics, Balkema, pp. 139–147 (2001)

    Google Scholar 

  • Ehlers, W., Graf, T.: Adaptive computation of localization phenomena in geotechnical applications. In: Labuz, J., Drescher, A. (eds.) Bifurcations and Instabilities in Geomechanics, Swets, Zeitlinger, pp. 247–262 (2003)

    Google Scholar 

  • Finno, R.J., Harris, W., Mooney, M., Viggiani, G.: Strain localization and undrained steady state of sand. Journal of Geotechnical Engineering ASCE 122(6), 462–473 (1996)

    Article  Google Scholar 

  • Gitman, I.: Representative volumes and multi-scale modeling of quasi-brittle materials. PhD Thesis, University of Delft (2006)

    Google Scholar 

  • Gudehus, G.: Einige Beiträge der Bodenmechanik zur Entstehung und Auswirkung von Diskontinuitäten. Felsbau 4, 190–195 (1986)

    Google Scholar 

  • Gudehus, G.: A comprehensive constitutive equation for granular materials. Soils Found. 36(1), 1–12 (1996)

    Google Scholar 

  • Gudehus, G., Nübel, K.: Evolution of shear bands in sand. Geotechnique 54(3), 187–201 (2004)

    Article  Google Scholar 

  • Gudehus, G.: Physical background of hypoplasticity. In: Wu, W., Yu, H.S. (eds.) Modern Trends in Geomechanics, pp. 17–37. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  • Gudehus, G.: Physical Soil Mechanics. Springer, Heidelberg (2007)

    Google Scholar 

  • Gutierrez, M., Vardoulakis, I.: Energy dissipation and post-bifurcation behaviour of granular soils. Int. J. Num. Anal. Meth. Geomech. 31, 435–455 (2007)

    Article  Google Scholar 

  • Han, C., Vardoulakis, I.: Plane strain compression experiments on water saturated fine-grained sand. Geotechnique 41, 49–78 (1991)

    Google Scholar 

  • Harris, W.W., Viggiani, G., Mooney, M.A., Finno, R.J.: Use of stereo photogrammetry to analyze the development of shear bands in sand. Geotech. Test. J. 18(4), 405–420 (1995)

    Article  Google Scholar 

  • Hassan, A.H.: Etude experimentale et numerique du comportement local et global d’une interface sol granulaire. PHD thesis, Grenoble University (1995)

    Google Scholar 

  • Hicks, M.A., Yap, T.Y., Bakar, A.A.: Adaptive and fixed mesh study of localisation in a strain-softening soil. In: Mühlhaus, H.B., Dyskin, A., Pasternak, E. (eds.) Bifurcation and Localisation Theory in Geomechanics, Balkema, pp. 147–155 (2001)

    Google Scholar 

  • Huang, W., Bauer, E.: Numerical investigations of shear localization in a micro-polar hypoplastic material. J. Num. Anal. Meth. Geomech. 27, 325–352 (2003)

    Article  MATH  Google Scholar 

  • Kolymbas, D.: Introduction to hypoplasticity. Advances in Geotechnical Engineering and Tunneling, Balkema, Rotterdam, Brookfield (2000)

    Google Scholar 

  • Lade, P.V.: Elasto-plastic stress-strain theory for cohesionless soil with curved yield surfaces. Int. J. Solid Structures 13, 1019–1035 (1977)

    Article  MATH  Google Scholar 

  • Lade, P.V.: Instability, shear banding and failure in granular materials. I. J. Solids Structures 39, 3337–3357 (2002)

    Article  Google Scholar 

  • Lai, T.Y., Borja, R.I., Duvernay, B.G., Meehan, R.L.: Capturing strain localization behind a geosynthetic-reinforced soil wall. I. J. Num. Anal. Meths. Geomech. 27, 425–451 (2003)

    Article  MATH  Google Scholar 

  • Larsson, J., Larsson, R.: Finite-element analysis of localization of deformation and fluid pressure in elastoplastic porous medium. Int. J. Solids Structures 37, 7231–7257 (2000)

    Article  MATH  Google Scholar 

  • LeÅ›niewska, D., Mróz, Z.: Study of evolution of shear band systems in sand retained by flexible wall. Int. J. Numer. Anal. Meth. Geomech. 25, 909–932 (2001)

    Article  MATH  Google Scholar 

  • Lodygowski, T., Perzyna, P.: Numerical modelling of localized fracture of inelastic solids in dynamic loading process. Int. J. Num. Meth. Eng. 40(22), 4137–4158 (1997)

    Article  MATH  Google Scholar 

  • Loret, B., Prevost, J.H.: Dynamic strain localization in fluid-saturated porous media. J. Engng. Mech. ASCE 117, 907–922 (1991)

    Article  Google Scholar 

  • Löffelmann, F.: Theoretische und experimentelle Untersuchungen zur Schüttgut-Wand-Wechselwirkung und zum Mischen und Entmischen von Granulaten. Publication Series of the Institut für Mechanische Verfahrenstechnik, Universität Karlsruhe (1989)

    Google Scholar 

  • Maier, T.: Numerische Modellierung der Entfestigung im Rahmen der Hypoplastizität. PhD Thesis, Dortmund University, Germany (2002)

    Google Scholar 

  • Mandel, J.: Conditions de stabilite et postulat de Drucker. In: Proceedings IUTAM Symposium Rheology and Soil Mechanics, pp. 58–68. Springer, Berlin (1966)

    Google Scholar 

  • Manzari, M.T.: Application of micropolar plasticity to post failure analysis in geomechanics. Int. J. Numer. Anal. Meths. Geomech. 28(10), 1011–1032 (2004)

    Article  MATH  Google Scholar 

  • Marcher, T., Vermeer, P.A.: Macromodelling of softening in non-cohesive soils. In: Vermeer, P.A., et al. (eds.) Continuous and Discontinuous Modelling of Cohesive-Frictional Materials, pp. 89–110. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  • Mühlhaus, H.B.: Berücksichtigung von Inhomogenitäten im Gebirge im Rahmen einer Kontinuumstheorie. Veröffentlichung des Instituts für Boden- und Felsmechanik, Universität Karlsruhe, Heft 106, 1-65 (1987)

    Google Scholar 

  • Mühlhaus, H.B.: Application of Cosserat theory in numerical solutions of limit load problems. Ing. Arch. 59, 124–137 (1989)

    Article  Google Scholar 

  • Mühlhaus, H.B., Vardoulakis, I.: The thickness of shear bands in granular materials. Geotechnique 37, 271–283 (1989)

    Google Scholar 

  • Mühlhaus, H.B.: Continuum models for layered and blocky rock. In: Hudson, J.A., Fairhurst, C. (eds.) Comprehensive Rock Engineering, vol. 2, pp. 209–231. Pergamon Press, Oxford (1990)

    Google Scholar 

  • Oda, M., Konishi, J., Nemat-Nasser, S.: Experimental micromechanical evaluation of strength of granular materials, effects of particle rolling. Mech. Mater. 1, 269–283 (1982)

    Article  Google Scholar 

  • Oda, M.: Micro-fabric and couple stress in shear bands of granular materials. In: Thornton, C. (ed.) Powders and Grains, Rotterdam, Balkema, pp. 161–167 (1993)

    Google Scholar 

  • Oda, M., Kazama, H.: Microstructure of shear bands and its relation to the mechanisms of dilatancy and failure of dense granular soils. Geotechnique 48, 465–481 (1998)

    Article  Google Scholar 

  • Oda, M., Iwashita, K.: Study on couple stresses and shear band development in granular media based on numerical simulation analyses. Int. J. of Enging. Science 38, 1713–1740 (2000)

    Article  Google Scholar 

  • Oka, F., Jing, M., Higo, Y.: Effect of transport of pore water on strain localisation analysis of fluid-saturated strain gradient dependent viscoplastic geomaterial. In: Mühlhaus, H.-B., et al. (eds.) Bifurcation and Localisation Theory in Geomechanics, Swets, Zeitlinger, Lisse, pp. 77–83 (2001)

    Google Scholar 

  • Ord, A., Hobbs, B., Regenauer-Lieb, K.: Shear band emergence in granular materials – a numerical study. Int. J. Num. Anal. Meth. Geomech. 31, 373–393 (2007)

    Article  Google Scholar 

  • Pamin, J.: Gradient-dependent plasticity in numerical simulation of localisation phenomena. PhD Thesis, Delft University, 1-134 (1994)

    Google Scholar 

  • Pamin, J., Askes, H., de Borst, R.: Two gradient plasticity theories discretized with the element-free Galerkin method. Comp. Meth. Appl. Mech. Enging. 192, 2377–2403 (2003)

    Article  MATH  Google Scholar 

  • Pamin, J.: Gradient-enhanced continuum models: formulations, discretization and applications. Monograph 301, 1–174 (2004)

    Google Scholar 

  • Pasternak, E., Mühlhaus, H.B.: Cosserat continuum modelling of granulate materials. In: Valliappan, S., Khalili, N. (eds.) Computational Mechanics – New Frontiers for New Millennium, pp. 1189–1194. Elsevier Science, Amsterdam (2001)

    Google Scholar 

  • Pastor, M., Peraire, J.: Capturing shear bands via adaptive remeshing techniques. Euromech. 248 (1989); Non-linear soil-structure interaction

    Google Scholar 

  • Pena, A.A., García-Rojo, R., Herrmann, H.J.: Influence of particle shape on sheared dense granular media. Granular Matter 3-4, 279–292 (2007)

    Article  Google Scholar 

  • Pestana, J.M., Whittle, A.J.: Formulation of a unified constitutive model for clays and sands. Int. J. Num. Anal. Meth. Geomech. 23, 1215–1243 (1999)

    Article  MATH  Google Scholar 

  • Rechenmacher, A.L.: Grain-scale processes governing shear band initiation and evolution in sands. J. Mech. Physics Solids 54, 22–45 (2006)

    Article  MATH  Google Scholar 

  • Regueiro, R.A., Borja, R.I.: Plane strain finite element analysis of pressure sensitive plasticity with strong discontinuity. Int. J. Solids Structures 38(21), 3647–3672 (2001)

    Article  MATH  Google Scholar 

  • Rudnicki, J.W., Rice, J.R.: Conditions of the localization of deformation in pressure-sensitive dilatant materials. J. Mech. Physics Solids 23, 371–394 (1975)

    Article  Google Scholar 

  • Schanz, T.: A constitutive model for cemented sands. In: Adachi, T., Oka, F., Yashima, A. (eds.) Localisation and Bifurcation Theory for Soils and Rocks, Balkema, Rotterdam, pp. 165–172 (1998)

    Google Scholar 

  • Shi, Q., Chang, C.S.: Numerical analysis for the effect of heterogeneity on shear band formation. In: Proc. 16th ASCE Engineering Mechanics Conference, University of Washington, Seattle, pp. 1–11 (2003)

    Google Scholar 

  • Simone, A., Sluys, L.J.: Continous-discountinous modeling of mode-I and mode-II failure. In: Vermeer, P.A., Ehlers, W., Herrmann, H.J., Ramm, E. (eds.) Modelling of Cohesive-Frictional Materials, Balkema, pp. 323–337 (2004)

    Google Scholar 

  • Sluys, L.J.: Wave propagation, localisation and dispersion in softening solids. PhD Thesis, Delft University of Technology (1992)

    Google Scholar 

  • Sluys, L.J., de Borst, R.: Dispersive properties of gradient and rate-dependent media. Mech. Mater. 183, 131–149 (1994)

    Article  Google Scholar 

  • Stoker, C.: Developments of the Arbitrary Lagrangian-Eulerian method in non-linear solid mechanics. PhD Thesis, University of Delft (1999)

    Google Scholar 

  • Tatsuoka, F., Nakamura, S., Huang, C.C., Tani, K.: Strength anisotropy and shear band direction In plane strain test of sand. Soils and Foundations 30(1), 35–54 (1990)

    Google Scholar 

  • Tatsuoka, F., Okahara, M., Tanaka, T., Tani, K., Morimoto, T., Siddiquee, M.S.A.: Progressive failure and particle size effect in bearing capacity of footing on sand. In: Proc. of the ASCE Geotechnical Engineering Congress, vol. 27(2), pp. 788–802 (1991)

    Google Scholar 

  • Tatsuoka, F., Siddiquee, M.S.A., Yoshida, T., Park, C.S., Kamegai, Y., Goto, S., Kohata, Y.: Testing methods and results of element tests and testing conditions of plane strain model bearing capacity tests using air-dried dense Silver Buzzard Sand. Internal Report of the University of Tokyo, pp. 1–129 (1994)

    Google Scholar 

  • Tatsuoka, F., Goto, S., Tanaka, T., Tani, K., Kimura, Y.: Particle size effects on bearing capacity of footing on granular material. In: Asaoka, A., Adachi, T., Oka, F. (eds.) Deformation and Progressive Failure in Geomechanics, pp. 133–138. Pergamon, Oxford (1997)

    Google Scholar 

  • Tejchman, J.: Scherzonenbildung und Verspannungseffekte in Granulaten unter Berücksichtigung von Korndrehungen. Publication Series of the Institute of Soil and Rock Mechanics, University Karlsruhe, vol. 117, pp. 1-236 (1989)

    Google Scholar 

  • Tejchman, J., Wu, W.: Numerical study on shear band patterning in a Cosserat continuum. Acta Mech. 99, 61–74 (1993)

    Article  MATH  Google Scholar 

  • Tejchman, J., Gudehus, G.: Silo-music and silo-quake, experiments and a numerical Cosserat approach. Powder Technology 76(2), 201–212 (1993)

    Article  Google Scholar 

  • Tejchman, J., Wu, W.: Experimental and numerical study of sand-steel interfaces. Int. J. Num. Anal. Meth. Geomech. 19(8), 513–537 (1995)

    Article  Google Scholar 

  • Tejchman, J., Bauer, E.: Numerical simulation of shear band formation with a polar hypoplastic model. Comp. Geotech. 19(3), 221–244 (1996)

    Article  Google Scholar 

  • Tejchman, J.: Modelling of shear localisation and autogeneous dynamic effects in granular bodies. Publication Series of the Institute of Soil and Rock Mechanics, University Karlsruhe, vol. 140, pp. 1-353 (1997)

    Google Scholar 

  • Tejchman, J., Herle, I., Wehr, J.: 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)

    Article  MATH  Google Scholar 

  • Tejchman, J., Gudehus, G.: Shearing of a narrow granular strip with polar quantities. J. Num. Anal. Methods in Geomechanics 25, 1–28 (2001)

    Article  MATH  Google Scholar 

  • Tejchman, J.: Influence of a characteristic length on shear zone thickness in hypoplasticity with different enhancements. Comp. Geotech. 31(8), 595–611 (2004)

    Article  Google Scholar 

  • Tejchman, J.: Finite element modeling of shear localization in granular bodies in hypoplasticity with enhancements. Gdansk University of Technology, GdaÅ„sk (2005)

    Google Scholar 

  • Thornton, C., Zhang, L.: Numerical simulations of the direct shear test. Chem. Eng. Technol. 26(2), 1–4 (2003)

    Article  Google Scholar 

  • Thornton, C., Ciomocos, M.T., Adams, M.J.: Numerical simulations of diametrical compression tests on agglomerates. Powder Technology 140, 258–267 (2004)

    Article  Google Scholar 

  • Tordesillas, A.: Force chain buckling, unjamming transitions and shear banding in dense granular assemblies. Philos. Mag. J. (in press, 2007)

    Google Scholar 

  • Tykhoniuk, R., Luding, S., Tomas, J.: Simulation der Scherdynamik kohäsiver Pulver. Chem.-Ing.-Technik 76, 59–62 (2004)

    Article  Google Scholar 

  • Uesugi, M., Kishida, H., Tsubakihara, Y.: Behaviour of sand particles in sand-steel friction. Soils Found. 28(1), 107–118 (1988)

    Google Scholar 

  • von Wolffersdorff, P.A.: A hypoplastic relation for granular materials with a predefined limit state surface. Mech. Coh.-Frict. Mater. 1, 251–271 (1996)

    Article  Google Scholar 

  • Wojcik, M., Tejchman, J.: Numerical simulations of granular material flow in silos with and without insert. Arch. Civil Enng. LIII 2, 293–322 (2007)

    Google Scholar 

  • Vardoulakis, I.: Shear band inclination and shear modulus in biaxial tests. Int. J. Num. Anal. Meth. Geomech. 4, 103–119 (1980)

    Article  MATH  Google Scholar 

  • Vardoulakis, I., Aifantis, E.C.: A gradient flow theory of plasticity for granular materials. Acta Mech. 87, 197–217 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  • Vardoulakis, I., Sulem, J.: Bifurcation Analysis in Geomechanics. Blackie Academic and Professional, Glasgow (1995)

    Google Scholar 

  • Vermeer, P.: A five-constant model unifying well-established concepts. In: Gudehus, G., Darve, F., Vardoulakis, I. (eds.) Proc. Int. Workshop on Constitutive Relations for Soils, Balkema, pp. 175–197 (1982)

    Google Scholar 

  • Vardoulakis, I., Goldschneider, M., Gudehus, G.: Formation of shear bands in sand bodies as a bifurcation problem. International Journal of Numerical and Anal. Methods in Geomechanics 2, 99–128 (1995)

    Article  Google Scholar 

  • Viggiani, G., Kuntz, M., Desrues, J.: An experimental investigation of the relationship between grain size distribution and shear banding in granular materials. In: Vermeer, P.A., et al. (eds.) Continuous and Discontinuous Modelling of Cohesive Frictional Materials, pp. 111–127. Springer, Berlin (2001)

    Chapter  Google Scholar 

  • Yoshida, T., Tatsuoka, F., Siddiquee, M.S.A.: Shear banding in sands observed in plane strain compression. In: Chambon, R., Desrues, J., Vardoulakis, I. (eds.) Localisation and Bifurcation Theory for Soils and Rocks, Balkema, Rotterdam, pp. 165–181 (1994)

    Google Scholar 

  • Yoshida, N., Arai, T., Onishi, K.: Elasto-plastic Cosserat finite element analysis of ground deformation under footing load. In: Asaoka, A., Adachi, T., Oka, F. (eds.) Deformation and Progressive Failure in Geomechanics, pp. 395–401. Pergamon, Oxford (1997)

    Google Scholar 

  • Zervos, A., Papanastasiou, P., Vardoulakis, I.: A finite element displacement formulation for gradient plasticity. Int. J. Numer. Meth. Engng. 50, 1369–1388 (2001)

    Article  MATH  Google Scholar 

Download references

Authors
  1. Jacek Tejchman
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Tejchman, J. (2008). Introduction. In: Shear Localization in Granular Bodies with Micro-Polar Hypoplasticity. Springer Series in Geomechanics and Geoengineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70555-0_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-70555-0_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70554-3

  • Online ISBN: 978-3-540-70555-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation