Effect of heterogeneity on shear zone formation during plane strain compression

• Autorzy: Tejchman J.
• Języki publikacji: EN

Abstrakty

EN

Heterogeneity of granular materials triggers shear zone formation. In the paper, the FE-analysis of the effect of the material heterogeneity on the formation of a spontaneous shear zone inside of granular materials during a plane strain compression test is presented. The numerical calculations are performed with a finite element method on the basis of a hypoplastic constitutive law extended by polar quantities: rotations, curvatures and couple stresses. A mean grain diameter is used as a characteristic length. The constitutive law takes into account the effect of pressure, void ratio, direction of deformation rate and mean grain diameter on the behaviour of granular bodies. The heterogeneity in the granular body is assumed in the form of spots with a different initial void ratio. The spots are single or distributed randomly and stochastically with an exponential probability function. The single spots are distributed sparsely and densely in an initially dense and loose granular specimen. Special attention is focused on the effect of heterogeneity on the onset of shear localization and its thickness at residual state.

Słowa kluczowe

EN

heterogeneity; mean grain diameter; polar continuum; shear zone; void ratio

• Wydawca: Institute of Hydro-Engineering of Polish Academy of Sciences
• Czasopismo: Archives of Hydro-Engineering and Environmental Mechanics
• Rocznik: 2004
• Tom: Vol. 51, nr 2
• Strony: 149--181
• Opis fizyczny: Bibliogr. 57 poz., il.

Twórcy

autor

Tejchman J.

• Civil Engineering Department, Gdańsk University of Technology 80-952 Gdańsk, Narutowicza 11/12, Poland,

Bibliografia

• Aifantis E. C. (1984), On the Microstructural Origin of Certain Inelastic Models, J. Eng. Mater. Technol., 106, 326–334.
• Bauer E. (1996), Calibration of a Comprehensive Hypoplastic Model for Granular Materials, Soils and Foundations, 36, 1, 13–26.
• Bauer E. (2000), Conditions of Embedding Casagrande’s Critical States into Hypoplasticity,Mechanics of Cohesive-Frictional Materials, 5, 125–148.
• Bazant Z., Lin, F. B. (1988), Nonlocal Yield Limit Degradation, Int. J. Num. Meth. Eng., 26, 1805–1823.
• Belytschko T., Chiang H., Plaskacz E. (1994), High Resolution Two Dimensional Shear Band Computations: Imperfections and Mesh Dependence, Com. Meth. Appl. Mech. Engng., 119, 1–15.
• de Borst R. (1991), Simulation of Strain Localization: a Reappraisal of the Cosserat Continuum, Engng. Computations, 8, 317–332.
• de Borst R., Mühlhaus H. B., Pamin J., Sluys L. Y. (1992), Computational Modelling of Localization of Deformation, Proc. of the 3rd Int. Conf. Comp. Plasticity (D. R. J. Owen, D. R. J. Onate, E., Hinton, eds.), Pineridge Press, Swansea, 483–508.
• Brinkgreve R. (1994), Geomaterial Models and Numerical Analysis of Softening, PhD Thesis, Delft University, 1–153.
• Chambon R., Caillerie D., El Hassan N. (1998), One-Dimensional Localization Studied with a Second Grade Model, European Journal of Mechanics, 17, 4, 637–656.
• Desrues J., Chambon R., Mokni M., Mazerolle F. (1996), Void Ratio Evolution inside Shear Bands in Triaxial Sand Specimens Studied by Computed Tomography, G´eotechnique, 46, 3, 529–546.
• Gudehus G. (1996), Comprehensive Equation of State of Granular Materials, Soils and Foundations, 36, 1, 1–12.
• Gudehus G., Nübel K. (2003), Evolution of Shear Bands in Sand, Geotechnique (in print).
• Gutierrez M. A., de Borst R. (1998), Energy Dissipation, Internal Length Scale and Localization Patterning – a Probabilistic Approach, [in:] ComputationalMechanics (S. Idelsohn, E. Onate, E. Dvorkin, eds,), CIMNE, Barcelona, 1–9.
• Herle I., Gudehus G. (1999), Determination of Parameters of a Hypoplastic Constitutive Model from Properties of Grain Assemblies, Mechanics of Cohesive-Frictional Materials, 4, 5, 461–486.
• Hobbs B. E., Ord A. (1989). Numerical Simulation of Shear Band Formation in Frictional-Dilational Materials, Ingenieur-Archiv, 59, 209–220.
• Huang W., Nübel K., Bauer E. (2002). A Polar Extension of Hypoplastic Model for Granular Material with Shear Localization, Mechanics of Materials, 34, 563–576.
• Kolymbas D. (1977), A Rate-Dependent Constitutive Equation for Soils, Mechanics Research Communications, 4, 367–372.
• Leśniewska D. (2000), Analysis of Shear Pattern Formation in Soil, Institute of Hydroengineering of the Polish Academy of Sciences, Gdansk, 1–204.
• Löffelmann F. (1989), Theoretische und Experimentelle Untersuchungen zur Sch¨uttgut-Wand-Wechselwirkung und zum Mischen und Entmischen von Granulaten, Dissertation, Karlsruhe University.
• Maier T. (2002), Numerische Modellierung der Entfestigung im Rahmen der Hypoplastizit¨at, PhD Thesis, Dortmund University, Germany.
• Marcher T., Vermeer P. A. (2001), Macromodelling of Softening in Non-Cohesive Soils, [in:] Continous and Discontinous Modelling of Cohesive-Frictional Materials, eds. P. A. Vermeer et al, Springer-Verlag, 89–110.
• Mühlhaus H. B. (1989), Application of Cosserat Theory in Numerical Solutions of Limit Load Problems, Ing. Arch., 59, 124–137.
• Mühlhaus H. B. (1990), Continuum Models for Layered and Blocky Rock, [in:] Comprehensive Rock Engineering, eds. J. A. Hudson, Ch. Fairhurst, Pergamon Press, 2, 209–231.
• Nübel K., Karcher C. (1998), FE Simulations of Granular Material with a Given Frequency Distribution of Voids as Initial Condition, Granular Matter, 1, 3, 105–112.
• Nübel K. (2002), Experimental and Numerical Investigation of Shear Localization in GranularMaterials, Publication Series of the Institute of Soil and Rock Mechanics, University Karlsruhe, 140, 1–159.
• Oda M., Konishi J., Nemat-Nasser S. (1982), Experimental Micromechanical Evaluation of Strength of Granular Materials, Effects of Particle Rolling, [in:] Mechanics of Materials, North-Holland Publishing Comp., 1, 269–283.
• Oda M. (1993), Micro-Fabric and Couple Stress in Shear Bands of Granular Materials, [in:] Powders and Grains, ed. C. Thornton, Rotterdam, Balkema, 161–167.
• Oda M., Tatsuoka F., Yoshida T. (1997), Void Ratio in Shear Band of Dense Granular Soils, [in:] Deformation and Progressive Failure in Geomechanics, eds. A. Asaoka, T. Adachi and F. Oka, Pergamon, 157–162.
• Pamin J. (1994), Gradient-Dependent Plasticity in Numerical Simulation of Localisation Phenomena, PhD Thesis, Delft University, 1–134.
• Schäfer H. (1962), Versuch einer Elastizit¨atstheorie des zweidimensionalen ebenen Cosserat-Kontinuums, Miszellaneen der Angewandten Mechanik, Festschrift Tolmien W., Berlin, Akademie-Verlag.
• Shahinpoor M. (1981), Statistical Mechanical Considerations on Storing Bulk Solids, Bulk Solid Handling, 1, 1, 31–36.
• Shi Q., Chang C. S. (2003), Numerical Analysis for the Effect of Heterogeneity on Shear Band Formation, Proc. 16th ASCE Engineering Mechanics Conference, University of Washington, Seattle, 1–11.
• Sluys L. J. (1992), Wave Propagation, Localisation and Dispersion in Softening Solids, PhD Thesis, Delft University of Technology.
• Steinmann P. (1995), Theory and Numerics of Ductile Micropolar Elastoplastic Damage, Int. J. for Num. Meth. in Engng., 38, 583–606.
• Tatsuoka F., Siddiquee M. S., Yoshida T., Park C. S., Kamegai Y., Goto S., Kohata Y. (1994), 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, University of Tokyo, 1–129.
• Tatsuoka F., Goto S., Tanaka T., Tani K., Kimura Y. (1997), Particle Size Effects on Bearing Capacity of Footing on Granular Material, [in:] Deformation and Progressive Failure in Geomechanics, eds.: A. Asaoka, T. Adachi and F. Oka, Pergamon, 133–139.
• Tejchman J. (1989), Scherzonenbildung und Verspannungseffekte in Granulaten unter Berücksichtigung von Korndrehungen, Publication Series of the Institute of Soil and Rock Mechanics, University Karlsruhe, 117, 1–236.
• Tejchman J., Wu W. (1993), Numerical Study on Shear Band Patterning in a Cosserat Continuum, Acta Mechanica, 99, 61–74.
• Tejchman J. (1997), Modelling of Shear Localisation and Autogeneous Dynamic Effects in Granular Bodies, Publication Series of the Institute of Soil and Rock Mechanics, University Karlsruhe, 140, 1–353.
• Tejchman J., Wu W. (1997), Dynamic Patterning of Shear Bands in a Cosserat Continuum, International Journal of Engineering Mechanics ASCE, 123, 2, 123–134.
• Tejchman J., Herle I., Wehr J. (1999), FE–Studies on the Influence of Initial Void Ratio, Pressure Level and Nean Grain Diameter on Shear Localisation, Int. J. Num. Anal. Meth. Geomech., 23, 2045–2074.
• Tejchman J., Gudehus G. (2001), Shearing of a Narrow Granular Strip with Polar Quantities, J. Num. and Anal. Methods in Geomechanics, 25, 1–18.
• Tejchman J. (2002), Patterns of Shear Zones in Granular Materials within a Polar Hypoplastic Continuum, Acta Mechanica, 155, 1–2, 71–95.
• Tejchman J. (2003a), FE-Studies on Formation of Shear Zones in Granular Bodies within a Polar Hypoplasticity, [in:] Bifurcation and Instabilities in Geomechanics, eds. J. F. Labuz and A. Drescher, Balkema, 133–149.
• Tejchman J. (2003b), A Non-Local Hypoplastic Constitutive Law to Describe Shear Localizations in Granular Bodies, Archives of Hydro-Engineering and Environmental Mechanics, 50, 4, 229–250.
• Tejchman J. (2004a), Comparative FE-Studies on Shear Localizations in Granular Bodies within a Polar and Non-Local Hypoplasticity, Mechanics Research Communications, 31, 341–354.
• Tejchman J. (2004b), A Gradient Hypoplastic Constitutive Law to Describe Shear Localizations in Granular Bodies, Archives of Hydro-Engineering and Environmental Mechanics (submitted).
• Tejchman J., Bauer E. (2004), Effect of Cyclic Shearing on Shear Localisation in Granular Bodies, Granular Matter, 5, 201–212.
• Uesugi M., Kishida H., Tsubakihara Y. (1988), Behaviour of Sand Particles in Sand-Steel Friction, Soils and Foundations, 28, 1, 107–118.
• Wang C. C. (1987), A New Representation Theorem for Isotropic Functions, J. Rat. Mech. Anal., 36, 166–223.
• von Wolffersdorff P. A. (1996), Hypoplastic Relation for Granular Materials with a Predefined Limit State Surface, Mechanics Cohesive-Frictional Materials, 1, 251–271.
• Wu W. (1992), Hypoplasticity as a Mathematical Model for the Mechanical Behaviour of Granular Materials, Publication Series of the Institute for Soil Mechanics, Karlsruhe University, 129, 1–154.
• Wu W., Niemunis A. (1996), Failure Criterion, Flow Rule and Dissipation Function Derived from Hypoplasticity, Mechanics of Cohesive-Frictional Materials, 1, 145–163.
• Vardoulakis I. (1977), Scherfugenbildung in Sandk¨orpern als Verzweigungsproblem, Dissertation, Institute for Soil and Rock Mechanics, University of Karlsruhe.
• Vardoulakis I. (1980), Shear Band Inclination and Shear Modulus in Biaxial Tests, Int. J. Num. Anal. Meth. Geomech., 4, 103–119.
• Yoshida Y., Tatsuoka T., Siddiquee M. (1994), Shear Banding in Sands Observed in Plane Strain Compression, [in:] Localisation and Bifurcation Theory for Soils and Rocks, eds.: R. Chambon, J. Desrues and I. Vardoulakis, Balkema, Rotterdam, 165–181.
• Zervos A., Papanastasiou P., Vardoulakis I. (2001), A Finite Element Displacement Formulation for Gradient Elastoplasticity, [in:] Bifurcation and Localisation Theory in Geomechanics eds.: H. B. M¨uhlhaus, A. Dyskin and E. Pasternak, Balkema, 177–187.