Dynamic Patterning of Shear Bands in Cosserat Continuum
Publication: Journal of Engineering Mechanics
Volume 123, Issue 2
Abstract
Numerical simulation of patterns of shear bands in plane-strain compression tests using an elastoplastic Cosserat constitutive equation with consideration of inertia is presented. Random distribution of the material properties acts as a trigger for the localized deformation. Two types of stress-strain curves, namely strain softening and strain softening followed by strain hardening, are investigated. The characteristic of the stress-strain curve is found to be crucial for the patterning of shear bands. While the calculations with a stress-strain curve with solely softening yield only one single shear band, a flock of shear bands can be obtained with a stress-strain curve with softening followed by hardening. Benefited from a characteristic length provided by a Cosserat elastoplastic constitutive equation, the dependence of calculations on the mesh size is avoided.
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References
1.
Aifantis, E. C.(1984). “On the microstructural origin of certain inelastic models.”J. Engrg. Mat. Technol., 106, 326–334.
2.
Bardet, J. P., and Proubet, J.(1992). “A numerical investigation of the structure of persistent shear bands.”Géotechnique, 41, 599–613.
3.
Bathe, K. J. (1982). Finite element procedures in engineering analysis. Prentice-Hall, Inc., Englewood Cliffs, N.J.
4.
Bazant, Z. P. (1982). “Crack band model for fracture of geomaterials.”Proc., 4th Int. Conf. in Numer. Methods in Geomech., Z. Eisenstein, ed., Vol. 3, Edmonton, Canada, 1137–1152.
5.
Bazant, Z. P., and Chang, T. P.(1987). “Nonlocal finite element analysis of strain softening solids.”J. Engrg. Mech., ASCE, 113, 89–105.
6.
Bazant, Z. P., and Lin, F. B.(1988). “Nonlocal yield limit degradation.”Int. J. Numer. Methods in Engrg., 26, 1805–1823.
7.
Becker, M., and Lippmann, H.(1977). “Plane plastic flow of granular model material, experimental set-up and results.”Arch. Mech., Warszawa, Poland, 29, 829–846.
8.
Belytschko, T., Chiang, H., and Plaskacz, E.(1994). “High resolution of two-dimensional shear band computations: imperfections and mesh dependence.”Comp. Methods in Appl. Mech. Engrg., 119, 1–15.
9.
Benallal, A., Billardon, R., and Geymonat, G. (1987). “Localisation phenomena at the boundaries and interfaces of solids.”Proc., 3rd Int. Conf. on Constitutive Laws for Engrg. Mat. Theory and Applications, C. S. Desai, E. Krempl, P. D. Kiousis, and T. Kundu, eds., Tucson, Arizona, 387–390.
10.
Brinkgreve, R. B. J. (1994). “Geomaterial models and numerical analysis of softening,”PhD dissertation, Delft Univ., Delft, The Netherlands.
11.
Cosserat, E., and Cosserat, F. (1896). “Sur la theorie de l'elasticite.”Ann. Toulouse, 10, 1–116 (in French).
12.
de Borst, R. (1990). “Simulation of localisation using Cosserat theory.”Proc., 2nd Int. Conf. on Comp. Aided Des. of Concrete Struct., N. Bicanic and H. A. Mang, eds., Pineridge Press, Swansea, Wales, U.K., 931–944.
13.
de Borst, R.(1991). “Simulation of strain localisation: a reappraisal of the Cosserat continuum.”Eng. Comp., 8, 317–332.
14.
de Borst, R., Mühlhaus, H. B., Pamin, J., and Sluys, L. Y. (1992). “Computational modelling of localization of deformation.”Proc., 3rd Int. Conf. Comp. Plasticity, Pineridge Press, Swansea, Wales, U.K., 483–508.
15.
Desrues, J. (1984). “La localisation de la deformation dans les materiaux granulaire,”PhD dissertation, Univ. Grenoble, Grenoble (in French).
16.
Dietsche, A. (1993). “Lokale effekte in linear-elastischen und elasto-plastischen Cosserat-Continua,”PhD dissertation, Univ. Karlsruhe, Karlsruhe, Germany (in German).
17.
Drescher, A., and Vardoulakis, I. (1982). “Geometric softening in triaxial tests on granular material.”Géotechnique, London, England, 32, 291–303.
18.
Eringen, A. C., and Suhubi, S.(1964). “Non-linear theory of microelastic solids.”Int. J. Engrg. Sci., 2, 189–204.
19.
Fukushima, S., and Tatsuoka, F.(1984). “Strength and deformation characteristics of saturated sand at extremely low pressures.”Solids and Found., 24, 30–48.
20.
Gudehus, G.(1986). “Einige Beitrage der Bodenmechanik zur Entstehung und Auswirkung von Diskontinitäten.”Felsbau, 4, 190–195.
21.
Gudehus, G., and Tejchman, J. (1991). “Some mechanisms of a granular mass in a silo—model tests and a numerical Cosserat approach.”Advances in continuum mechanics, Springer-Verlag, New York, N.Y., 178–194.
22.
Gudehus, G. (1994). “Localisation in granular bodies—position and objectives.”Localisation and bifurcation theory for soils, R. Chambon, J. Desrues, and I. Vardoulakis, eds., A. A. Balkema, Rotterdam, The Netherlands, 1–15.
23.
Günther, W. (1958). “Zur statik und kinematik des Cosserat-kontinuums.”Abh. Braunschweigische Wiss., 10, 195–213 (in German).
24.
Han, C., and Vardoulakis, I.(1991). “Plane-strain compression experiments on water saturated fine-grained sand.” Géotechnique, London, England, 41, 49–78.
25.
Joseph, D. D., and Saut, J. C. (1990). “Short-wave instabilities and ill-posed initial value problems.”Theoretical Comp. Fluid Dyn., 1, 191–227.
26.
Kanatani, K.(1979). “A micropolar continuum theory for granular materials.”Int. J. Engrg. Sci., 17, 419–432.
27.
Leroy, Y., and Ortiz, H.(1989). “Finite element analysis of strain localization in frictional materials.”Int. J. Numer. Anal. Methods in Geomech., 13, 53–74.
28.
Loret, B., and Prevost, J. H.(1991). “Dynamic strain localization in fluid-saturated porous media.”J. Engrg. Mech., ASCE, 117, 907–922.
29.
Mandl, G. (1988). Mechanics of tectonic faulting. Elsevier, Amsterdam, The Netherlands.
30.
Mindlin, R. D.(1964). “Microstructure in linear elasticity.”Arch. Rational Mech. Anal., 16, 51–78.
31.
Molenkamp, F.(1985). “Comparison of frictional material models with respect to shear band initiation.” Géotechnique, London, England, 35, 127–143.
32.
Mühlhaus, H. B. (1987). “Berücksichtigung von Inhomogenitäten im Gebirge im Rahmen einer Kontinuumstheorie.”Habilitation, Univ. Karlsruhe, Karlsruhe, Germany (in German).
33.
Mühlhaus, H. B., and Vardoulakis, I.(1987). “The thickness of shear bands in granular materials.” Géotechnique, London, England, 37, 271–283.
34.
Mühlhaus, H. B.(1989). “Application of Cosserat theory in numerical solutions of limit load problems.”Ing. Arch., 59, 124–137.
35.
Mühlhaus, H. B. (1990). “Continuum models for layered and blocky rock.”Comprehensive rock engineering, J. A. Hudson and C. Fairhurst, eds., Pergamon Press, Inc., Tarrytown, N.Y., 209–231.
36.
Muir Wood, D., and Stone, K. J. (1994). “Some observations of zones of localisation in model tests on dry sand.”Localisation and bifurcation theory for soils, R. Chambon, J. Desrues, and I. Vardoulakis, eds., A. A. Balkema, Rotterdam, The Netherlands, 155–165.
37.
Nadai, A. (1950). Theory of flow and fracture of solids. McGraw-Hill Book Co., Inc., New York, N.Y.
38.
Nagtegaal, J. C., Parks, D. M., and Rice, J. R.(1974). “On numerically accurate finite element solutions in the fully plastic range.”Comp. Methods in Appl. Mech. Engrg., 4, 153–177.
39.
Oda, M., Konishi, J., and Nemat-Nasser, S.(1982). “Experimental micromechanical evaluation of strength of granular materials, effects of particle rolling.”Mech. Mat., 1, 269–283.
40.
Oda, M. (1993). “Micro-fabric and couple stress in shear bands of granular materials.”Powders and grains, C. Thornton, ed., A. A. Balkema, Rotterdam, The Netherlands, 161–167.
41.
Ortiz, M., and Simo, I. C.(1986). “An analysis of a new class of integration algorithms for elastoplastic constitutive relation.”Int. J. Numer. Methods in Engrg., 23, 353–366.
42.
Palmer, A. C., and Rice, J. R. (1972). “The growth of slip surfaces in the progressive failure of overconsolidated clay.”Proc., Royal Soc., London, England, 527–548.
43.
Rudnicki, J. W., and Rice, J. R.(1975). “Conditions for the localization of deformation in pressure-sensitive dilatant solid.”J. Mech. Phys. Solids, 23, 371–394.
44.
Sandler, I. S. (1984). “Strain softening for static and dynamic problems.”Constitutive Equations—Macro and Computational Aspects, K. J. William, ed., ASCE, N.Y., 217–231.
45.
Schaeffer, D. G.(1990). “Instability and ill-posedness in the deformation of granular materials.”Int. J. Numer. Anal. Methods in Geomech., 14, 253–278.
46.
Schäfer, H. (1962). “Versuch einer Elastizitätstheorie des zweidimensionalen ebenen Cosserat-Kontinuums.”Miszellaneen der Angewandten Mechanik, Festschrift Tolmien, W., Akademie-Verlag, Berlin, Germany, 277–292 (in German).
47.
Sluys, L. J. (1992). “Wave propagation, localisation and dispersion in softening solids,”PhD dissertation, Univ. Delft, Delft, The Netherlands.
48.
Tatsuoka, F., Nakamura, S., Huang, C. C., and Tani, K.(1990). “Strength anisotropy and shear band inclination in plane strain tests of sand.”Soils and Found., 30, 35–54.
49.
Tejchman, J. (1989). “Scherzonenbildung und Verspannungseffekte in Granulaten unter Berücksichtigung von Korndrehungen,”dissertation, Univ. Karlsruhe, Karlsruhe, Germany (in German).
50.
Tejchman, A., and Tejchman, J. (1990). “Scale effect in pile model tests.”Archiwum Hydrotechniki, Warszawa, Poland, 3–4, 97–126 (in English).
51.
Tejchman, J., and Wu, W.(1993). “Numerical study on patterning of shear bands in a Cosserat continuum.”Acta Mechanica, 99, 61–74.
52.
Tejchman, J. (1994a). “Numerical study on localised deformation in a Cosserat continuum.”Localisation and bifurcation theory for soils, R. Chambon, J. Desrues, and I. Vardoulakis, eds., Rotterdam, Balkema, 257–274.
53.
Tejchman, J. (1994b). “Numerical study on localised deformation in a Cosserat continuum.”Proc., 8th Int. Conf. on Comp. Methods and Adv. in Geomech., H. J. Siriwardane and M. M. Zaman, eds., Balkema, Rotterdam, 695–700.
54.
Tejchman, J., and Wu, W.(1995). “Experimental and numerical study of sand-steel interfaces.”Int. J. Numer. Anal. Methods in Geomech., 18(8), 513–537.
55.
Tejchman, J. (1995). “Silo quake—experiments and a polar hypoplastic model.”Proc., 3rd Eur. Symp. on Storage and Flow of Particulate Solids, Nürnberg Messe GmbH, Nürnberg, 151–163.
56.
Tejchman, J. (1996). “Modelling of shear localisation and autogeneous dynamic effects in granular bodies.”Habilitation, Univ. Karlsruhe, Karlsruhe, Germany.
57.
Tejchman, J., and Bauer, E.(1996). “Numerical simulation of shear band formation with a polar hypoplastic model.”Comp. and Geotechnics, 19(3), 221–244.
58.
Thornton, C., and Sun, G. (1993). “Axisymmetric compression of 3D polydisperse systems of spheres.”Powders and grains, C. Thornton, ed., A. A. Balkema, Rotterdam, The Netherlands, 129–134.
59.
Uesugi, M. (1987). “Friction between dry sand and construction,”PhD dissertation, Tokyo Inst. of Technol., Tokyo, Japan.
60.
Unterreiner, P., Vardoulakis, I., Boulon, M., and Sulem, J. (1994). “Essential features of a Cosserat continuum in interfacial localisation.”Localisation and bifurcation theory for soils, R. Chambon, J. Desrues, and I. Vardoulakis, eds., A. A. Balkema, Rotterdam, The Netherlands, 141–155.
61.
Vardoulakis, I.(1980). “Shear band inclination and shear modulus of sand in biaxial tests.”Int. J. Numer. Anal. Methods in Geomech., 4, 103–119.
62.
Wu, W. (1990). “A unified numerical integration formula for the perfectly plastic von Mises model.”Int. J. Numer. Methods in Engrg., 30, 491–504.
63.
Wu, W., and Sikora, Z.(1991). “Localized bifurcation in hypoplasticity.”Int. J. Engrg. Sci., 20, 195–201.
64.
Wu, W., and Kolymbas, D.(1991). “On some issues in triaxial extension tests.”ASTM Geotech. Testing J., 14, 276–287.
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Published In
Journal of Engineering Mechanics
Volume 123 • Issue 2 • February 1997
Pages: 123 - 133
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Copyright © 1997 American Society of Civil Engineers.
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Published online: Feb 1, 1997
Published in print: Feb 1997
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