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Micropolar hypoplasticity for persistent shear band in heterogeneous granular materials. (English) Zbl 1423.74204

Summary: Persistent shear bands in heterogeneous materials develop progressively, rather than instantaneously. For a meaningful capture of this deformation pattern, the band must develop naturally and freely up to the peak load and well into the softening regime. We use a new micropolar hypoplastic framework to capture the development and propagation of a persistent shear band in a rectangular specimen of silica-concrete sand with spatially varying density. The constitutive framework includes a characteristic length as a regularization parameter, as well as a couple stress representing the angular momentum generated by particle spins. We use computed tomography (CT) imaging and digital image processing to quantify the spatial density variation of the sand, and a void ratio-dependent constitutive model to capture the effect of variable density. Results of the numerical simulations demonstrate the capability of the proposed micropolar hypoplastic framework to track the development and propagation of a persistent shear band in a heterogeneous sand up to the peak load and well into the softening regime.

MSC:

74E20 Granularity
74S05 Finite element methods applied to problems in solid mechanics
74Cxx Plastic materials, materials of stress-rate and internal-variable type
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[1] Alikarami, R.; Andó, E.; Gkiousas-Kapnisis, M.; Torabi, A.; Viggiani, G., Strain localisation and grain breakage in sand under shearing at high mean stress: insights from in situ X-ray tomography, Acta Geotech., 10, 15-30 (2015)
[2] Andrade, J. E.; Borja, R. I., Capturing strain localization in dense sands with random density, Internat. J. Numer. Methods Engrg., 67, 1531-1564 (2006) · Zbl 1113.74012
[3] Borja, R. I.; Song, X.; Rechenmacher, A.; Abedi, S.; Wu, W., Shear band in sand with spatially varying density, J. Mech. Phys. Solids, 61, 219-234 (2013)
[4] Borja, R. I.; Andrade, J. E., Critical state plasticity. Part VI: Meso-scale finite element simulation of strain localization in discrete granular materials, Comput. Methods Appl. Mech. Engrg., 195, 5115-5140 (2006) · Zbl 1193.74024
[5] Borja, R. I.; Song, X.; Wu, W., Critical state plasticity, Part VII: Triggering a shear band in variably saturated porous media, Comput. Methods Appl. Mech. Engrg., 261-262, 66-82 (2013) · Zbl 1286.74027
[6] Song, X.; Borja, R. I., Mathematical framework for unsaturated flow in the finite deformation range, Internat. J. Numer. Methods Engrg., 37, 658-682 (2014) · Zbl 1352.76115
[8] Tong, Z.; Fu, P.; Zhou, S.; Dafalias, Y. F., Experimental investigation of shear strength of sands with inherent fabric anisotropy, Acta Geotech., 2, 257-275 (2014)
[9] Zhuang, L.; Nakata, Y.; Kim, U.; Kim, D., Influence of relative density, particle shape, and stress path on the plane strain compression behavior of granular materials, Acta Geotech., 2, 241-255 (2014)
[10] Rudnicki, J. W.; Rice, J. R., Conditions for the localization of deformation in pressure sensitive dilatant materials, J. Mech. Phys. Solids, 23, 371-394 (1975)
[11] Borja, R. I., Plasticity Modeling and Computation (2013), Springer-Verlag: Springer-Verlag Berlin-Heidelberg · Zbl 1279.74003
[12] Mihalache, C.; Buscarnera, G., Mathematical identification of diffuse and localized instabilities in fluid-saturated sands, Int. J. Numer. Anal. Methods Geomech., 38, 111-141 (2014)
[13] Borja, R. I., A finite element model for strain localization analysis of strongly discontinuous fields based on standard Galerkin approximations, Comput. Methods Appl. Mech. Engrg., 190, 1529-1549 (2000) · Zbl 1003.74074
[14] Borja, R. I.; Regueiro, R. A., Strain localization of frictional materials exhibiting displacement jumps, Comput. Methods Appl. Mech. Engrg., 190, 2555-2580 (2001) · Zbl 0997.74009
[15] Linder, C.; Armero, F.; F., Finite elements with embedded strong discontinuities for the modeling of failure in solids, Internat. J. Numer. Methods Engrg., 72, 1391-1433 (2007) · Zbl 1194.74431
[16] Mosler, J.; Meschke, G., 3D modelling of strong discontinuities in elastoplastic solids: fixed and rotating localization formulations, Internat. J. Numer. Methods Engrg., 57, 1553-1576 (2003) · Zbl 1062.74623
[17] Liu, F.; Borja, R. I., A contact algorithm for frictional crack propagation with the extended finite element method, Internat. J. Numer. Methods Engrg., 76, 1489-1512 (2008) · Zbl 1195.74186
[18] Liu, F.; Borja, R. I., Stabilized low-order finite elements for frictional contact with the extended finite element method, Comput. Methods Appl. Mech. Engrg., 199, 2456-2471 (2010) · Zbl 1231.74426
[19] Liu, F.; Borja, R. I., Extended finite element framework for fault rupture dynamics including bulk plasticity, Int. J. Numer. Anal. Methods Geomech., 37, 3087-3111 (2013)
[20] Ida, Y., Cohesive force across the tip of a longitudinal shear crack and Griffith’s specific surface energy, J. Geophys. Res., 77, 3796-3805 (1972)
[21] Palmer, A. C.; Rice, J. R., The growth of slip surfaces in the progressive failure of overconsolidated clay, Proc. R. Soc. Lond. Ser. A, 332, 527-548 (1973) · Zbl 0273.73059
[22] Borja, R. I.; Foster, C. D., Continuum mathematical modeling of slip weakening in geological systems, J. Geophys. Res., 112, B04301 (2007)
[23] Gylland, A. S.; Jostad, H. P.; Nordal, S., Experimental study of strain localization in sensitive clays, Acta Geotech., 2, 227-240 (2014)
[24] Mindlin, R. D.; Eshel, N. N., On first strain-gradient theories in linear elasticity, Int. J. Solids Struct., 4, 109-124 (1968) · Zbl 0166.20601
[25] Germain, P., Cours de Mécanique des Milieux Continus (1973), Tome 1.Théorie générale · Zbl 0254.73001
[26] Cosserat, E.; Cosserat, F., Théorie des Corps Déformables (1909), A. Hermann et Fils · JFM 40.0862.02
[27] Ericksen, J.; Truesdell, C., Exact theory of stress and strain in rods and shells, Arch. Ration. Mech. Anal., 1, 295-323 (1957) · Zbl 0081.39303
[28] Eringen, A., Continuum Physics: Polar and Non-local Field Theories (1976), Academic Press
[29] Eringen, A., Microcontinuum Field Theories (2001), Springer-Verlag · Zbl 0972.76001
[30] Gerolymatou, E., A micromechanically derived anisotropic micropolar constitutive law for granular media: Elasticity, Int. J. Numer. Anal. Methods Geomech., 38, 1761-1775 (2014)
[31] (Kröner, E., Mechanics of Generalized Continua: Proceedings of the IUTAM-Symposium on the Generalized Cosserat Continuum and the Continuum Theory of Dislocations with Applications (1968), Springer-Verlag: Springer-Verlag Freudenstadt and Stuttgart (Germany)) · Zbl 0169.00201
[32] Tordesillas, A.; Pucilowski, S.; Walker, D. M.; Peters, J. F.; Walizer, L. E., Micromechanics of vortices in granular media: connection to shear bands and implications for continuum modelling of failure in geomaterials, Int. J. Numer. Anal. Methods. Geomech., 38, 1247-1275 (2014)
[33] Mühlhaus, H.-B.; Vardoulakis, I., Thickness of shear bands in granular materials, Géotechnique, 37, 271-283 (1987)
[34] Tejchman, J.; Bauer, E., Numerical simulation of shear band formation with a polar hypoplastic constitutive model, Comput. Geotech., 19, 221-244 (1996)
[35] Liang, L.; Saada, A.; Figueroa, J. L.; Cope, C. T., The use of digital image processing in monitoring shear band development, Geotech. Test. J., 20, 324-339 (1997)
[36] Alshibli, K. A.; Sture, S., Shear band formation in plane strain compression, Journal of Geotechnical and Geoenvironmental Engineering, 126, 495-503 (2000)
[37] Coumoulos, D. G., A radiographic study of soils (1968), Cambridge University: Cambridge University Cambridge, U.K., (Ph.D. Dissertation)
[38] Desrues, J.; Lanier, J.; Stutz, P., Localization of the deformation in tests on sand sample, Eng. Fract. Mech., 21, 909-921 (1985)
[39] Desrues, J.; Chambon, R.; Mokni, M.; Mazerolle, F., Void ratio evolution Inside shear bands in triaxial sand specimens studied by computed tomography, Géotechnique, 46, 529-546 (1996)
[40] Alshibli, K. A.; Sture, S.; Costes, N. C.; Frank, M. L.; Lankton, F. R.; Batiste, S. N.; Swanson, R. A., Assessment of localized deformations in sand using X-ray computed tomography, Geotech. Test. J., 23, 274-299 (2000)
[41] Alshibli, K. A.; Sture, S., Sand shear band thickness measurements by digital imaging techniques, J. Comput. Civil Eng., 13, 103-109 (1999)
[42] Rechenmacher, A. L.; Abedi, S.; Chupin, O.; Orlando, A., Characterization of mesoscale instabilities in localized granular shear using digital image correlation, Acta Geotech., 6, 205-217 (2011)
[43] Rechenmacher, A. L., Grain-scale processes governing shear band initiation and evolution in sands, J. Mech. Phys. Solids, 54, 22-45 (2006) · Zbl 1120.74631
[44] Rechenmacher, A. L.; Abedi, S.; Chupin, O., Evolution of force chains in shear bands in sands, Géotechnique, 60, 343-351 (2011)
[45] Chupin, O.; Rechenmacher, A. L.; Abedi, S., Finite strain analysis of nonuniform deformation inside shear bands in sands, Int. J. Numer. Anal. Methods Geomech., 36, 1651-1666 (2012)
[46] Hughes, T. J.R., Generalization of selective integration procedures to anisotropic and nonlinear media, Internat. J. Numer. Methods Engrg., 15, 1413-1418 (1980) · Zbl 0437.73053
[47] Huang, W.; Nübel, K.; Bauer, E., Polar extension of a hypoplastic model for granular materials with shear localization, Mech. Mater., 34, 563-576 (2002)
[48] Fuentes, W.; Triantafyllidis, T.; Lizcano, A., Hypoplastic model for sands with loading surface, Acta Geotech., 7, 177-192 (2012)
[49] Trinh, B.; Hackl, K., Performance of mixed and enhanced finite elements for strain localization in hypoplasticity, Int. J. Numer. Anal. Methods Geomech., 36, 1125-1150 (2012)
[50] Wu, W.; Sikora, Z., Localized bifurcation in hypoplasticity, Internat. J. Engrg. Sci., 29, 195-201 (1991) · Zbl 0762.73017
[51] Tejchman, J.; Wu, W., Numerical simulation of shear band formation with a hypoplastic constitutive model, Comput. Geotech., 18, 71-84 (1996)
[52] Wu, W., Non-linear analysis of shear band formation in sand, Int. J. Numer. Anal. Methods Geomech., 24, 245-263 (2000) · Zbl 0955.74044
[53] Tejchman, J.; Wu, W., FE-calculations of stress distribution under prismatic and conical sandpiles within hypoplasticity, Granular Matter, 10, 399-405 (2008) · Zbl 1258.74147
[54] Wu, W., On high-order hypoplastic models for granular materials, J. Engrg. Math., 56, 23-34 (2006) · Zbl 1103.74019
[55] Fang, C.; Wu, W., On the weak turbulent motions of an isothermal dry granular dense flow with incompressible grains: part II. Complete closure models and numerical simulations, Acta Geotech., 9, 739-752 (2014)
[56] Mašín, D.; Rott, J., Small strain stiffness anisotropy of natural sedimentary clays: review and a model, Acta Geotech., 9, 299-312 (2014)
[57] Hleibieh, J.; Wegener, D.; Herle, I., Numerical simulation of a tunnel surrounded by sand under earthquake using a hypoplastic model, Acta Geotech., 9, 631-640 (2014)
[58] Wu, W.; Kolymbas, D., Numerical testing of the stability criterion for hypoplastic constitutive equations, Mech. Mater., 9, 245-253 (1990)
[59] Tejchman, J.; Wu, W., Non-coaxiality and stress-dilatancy rule in granular materials: FE investigation within micro-polar hypoplasticity, Int. J. Numer. Anal. Methods Geomech., 117-142 (2009) · Zbl 1272.74113
[60] Tejchman, J.; Wu, W., Dynamic patterning of shear bands in Cosserat continuum, J. Eng. Mech., 123, 123-133 (1997)
[61] Lin, J., Linking DEM with micropolar continuum (2013), Universität für Bodenkultur: Universität für Bodenkultur Vienna, Austria, (Ph.D. Dissertation)
[62] Wu, W.; Bauer, E., A simple hypoplastic constitutive model for sand, Int. J. Numer. Anal. Methods Geomech., 18, 833-862 (1994) · Zbl 0818.73057
[63] Wu, W., Hypoplastizität als mathematisches Modell zum mechanischen Verhalten granularer Stoffe (1992), Karlsruhe University, (Ph.D. Dissertation)
[64] Wu, W.; Bauer, E.; Kolymbas, D., Hypoplastic constitutive model with critical state for granular materials, Mech. Mater., 23, 45-69 (1996)
[66] Buscarnera, G., Mathematical identification of diffuse and localized instabilities in fluid-saturated sands, Int. J. Numer. Anal. Methods Geomech., 38, 111-141 (2014)
[67] Wan, R.; Pinheiro, M.; Daouadji, A.; Jrad, M.; Darve, F., Diffuse instabilities with transition to localization in loose granular materials, Int. J. Numer. Anal. Methods Geomech., 37, 1292-1311 (2013)
[68] Wang, G. S.; Kong, L. W.; Wei, C. F., An approach to determining the thicknesses of shear bands with an echelon-crack structure, Int. J. Numer. Anal. Methods Geomech., 37, 618-640 (2013)
[69] Guo, P., Critical length of force chains and shear band thickness in dense granular materials, Acta Geotech., 7, 41-55 (2012)
[70] Nguyen, N.-S.; Magoariec, H.; Cambou, B., Local stress analysis in granular materials at a mesoscale, Int. J. Numer. Anal. Methods Geomech., 36, 1609-1635 (2012)
[71] Tejchman, J.; Wu, W., Numerical study on patterning of shear bands in a Cosserat continuum, Acta Mech., 99, 61-74 (1993) · Zbl 0784.73029
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