Abstract
Strain localization, usually manifesting as shear bands, is frequently observed in geomaterials and is of the essential reason inducing the failure of geostructures. Anisotropic characteristics of soils has an important effect on the shear band behavior. This paper is devoted to study the effect of the fabric anisotropy on the initiation and evolution of the shear bands. In particular, the anisotropy is introduced to the strength parameter of the yield criterion by incorporating the material principal direction and the joint invariant of the stress tensor and the microstructure tensor. Furtherly, an elasto-plastic constitutive model considering the fabric anisotropy is established in the micropolar theory framework, and is then applied to simulate the shear bands in transversely geomaterials via three numerical examples, including the plane strain compression test, slope stability and the shallow foundation problems. Moreover, the mesh independency of the proposed model is discussed. Results show that the bifurcation, the shear bands pattern, and the bearing capacity highly depend on the material principal orientation and the anisotropic degree. Comparison with existing study indicates that the proposed model has a good performance in simulating the typical pre and post strain localization behaviors of transversely isotropic geomaterials.
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02 June 2021
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References
Alsaleh MI, Voyiadjis GZ, Alshibli KA (2010) Modelling strain localization in granular materials using micropolar theory: Mathematical formulations. International Journal for Numerical and Analytical Methods in Geomechanics 30(15):1501–1524, DOI: https://doi.org/10.1002/nag.533
Alshibli KA, Alsaleh MI, Voyiadjis GZ (2010) Modelling strain localization in granular materials using micropolar theory: Numerical implementation and verification. International Journal for Numerical & Analytical Methods in Geomechanics 30(15):1525–1544, DOI:https://doi.org/10.1002/nag.534
Areias P, Belytschko T (2006) Two-scale shear band evolution by local partition of unity. International Journal for Numerical Methods in Engineering 66:878–910, DOI: https://doi.org/10.1002/nme.1589
Areias P, Msekh MA, Rabczuk T (2016) Damage and fracture algorithm using the screened poisson equation and local remeshing. Engineering Fracture Mechanics 158:116–143, DOI: https://doi.org/10.1016/j.engfracmech.2015.10.042
Areias P, Rabczuk T (2017) Steiner-point free edge cutting of tetrahedral meshes with applications in fracture. Finite Elements in Analysis & Design 132:27–41, DOI: https://doi.org/10.1016/jfinel.2017.05.001
Azami A, Pietruszczak S, Guo P (2010) Bearing capacity of shallow foundations in transversely isotropic granular media. International Journal for Numerical and Analytical Methods in Geomechanics 34(8):771–793, DOI: https://doi.org/10.1002/nag.827
Bardet JP (1990) A comprehensive review of strain localization in elastoplastic soils. Computers & Geotechnics 10(3):163–188, DOI:https://doi.org/10.1016/0266-352x(90)90034-s
Borst RD (1993) A generalisation of J2-flow theory for polar continua. Computer Methods in Applied Mechanics and Engineering 103(3): 347–362, DOI: https://doi.org/10.1016/0045-7825(93)90127-j
Borst RD, Sluys LJ, Mühlhaus HB, Pamin (1993) Fundamental issues in finite element analyses of localization of deformation. Engineering Computations 10(2):99–121, DOI: https://doi.org/10.1016/0148-9062(93)91504-c
Chang JF, Wang W, Wen L, Yuan W (2019) Localization and bifurcation analysis of granular materials in micropolar continuum. International Journal of Geomechanics 19(7):04019064, DOI: https://doi.org/10.1061/(asce)gm.1943-5622.0001433
Cosserat E, Cosserat F (1909) Théorie des corps déformables. A. Hermann et Fils, Paris, France, DOI: https://doi.org/10.1038/081067a0
Dietsche A, Steinmann P, Willam K (1993) Micropolar elastoplasticity and its role in localization. International Journal of Plasticity 9(7): 813–831, DOI: https://doi.org/10.1016/0749-6419(93)90053-s
Gao ZW, Zhao JD, Yao YP (2010) A generalized anisotropic failure criterion for geomaterials. International Journal of Solids and Structures 47(22):3166–3185, DOI: https://doi.org/10.1016/j.ijsolstr.2010.07.016
Hill R (1958) A general theory of uniqueness and stability in elasto-plastic solids. Journal of the Mechanics and Physics of Solids 6: 236–249, DOI: https://doi.org/10.1016/j.ijsolstr.2010.07.016
Huang WX, Hjiaj M, Sloan SW (2005) Bifurcation analysis for shear localization in non-polar and micro-polar hypoplastic continua. Journal of Engineering Mathematics 52(1):167–184, DOI: https://doi.org/10.1007/bf02694036
Iordache MM, Willam K (1998) Localized failure analysis in elastoplastic cosserat continua. Computer Methods in Applied Mechanics & Engineering 151(3–4):559–586, DOI: https://doi.org/10.1016/s0045-7825(97)00166-7
Jin YH, Sun Y, Qian YL (2008) Analysis of displacement of transversely isotropic foundation under level strip uniformly distributed load. Rock and Soil Mechanics 26(sup 1):163–167
Khoei AR, Yadegari S, Biabanaki SOR (2010) 3D finite element modeling of shear band localization via the micro-polar Cosserat continuum theory. Computational Materials Science 49(4):720–733, DOI: https://doi.org/10.1016/j.commatsci.2010.06.015
Liu Y, Zhang D, Wang XX, Yu PQ, Hu W (2019) Anisotropic strength of granular material considering fabric evolution. Latin American Journal of Solids and Structures 16(3), DOI: https://doi.org/10.1590/1679-78255475
Lu XL, Huang MS, Qian JG (2014) Prediction of plane strain undrained diffuse instability and strain localization with non-coaxial plasticity. Soils & Foundations 54(6):1070–1080, DOI: https://doi.org/10.1016/j.sandf.2014.11.003
Matsuoka H, Nakai T (1974) Stress-deformation and strength characteristics of soil under three different principal stresses. Proceedings of the Japan Society of Civil Engineers 232:59–70, DOI: https://doi.org/10.2208/jscej1969.1974.232_59
Mihalache C, Buscarnera G (2014) Mathematical identification of diffuse and localized instabilities in fluid-saturated sands. International Journal for Numerical and Analytical Methods in Geomechanics 38(2):111–141, DOI: https://doi.org/10.1002/nag.2196
Mühlhaus HB (1986) Scherfugenanalyse bei granularem material im rahmen der Cosserat-theorie. Ingenieur-Archiv 56(5):389–399, DOI:https://doi.org/10.1007/bf02570619
Mühlhaus HB, Vardoulakis I (1987) The thickness of shear bands in granular materials. Geotechnique 37:271–283, DOI: https://doi.org/10.1680/geot.1987.37.3.271
Nicot F, Darve F (2011) Diffuse and localized failure modes: Two competing mechanisms. International Journal for Numerical and Analytical Methods in Geomechanics 35(5):586–601, DOI: https://doi.org/10.1002/nag.912
Oda M (1993) Inherent and induced anisotropy in plasticity theory of granular soils. Mechanics of Materials 16(1–2):35–45, DOI: https://doi.org/10.1016/0167-6636(93)90025-m
Pietruszczak S, Mroz Z (2000) Formulation of anisotropic failure criteria incorporating a microstructure tensor. Computers and Geotechnics 26(2):105–112, DOI: https://doi.org/10.1016/s0266-352x(99)00034-8
Pietruszczak S, Mroz Z (2001) On failure criteria for anisotropic cohesive-frictional materials. International Journal for Numerical and Analytical Methods in Geomechanics 25(5):509–524, DOI:https://doi.org/10.1002/nag.2366
Rabczuk T, Areias PMA (2006) A new approach for modelling slip lines in geological materials with cohesive models. International Journal for Numerical and Analytical Methods in Geomechanics 30:1159–1172, DOI: https://doi.org/10.1002/nag.522
Rabczuk T, Belytschko T (2004) Cracking particles: A simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering 61(13):2316–2343, DOI: https://doi.org/10.1002/nme.1151
Rabczuk T, Belytschko T (2007) A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering 196(29–30):2777–2799, DOI: https://doi.org/10.1016/j.cma.2006.06.020
Rice JR, Rudnicki JW (1980) A note on some features of theory of the localization of deformation. International Journal of Solids and Structure 16:507–605, DOI: https://doi.org/10.1016/0020-7683(80)90019-0
Rudnicki JW, Rice JR (1975) Conditions for the localization of deformation in pressure-sensitive dilatant materials. Journal of the Mechanics & Physics of Solids 23(6):371–394, DOI: https://doi.org/10.1016/0022-5096(75)90001-0
Sharbati E, Naghdabadi R (2007) Computational aspects of the Cosserat finite element analysis of localization phenomena. Computational Materials Science 38(2):303–315, DOI: https://doi.org/10.1016/j.commatsci.2006.03.003
Song J H, Areias P, Belytschko T (2010) A method for dynamic crack and shear band propagation with phantom nodes. International Journal for Numerical Methods in Engineering 67(6):868–893, DOI: https://doi.org/10.1002/nme.1652
Sun WC (2013) A unified method to predict diffuse and localized instabilities in sands. Geomechanics & Geoengineering 8(2):65–75, DOI: https://doi.org/10.1080/17486025.2012.695403
Tabarraei A, Song J H, Waisman H (2013) A two-scale strong discontinuity approach for evolution of shear bands under dynamic impact loads. International Journal for Multiscale Computational Engineering 11(6):543–563, DOI: https://doi.org/10.1615/intjmultcompeng.2013005506
Tang HX, Dong Y, Wang T, Dong YF (2018) Simulation of strain localization with discrete element-cosserat continuum finite element two scale method for granular materials. Journal of the Mechanics and Physics of Solids 122:450–471, DOI: https://doi.org/10.1016/j.jmps.2018.09.029
Tang HX, Wei WC, Liu F, Chen GQ (2020) Elastoplastic cosserat continuum model considering strength anisotropy and its application to the analysis of slope stability. Computers and Geotechnics 117: 103235, DOI: https://doi.org/10.1016/j.compgeo.2019.103235
Tejchman J, Bauerh E (1996) Numerical simulation of shear band formation with a hypoplastic constitutive model. Computers and Geotechnics 18(1):71–84, DOI: https://doi.org/10.1016/0266-352X(95)00018-6
Tejchman J, Wu W (1993) Numerical study on patterning of shear bands in a Cosserat continuum. Acta Mechanica 99(1–4):61–74, DOI:https://doi.org/10.1007/bf01177235
Tejchman J, Wu W (2007) Modeling of textural anisotropy in granular materials with stochastic micro-polar hypoplasticity. International Journal of Non-Linear Mechanics 42(6):882–894, DOI: https://doi.org/10.1016/j.ijnonlinmec.2007.03.015
Vu-Bac N, Lahmer T, Zhuang X, Nguyen-Thoi T, Rabczuk T (2016) A software framework for probabilistic sensitivity analysis for computationally expensive models. Advances in Engineering Software 100:19–31, DOI: https://doi.org/10.1016/j.advengsoft.2016.06.005
Wan R, Pinheiro M, Daouadji A, Jrad M, Darve F (2013) Diffuse instabilities with transition to localization in loose granular materials. International Journal for Numerical & Analytical Methods in Geomechanics 37(10), DOI: https://doi.org/10.1002/nag.2085
Yang X, Liu HL, Yang G (2012) Formulation of cross-anisotropic failure criterion for granular material. International Journal of Geomechanics 12(2):182–188, DOI: https://doi.org/10.1061/(asce)gm.1943-5622.0000309
Zhao J, Guo N (2015) The interplay between anisotropy and strain localization in granular soils: A multiscale insight. Geotechnique 65(8):642–656, DOI: https://doi.org/10.1680/geot.14.p.184
Zhong SY, Xu WY, Ling DS (2011) Influence of the parameters in the Pietruszczak-Mroz anisotropic failure criterion. International Journal of Rock Mechanics &Mining Sciences 48(6):1034–1037, DOI:https://doi.org/10.1016/j.ijrmms.2011.06.002
Zhu HX, Nguyen HNG, Nicot F, Darve F (2016) On a common critical state in localized and diffuse failure modes. Journal of the Mechanics and Physics of Solids 95:112–131, DOI: https://doi.org/10.1016/j.jmps.2016.05.026
Acknowledgments
This work was supported by National Natural Science Foundation of China (Grant numbers 11902208, U1967208, and 51979170), the State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures (Grant No. ZZ2020-22), and the Natural Science Foundation of Hebei Province (Grant No. A2020210030). The authors acknowledge the computational support in software and hardware provided by the Hebei Province technical innovation center of safe and effective mining of metal mines at Shijiazhuang Tiedao University.
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Chang, J., Wang, W., Niu, Q. et al. Effect of Fabric Anisotropy on Bifurcation and Shear Band Evolution in Granular Geomaterials. KSCE J Civ Eng 25, 2893–2910 (2021). https://doi.org/10.1007/s12205-021-2164-5
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DOI: https://doi.org/10.1007/s12205-021-2164-5