3D multiscale modeling of strain localization in granular media

Abstract A hierarchical multiscale modeling approach is used to investigate three-dimensional (3D) strain localization in granular media. Central to the multiscale approach is a hierarchical coupling of finite element method (FEM) and discrete element method (DEM), wherein the FEM is employed to treat a boundary value problem of a granular material and the required constitutive relation for FEM is derived directly from the DEM solution of a granular assembly embedded at each of the FEM Gauss integration points as the representative volume element (RVE). While being effective in reproducing the complex mechanical responses of granular media, the hierarchical approach helps to bypass the necessity of phenomenological constitutive models commonly needed by conventional FEM studies and meanwhile offers a viable way to link the macroscopic observations with their underlying microscopic mechanisms. To model the phenomenon of strain localization, key issues pertaining to the selection of proper RVE packings are first discussed. The multiscale approach is then applied to simulate the strain localization problem in a cubical specimen and a cylindrical specimen subjected to either conventional triaxial compression (CTC) or conventional triaxial extension (CTE) loading, which is further compared to a case under plane-strain biaxial compression (PBC) loading condition. Different failure patterns, including localized, bulging and diffuse failure modes, are observed and analyzed. Amongst all testing conditions, the PBC condition is found most favorable for the formation of localized failure. The CTC test on the cubical specimen leads to a 3D octopus-shaped localization zone, whereas the cylindrical specimen under CTC shows seemingly bulging failure from the outlook but rather more complex failure patterns within the specimen. The CTE test on a uniform specimen normally ends in a diffuse failure. Different micro mechanisms and controlling factors underlying the various interesting observations are examined and discussed.

[1]  N. P. Kruyt,et al.  Statistical theories for the elastic moduli of two-dimensional assemblies of granular materials , 1998 .

[2]  Gaël Combe,et al.  Experimental micromechanical analysis of a 2D granular material: relation between structure evolution and loading path , 1997 .

[3]  Lutz Gross,et al.  Interface modeling in incompressible media using level sets in Escript , 2007 .

[4]  Gioacchino Viggiani,et al.  Discrete and continuum analysis of localised deformation in sand using X-ray mu CT and volumetric digital image correlation , 2010 .

[5]  Ning Guo,et al.  Unique critical state characteristics in granular media considering fabric anisotropy , 2013 .

[6]  J. Rice,et al.  CONDITIONS FOR THE LOCALIZATION OF DEFORMATION IN PRESSURE-SENSITIVE DILATANT MATERIALS , 1975 .

[7]  Gioacchino Viggiani,et al.  Multiscale modeling and characterization of granular matter: From grain kinematics to continuum mechanics , 2011 .

[8]  Kenji Ishihara,et al.  Effects of principal stress direction and intermediate principal stress on undrained shear behavior of sand. , 1998 .

[9]  R. Chambon,et al.  Void ratio evolution inside shear bands in triaxial sand specimens studied by computed tomography , 1996 .

[10]  M. Goldscheider,et al.  Formation of shear bands in sand bodies as a bifurcation problem , 1978 .

[11]  Jidong Zhao,et al.  A Hierarchical Model for Cross-scale Simulation of Granular Media , 2013 .

[12]  Mario A. Storti,et al.  MPI for Python: Performance improvements and MPI-2 extensions , 2008, J. Parallel Distributed Comput..

[13]  Takashi Kyoya,et al.  Global–local analysis of granular media in quasi-static equilibrium , 2003 .

[14]  Gaël Combe,et al.  FEM × DEM modelling of cohesive granular materials: Numerical homogenisation and multi-scale simulations , 2014, Acta Geophysica.

[15]  Z. Hashin.  Analysis of Composite Materials—A Survey , 1983 .

[16]  D. Bigoni,et al.  On strain localization analysis of elastoplastic materials at finite strains , 1993 .

[17]  W. Drugan,et al.  A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites , 1996 .

[18]  Stein Sture,et al.  Strain Localization in Sand: Plane Strain versus Triaxial Compression , 2003 .

[19]  Christophe Geuzaine,et al.  Gmsh: A 3‐D finite element mesh generator with built‐in pre‐ and post‐processing facilities , 2009 .

[20]  N. Guo.  Multiscale characterization of the shear behavior of granular media , 2014 .

[21]  Jidong Zhao,et al.  The interplay between anisotropyand strain localisation in granular soils: a multiscale insight , 2015 .

[22]  M. Satake,et al.  Fabric tensor in granular materials , 1982 .

[23]  François Kneib,et al.  Using And Programming , 2015 .

[24]  F. Oka,et al.  STUDY OF STRAIN LOCALIZATION AND MICROSTRUCTURAL CHANGES IN PARTIALLY SATURATED SAND DURING TRIAXIAL TESTS USING MICROFOCUS X-RAY CT , 2011 .

[25]  Bernard Schrefler,et al.  A mixed finite element procedure of gradient Cosserat continuum for second-order computational homogenisation of granular materials , 2014 .

[26]  Guilhem Mollon,et al.  Generating realistic 3D sand particles using Fourier descriptors , 2013 .

[27]  Jidong Zhao,et al.  The signature of shear-induced anisotropy in granular media , 2013 .

[28]  François Nicot,et al.  Bifurcation and second-order work in geomaterials , 2007 .

[29]  Guilhem Mollon,et al.  Fourier–Voronoi-based generation of realistic samples for discrete modelling of granular materials , 2012, Granular Matter.

[30]  Ning Guo,et al.  A coupled FEM/DEM approach for hierarchical multiscale modelling of granular media , 2014 .

[31]  Ning Guo,et al.  Multiscale insights into classical geomechanics problems , 2016 .

[32]  S. Sloan,et al.  Analysis of the failure mode and softening behaviour of sands in true triaxial tests , 2007 .

[33]  Wei Wu,et al.  Non‐coaxiality and stress–dilatancy rule in granular materials: FE investigation within micro‐polar hypoplasticity , 2009 .

[34]  D. V. Griffiths,et al.  Three-dimensional slope stability analysis by elasto-plastic finite elements , 2007 .

[35]  Hb Seed,et al.  Plane-Strain Testing of Sand , 1981 .

[36]  Hajime Matsuoka,et al.  Deformation and Failure of Granular Materials , 1988 .

[37]  José E. Andrade,et al.  Capturing strain localization in dense sands with random density , 2006 .

[38]  Mario A. Storti,et al.  MPI for Python , 2005, J. Parallel Distributed Comput..

[39]  Christian Miehe,et al.  Homogenization and two‐scale simulations of granular materials for different microstructural constraints , 2010 .

[40]  C. Thornton.  NUMERICAL SIMULATIONS OF DEVIATORIC SHEAR DEFORMATION OF GRANULAR MEDIA , 2000 .

[41]  Zhiwei Gao,et al.  Strain localization and fabric evolution in sand , 2013 .

[42]  S. Hall,et al.  Grain-scale experimental investigation of localised deformation in sand: a discrete particle tracking approach , 2012 .

[43]  Jidong Zhao,et al.  3D generation of realistic granular samples based on random fields theory and Fourier shape descriptors , 2014 .

[44]  Y P Vaid,et al.  Static liquefaction of sands under multiaxial loading , 1998 .

[45]  A. Eulitz,et al.  Yade Documentation 2nd ed , 2015 .

[46]  Kenneth L. Lee.  CLOSURE OF COMPARISON OF PLANE STRAIN AND TRIAXIAL TESTS ON SAND , 1970 .

[47]  Jean-Pierre Bardet,et al.  A numerical investigation of the structure of persistent shear bands in granular media , 1991 .

[48]  John F. Peters,et al.  Shear Band Formation in Triaxial and Plane Strain Tests , 1988 .

[49]  Takeshi Kodaka,et al.  Effects of sample shape on the strain localization of water‐saturated clay , 2007 .

[50]  Ronaldo I. Borja,et al.  Micromechanics of granular media. Part II : Overall tangential moduli and localization model for periodic assemblies of circular disks , 1997 .

[51]  L. J. Sluys,et al.  Numerical determination of representative volumes for granular materials , 2004 .