Modelling strain localization in granular materials using micropolar theory: numerical implementation and verification

Abstract

SUMMARYImplementation and applications for a constitutive numerical model on F-75 silica sand, course silica sand and two sizes of glass beads compressed under plane strain conditions are presented in this work. The numerical model is used to predict the stress versus axial strain and volumetric strain versus axial strain relationships of those materials; moreover, comparisons between measured and predicted shear band thickness and inclination angles are discussed and the numerical results compare well with the experimental measurements. The numerical model is found to respond to the changes in confining pressure and the initial relative density of a given granular material. The mean particle size is used as an internal length scale. Increasing the confining pressure and the initial density is found to decrease the shear band thickness and increase the inclination angle. The micropolar or Cosserat theory is found to be effective in capturing strain localization in granular materials. The finite element formulations and the solution method for the boundary value problem in the updated Lagrangian frame (UP) are discussed in the companion paper.

Finite element simulation of localization in granular materials by micropolar continuum approach

“…The mesh dependent solutions might lead to a vanishing shear band thickness as the mesh size is refined in the finite element solution. Tejchman [19], Tejchman et al [20], Maier [21], Manzari [22], Voyiadis et al [23], Alsaleh et al [24,25], Alshibli et al [26], Arslan [27] confirmed that the shear band formation is mesh independent in Cosserat continuum analysis due to the regularization of the deformations by additional (rotational) degrees of freedom.…”

“…Localization analysis in Cosserat continua has typically focused on analytical and finite element simulation [20][21][22]26,[47][48][49]55]. Main research interests have been to illustrate the applicability of the higher order micro-continuum theory to elastic-plastic solid mechanics analysis.…”

Micromechanical analysis of failure propagation in frictional granular materials

“…In this section, we summarize the key features of the constitutive model and delineate the procedure for expressing the model in the form given in (3) and (4). The physical meaning of the internal variables and their evolution laws are discussed, with explicit connections made to the underpinning event of force chain buckling under lateral confinement from weak network neighbors.…”

Description of local dilatancy and local rotation of granular assemblies by microstretch modeling

“…In addition to the dilatant degree of freedom, particle rotation is important when a granular assembly is subjected to shear forces. This necessitates the introduction of the rotational degree of freedom and leads to a vast number of studies on the micropolar continuum modeling of granular materials (Ehlers and Volk, 1998;Alshibli et al, 2006). Due to the fact that (i) the dilatant motion is caused by grain rearrangement, which in turn comes from grain slide or grain rotation, and (ii) even an applied shear force can induce a volume change for a granular material, a continuum theory without a description of both dilatant and rotational effects might not be a satisfactory tool to model the behavior of these materials.…”