Numerical investigations of shear localization in a micro‐polar hypoplastic material

Abstract

SUMMARYIn this paper a micro-polar continuum approach is proposed to model the essential properties of cohesionless granular materials like sand. The model takes into account the influence of particle rotations, the mean grain size, the void ratio, the stresses and couple stresses. The constitutive equations for the stresses and couple stresses are incrementally non-linear and based on the concept of hypoplasticity. For plane strain problems the implementation of the model in a finite element program is described. Numerical studies of the evolution of micro-polar effects within a granular strip under plane shearing are presented. It is shown that the location and evolution of shear localization is strongly influenced by the initial state and the micro-polar boundary conditions. For large shearing the state quantities tend towards a stationary state for which a certain coupling between the norm of the stress deviator and the norm of the couple stress tensor can be derived.

Granular hypoplasticity with Cosserat effects

“…This more general version of hypoplasticity, anticipated in early works on the subject [19,15] has been computationally implemented in numerous works by Tejchman, Bauer and co-workers [20,7,12,8,21,22] for polar as well as non-polar media. In the non-polar form, these models involve internal variables whose history dependence is determined by ODEs having the pseudo-linear form:…”

“…Here, we have chosen the simplest possible norm |D| involving a material length scale ξ referred to above, which we recall is associated with a representative particle diameter by other workers [7,8,21]. With the replacement of D by D in (11), (13) and (14) one obtains the complete parametric Cosserat hypoplasticity, for which some special cases are worth noting.…”

“…For the isotropic case, Appendix B gives the general form of (36), with a more concrete form of (37), the latter of which involves a total of twelve functions representing various elasticities and compliances. At the time of this writing, the author has not attempted a detailed comparison of the latter against various empiricisms [12,8,9,21,2].…”

The importance of Thermo-Hydro-Mechanical couplings and microstructure to strain localization in 3D continua with application to seismic faults. Part II: Numerical implementation and post-bifurcation analysis

“…Alternatively to the 320 flow theory of plasticity that is used in the present paper, a Cosserat continuum within the framework of hypoplasticity can be used to model granular materials (Huang andBauer, 2003, Tejchman, 2008). …”

A Semi-Implicit Microplar Discrete-to-Continuum Method for Granular Materials

“…A micropolar continuum is different than the classical Cauchy-Boltzmann continuum in the sense that material points are associated with microstructures that have orientations characterized by micro-rotation [12,13]. This additional degree of freedom allows characteristic length or physical length scale to be introduced into the micropolar constitutive law and hence can be used as a mean to resolve the mesh sensitivity issue and captured the material size effects [14,15,16].…”