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Fabric tensor within ansiotorpic critical state theory: from DEM to continuum

The spatial arrangement of particles and voids in a granular material can be statistically characterized by a continuum fabric tensor F (Satake, 1982). There are several fabric tensors definitions that are symmetric, deviatoric and of second-order (Oda 1982). The unit norm direction nF of F characterizes the orientation of fabric anisotropy while its norm F measures its intensity. In classical Critical State Theory (CST) granular materials will approach a state of constant stress ratio and volume, with a unique e-p (e=void ratio and p=confining pressure) Critical State Line (CSL), which is independent of fabric anisotropy. Yet, at critical state material is highly anisotropic but its anisotropy plays no role in the definition of CSL. Li and Dafalias (2012) resolved this paradox by proposing an Anisotropic Critical State Theory (ACST), where in addition to the foregoing conditions of CST, F has its own unique critical state value Fc such that nF is along the loading direction n and the norm Fc is a sole function of the Lode angle of n. Thus, an additional critical state condition can conveniently be introduced via the Fabric Anisotropy Variable A=F:n/Fc, with A=1 at critical state. Similarly to the role of critical state void ratio, A establishes an intrinsic reference of fabric anisotropy evolution, with which the deformation process involving highly anisotropic fabric can be described accurately. DEM can provide accurate evaluation of fabric tensors, among them the most popular one based on contact normal directions. An attempt to extend such evaluation to a continuum internal variable entity within plasticity theory negates the requirement that such internal variable must be measured per unit volume because a usual DEM definition is not, thus, violating fundamental thermodynamic law of per volume dissipation. This violation is addressed within ACST and a normalization procedure is proposed for correcting it.

Author(s):

Yannis F. Dafalias    
National Technical University of Athens
Greece

Xiang Song Li    
Hong Kong University of Science and Technology
China