Abstract
ABSTRACT In an effort to develop a constitutive equation associated with more deformation and failure features of granular materials, the constitutive formulation is studied taking into account the fabric tensors as internal variables and their evolution modes. In order to render the constitutive equation satisfy the principle of material objectivity, the representation theorem of isotropic functions is effectively used. The theorem is reviewed with a particular reference to the rate type constitutive equation which gives rise to the rate of deformation tensor as a function of the stress, stress rate and fabric tensors. After discussing the relationship between essential independent variables in constitutive equations and the state of granular materials from a viewpoint of the evolution mode of the fabric tensors, particular problems are studied with the result that: (1) Granular materials can show less summetry (more anisotropic) than orthotropic when the general stress states and paths are concerned; (2) In two dimensions, the introduction of the (anisotropic) fabric tensor is essential in order to describe the non-coaxial and dilatant behavior under the rotation of principal stress axes.
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