Abstract
Stress–dilatancy theories play a central role in the modeling of the plastic dissipation of geomaterials. There exist several mathematical frameworks for describing the stress–dilatancy behavior of soils. One of the limiting assumptions often introduced is coaxiality between principal directions of stresses and plastic strain increments. However, experimental evidences suggest that this assumption is generally invalid for the deformation behavior of granular materials. In this paper, non-coaxial stress–dilatancy framework is developed first in axis symmetric, plane strain and then for general stress–strain conditions. To facilitate the use of the stress–dilatancy framework for cyclic loading conditions, loading and unloading are explicitly considered in the development of the framework. Furthermore, a possible way of establishing the evolution of the degree of non-coaxiality in plane strain and axis symmetric cases is presented. Then the approach is applied to selected yield functions.
Highlights
Coaxiality between principal stresses and principal plastic strain rates was first postulated by Saint–Venant [27]
This tendency has been attributed mainly to rotation of principal stresses because of ‘‘a simple shear loading condition imposed in the shear band.’’ Tejchman and Wu [28] carried out a numerical investigation of shear localization in dilatant bodies using a micro-polar hypoplastic model with a focus on non-coaxiality and stress–dilatancy behavior of an initially medium dense Karlsruhe Sand
We begin to lay down the theory first in the plane strain and in the axisymmetric condition, and we will continue to apply the same approach for establishing plastic dissipation and stress– dilatancy relation considering the full stress and plastic strain rate tensors
Summary
Coaxiality between principal stresses and principal plastic strain rates was first postulated by Saint–Venant [27]. Maximization of dissipation is subjected to, for example, kinematic constraints in the medium. In granular materials, such constraints may arise due to anisotropy, non-homogeneity and bifurcation. Et al [15] employed the hollow cylinder apparatus to investigate deformation behavior of dense air-pulviated Toyoura Sand subjected to proportional stress path, pure principal stress rotation and loading with increasing deviatoric stress combined with principal stress rotation. Their test results show that loading conditions that involve principal stress rotations are in general non-coaxial. Non-coaxiality has been observed in discrete element model (DEM) setups [1, 3, 29, 35]
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