Cyclic stress-dilatancy relations and associated flow for soils based on hypothesis of complementarity of stress-dilatancy conjugates

Abstract

Applicability of associated plasticity for particulate materials such as soils does not yield satisfactory results when Coulomb's theory of shear strength of soils is assumed, and the yield function derived accordingly is used to define both the stress state and the direction of plastic flow. The limitation mainly stems from the fact that Coulomb's theory (and its derivatives) is a simplification that intentionally ignores deformation characteristics that manifest from the particulate nature of such materials. It is thus customary to apply a branch of plasticity called non-associated plasticity for soils and similar materials. In the non-associated plasticity framework, yield functions and plastic potential functions are different. The former defines the mobilization of the stress state while the later defines the direction of plastic flow. For soils, stress-dilatancy theories have become central in the formulation of non-associated flow rules. In this paper, cyclic stress-dilatancy relations are derived based on complementarity hypothesis of stress-dilatancy conjugates. Both loading and unloading are explicitly considered. Then, yield functions are derived based on the resulting stress-dilatancy relations. In so doing, the resulting yield functions are rendered with a quality to be used for the modelling of deformation behavior of soils subjected to monotonic and cyclic loading conditions. The newly derived yield functions are called Associated Cyclic Stress Dilatancy yield functions for which the abbreviation ACStD is used. The theoretical framework is established first for special cases of deformation modes-plane strain and axisymmetric. The framework is generalized for considering Lode angle dependency of the yield function and extending the Matusoka-Nakai criterion.