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# The Mathematical Structure of the Equations for Quasi-Static Plane Strain Deformations of Granular Material

## Abstract

An analysis of the quasi-static, plane strain, deformation of a rigid/plastic material whose yield stress depends on the current material density is presented. Such constitutive equations are widely used to model the initial yielding, final failure and flow of granular materials in what is generally known as “critical state soil mechanics”. It will be shown that the mathematical structure of these problems is rather more complex than seems to have been hitherto realized. It will be shown that there exist families of weak discontinuities other than “the stress and velocity characteristics” and that they provide a key to the resolution of the long standing debate regarding the non-coincidence of stress and velocity characteristics for frictional materials. The role of isotropy, anisotropy, normal flow rules and non-normal flow rules will be discussed.

## Keywords

Critical State Granular Material Yield Surface Velocity Characteristic Flow Rule## Preview

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