On convexity, normality, pre-consolidation pressure, and singularities in modelling of granular materials

The issues of convexity, normality, pre- consolidation pressure, and singularities of yield surfaces are discussed in the context of granular materials and soil mechanics. We approach those subjects from a rather unusual direction, by expressing yield surfaces in strain space. It is shown that the convexity assumption in strain space is justified when the elastic behaviour is linear, but not otherwise. As the effective bulk modulus of granular matter is generally pressure dependent, strain space yield surfaces are non-convex. However, strain space non-convexity does not necessarily violate the laws of thermodynamics, and by acknowledging that, arguments in favor of strain space elasto-plasticity could be made. We then define the pre-consolidation pressure directly using the total volumetric strain. The new definition offers to combine the advantages of the classical definition based on the void-ratio and a theoretically consistent definition using the plastic volumetric strain. It also allows removing singularities that may occur due to a zero denominator in the definition of the non- negative plasticity multiplier.

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