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

机译：关于颗粒材料建模中的凸度，正态性，预固结压力和奇异性

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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.
机译：在颗粒材料和土壤力学的背景下，讨论了屈服面的凸度，正态性，预固结压力和奇异性问题。我们通过表达应变空间中的屈服面，从一个非常不寻常的方向来对待那些主题。结果表明，当弹性行为为线性时，在应变空间中的凸度假设是合理的，但在其他情况下则没有。由于颗粒物质的有效体积模量通常与压力有关，因此应变空间屈服面是非凸的。但是，应变空间的非凸性并不一定违反热力学定律，并且通过承认这一点，可以提出支持应变空间弹塑性的论点。然后，我们直接使用总体积应变定义预固结压力。新的定义提供了结合基于空隙比的经典定义和使用塑性体积应变的理论上一致的定义的优点。在非负塑性乘数的定义中，它还允许消除由于零分母而可能出现的奇异点。

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