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A constitutive model for granular materials with evolving contact structure and contact forces-part Ⅱ: constitutive equations

机译：采用切换接触结构的粒状模型和接触力部分Ⅱ：构成方程

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摘要

This and the companion paper present a constitutive model for granular materials with evolving contact structure and contact forces, where the contact structure and contact forces are characterised by some statistics of grain-scale entities such as contact normals and contact forces. And these statistics are actually the fabric or force terms in the stress-force-fabric (SFF) equation. The stress-strain response is obtained by inserting the predicted fabric or force terms from evolution equations into the SFF equation. In the model, the critical state is characterised by two fitting equations and three critical state parameters. A semi-mechanistic analysis is conducted about the change of the contact number and the obtained results are combined with observed phenomena in DEM virtual experiments to give the constitutive equations for the fabric terms. The change of fabric anisotropy is related to the strain rate, current fabric anisotropy and also contact forces. The change of coordination number is induced by two terms related to volumetric and shear deformations, and also an additional term related to the change of fabric anisotropy. The constitutive equations regarding the force terms are also proposed. All the fabric or force terms are modelled to tend toward their critial state value, which agrees with Li and Dafalias's (J Eng Mech 138(3):263-275, 2012. 10.1061/(ASCE)EM.1943-7889.0000324) basic philosophy in their evolution equation for the fabric tensor. These equations along with the SFF equation form a constitutive model.
机译：该和伴随纸具有颗粒材料的构成模型，具有演进的接触结构和接触力，其中接触结构和接触力的特征在于晶粒规格的一些统计数据，例如接触法线和接触力。这些统计数据实际上是应力 - 织物（SFF）方程中的织物或力术语。通过将预测的织物或力术语从进化方程插入SFF方程来获得应力 - 应变响应。在该模型中，临界状态的特征在于两个拟合方程和三个临界状态参数。关于接触数的变化进行半机械分析，并且将得到的结果与DEM虚拟实验中观察到的现象组合，以给出织物术语的组成方程。织物各向异性的变化与应变速率，电流织物各向异性以及接触力有关。协调数的变化由与体积和剪切变形相关的两个术语引起，以及与织物各向异性的变化有关的额外术语。还提出了关于力术语的构成方程。所有织物或强制术语都被建模，倾向于倾向于他们的批判状态价值，这与Li和Dafalias（J Eng Mech 138（3）：263-275,2012.1061 /（asce）Em.1943-7889.0000324）基本哲学在织物张量的演化方程中。这些方程与SFF方程一起形成构成型模型。

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