The constitutive behaviour of a granular material with deformable particles interacting through Coulomb friction is analysed with numerical homogenisation techniques. Using periodic boundary conditions and the finite element method, the influence of friction coefficient, hardening behaviour and particle size distribution on the stress response of an assembly of frictional elasto-plastic particles to different deformation paths is investigated. Yield surfaces and the direction of inelastic flow are computed and particular attention is paid to the flow behaviour for low stress triaxialities. It is found that densely compacted assemblies exhibit associated flow to a good approximation despite the fact that frictional sliding (as opposed to plastic deformation) constitutes the relevant deformation mechanism on the microscale; a deviation from normality is observed for low density assemblies. The numerical results are discussed against the background of theoretical models.

可变形颗粒通过库仑摩擦相互作用的粒状材料的本构行为用数值均化技术进行分析。使用周期性边界条件和有限元方法，研究了摩擦系数、硬化行为和粒度分布对摩擦弹塑性颗粒组件对不同变形路径的​​应力响应的影响。计算屈服面和非弹性流动方向，并特别注意低应力三轴的流动行为。发现尽管摩擦滑动（与塑性变形相反）构成了微观尺度上的相关变形机制，但密集压实的组件表现出良好的近似相关流动；对于低密度组件，观察到偏离正态性。数值结果是在理论模型的背景下讨论的。