In the discrete element simulation of granular materials, the modelling of contacts is crucial for the prediction of the macroscopic material behaviour. From the tribological point of view, friction at contacts needs to be modelled carefully, as it depends on several factors, e.g. contact normal load or temperature to name only two. In discrete element method (DEM) simulations the usage of Coulomb’s law of friction is state of the art in modelling particle–particle contacts. Usually in Coulomb’s law, for all contacts only one constant coefficient of friction is used, which needs to reflect all tribological effects. Thus, whenever one of the influence factors of friction varies over a wide range, it can be expected that the usage of only one constant coefficient of friction in Coulomb’s law is an oversimplification of reality. For certain materials, e.g. steel, it is known that a dependency of the coefficient of friction on the contact normal load exists. A more tribological tangential contact law is implemented in DEM, where the interparticle friction coefficient depends on the averaged normal stress in the contact. Simulations of direct shear tests are conducted, using steel spheres of different size distributions. The strong influence of interparticle friction on the bulk friction is shown via a variation of the constant interparticle friction coefficient. Simulations with constant and stress-dependent interparticle friction are compared. For the stress-dependent interparticle friction, a normal stress dependency of the bulk friction is seen. In the literature, measurements of different granular materials and small normal loads also show a stress dependency of the bulk friction coefficient. With increasing applied normal stress, the bulk friction coefficient reduces both in the experiments and in the simulations.

中文翻译：

---

摩擦现象及其对粒状材料剪切行为的影响。

在粒状材料的离散元素模拟中，接触的建模对于宏观材料行为的预测至关重要。从摩擦学的角度来看，接触点的摩擦需要仔细建模，因为它取决于多个因素，例如接触点的正常负​​载或温度仅举两个例子。在离散元方法（DEM）模拟中，使用库仑摩擦定律对粒子-粒子接触进行建模是最新技术。通常在库仑定律中，对于所有接触，仅使用一个恒定的摩擦系数，这需要反映所有摩擦学效应。因此，只要摩擦的影响因素之一在很大范围内变化，就可以预期在库仑定律中仅使用一个恒定的摩擦系数是对现实的过分简化。对于某些材料，众所周知，例如钢，存在摩擦系数对接触法向载荷的依赖性。DEM中采用了更摩擦学的切向接触定律，其中颗粒间摩擦系数取决于接触中的平均法向应力。使用不同尺寸分布的钢球进行直接剪切试验的模拟。通过恒定的颗粒间摩擦系数的变化，可以看出颗粒间摩擦对整体摩擦的强烈影响。比较了恒定且依赖于应力的粒子间摩擦的模拟。对于取决于应力的颗粒间摩擦，可以看到整体摩擦的法向应力依赖性。在文献中 不同粒状材料和小的法向载荷的测量结果也显示出整体摩擦系数的应力依赖性。随着法向应力的增加，整体摩擦系数在实验和模拟中均减小。