三维距离势离散单元法

Discrete element method using three dimensional distance potential

通过定义距离势函数,提出一种适用于空间任意凸多面体单元的三维距离势函数离散单元法。该方法采用归一化的计算方式,将势函数表征为接触体间的距离函数,并基于此建立接触力计算方程,明确了势函数的物理意义,使接触力计算更加合理,无需对各种可能的接触形式进行差异化处理。新方法克服了原有势函数物理意义不明、接触力计算受单元形式影响等重要缺陷,并突破了四面体单元的限制,可采用空间任意凸多面体单元。通过若干算例说明新方法的正确性和有效性。数值模拟结果表明新方法能够很好处理空间任意多面体单元复杂接触变换过程,准确处理复杂非连续介质的运动过程。

A 3-D discrete element method is presented on the basis of new definition of distance potential function, which is suitable for the arbitrary polyhedral elements. In this approach, the potential function is characterized as a distance function between the contacts using a normalized computational algorithm. Meanwhile, the calculation formulations for contact interaction are deduced with the new function. Thus this new distance potential function implies sound physical meaning, and is reasonable and concise to avoid different contact situations. This method overcomes the problems of the original potential method in which the physical meaning of potential function is not clear and the calculation of contact force is affected by the element form. Furthermore, it gets rid of the restrain of tetrahedral shape and can be applied to arbitrary polyhedrons. Several examples are analyzed to demonstrate the accuracy and efficiency of this new method. This method shows good capability of handling the problem of contact transformation for arbitrary polyhedrons and the motion process of the complex discontinuous media.