距离势离散单元法

Discrete element method based on distance potential

势函数离散单元法在接触力计算中存在势函数物理意义不明确、接触力计算与客观实际不符等重大缺陷。在已有研究的基础上,提出一种新型任意形状块体距离势离散单元法。该方法将势函数定义为接触体间归一化的距离函数,可以客观衡量单元间的嵌入程度,具有明确的物理意义,真实反映单元的接触刚度,使法向接触力计算更为合理。此外,新方法重新定义了切向方向矢量,提出切向接触力计算方法。新方法保留原势函数法所有优点,同时完善接触力计算受单元形式影响的不足,并突破三角形单元的限制,能够应用于任意凸多边形单元。通过若干算例说明新方法的正确性和有效性,可用于精确描述复杂非连续介质的运动过程。

The discrete element method based on the potential function has many deficiencies. The physical meaning of the potential function is not clear and the contact force calculation is inconsistent with the reality. A novel discrete element method based on the distance potential for the arbitral convex polygonal elements was thus proposed using the new definition of the distance potential function. This method describes the potential function as a normalized distance function between the contact couples. The distance potential function has the physical meaning and gives an accurate measurement for the embedded extent of the contact couples. Furthermore,the tangential vector is redefined and calculated in this approach. This method retains all the merits of the original potential method and remedies the problem in which the contact force calculation is affected by the element form. In addition,the method gets rid of the restrain of the triangular shape completely and can be applied to the arbitrary polygonal elements. It was illustrated with several examples that the method can accurately simulate the motion of the complex discontinuous media.