摘要
传统的离散元类数值方法存在处理角-角接触时接触力方向不确定、三维情形时接触计算极其复杂等问题。Munjiza提出的基于势的接触力计算方法很好地解决了这一问题,但同时存在势的物理意义不明确,计算出的接触力与物理直观不符、相同嵌入量计算的接触力大小不一致等问题。在已有研究的基础上,提出了一种基于统一标定的势接触力计算方法,该方法重新定义了势函数,即三角形单元内一点的势与该点到3条边的最短距离成正比。采用这种势函数定义可以对嵌入量进行统一表征。在相同的嵌入量下,计算的接触力大小是一致的,同时保留基于势的接触力计算方法所有优点。新定义的势函数,解决了原有势函数所存在的重大缺陷,只要重叠区域不变,计算的总接触力是不变的,接触力计算具有局部特性,而与划分的三角形单元的整体形状和大小无关,即新的接触力计算方法,具有更好的网格鲁棒性。该方法使得基于势的接触力计算方法建立在坚实的物理基础之上,意义重大。
The direction of contact force is uncertain in dealing with corner-corner contact when the traditional discrete element numerical methods are used. At the same time the contact force calculation in three dimensions is extremely complex. Contact force calculation method based on potential proposed by Munjiza is a good solution to this problem. But the physical meaning of the potential is not clear. The calculated contact force does not match the physical intuition when embedding capacity is the same and the contact force is different. A new potential contact force calculation method is proposed using a unified calibration. The method redefines the potential function as the potential of a point in triangular proportional to the shortest distance from the point to the three sides of the triangular. This potential function definition can characterize the embedded amount in a unified way. When the embedding capacity is same, the calculated contact force is same, while all the advantages of the contact force with the potential can be kept. This redefined potential function overcomes the significant deficiencies of the original potential function. As long as the overlapping areas are constant, the total calculated contact force would be the same. The contact force calculation has local features, regardless of the overall shape and size of triangular element. The new contact force calculation method has better robustness grid. The method enables the contact force calculation with potential methods to build on a solid foundation of physics, which is significant.
出处
《岩土力学》
EI
CAS
CSCD
北大核心
2015年第1期249-256,共8页
Rock and Soil Mechanics
基金
国家自然科学基金项目(No.11202223)
国家重点基础研究发展计划(973)项目(No.2011CB013505
No.2014CB047100)
关键词
有限元-离散元法
势接触力
统一标定
离散元
finite-discrete element method（FDEM）
potential contact force
unified calibration
discrete element method
作者简介
严成增，男，1986年生，博士研究生，主要从事离散元有限元耦合、离散元、颗粒物质物理与力学、多物理场耦合、DDA、大规模高性能并行计算以及软件工程方面的研究工作。E-mail：yanchengzheng86@gmail．com
