可变形圆化多边形离散单元法

将基于圆化多边形离散单元法与有限元方法结合，提出一种可变形圆化多边形离散单元法。此法对块体离散元进行圆化处理，可较好地表征不规则块体外形，又保留了颗粒离散元计算高效的优势。在求解接触力时，消除了角点处法向奇异等问题，同时增强计算的稳定性和简化接触判断。同时对切向接触力计算模型进行修正，使得接触力计算效率得到提高。此法突破了圆化多边形刚体假设的限制，可以精确计算任意形状不规则离散单元之间的相互作用，对单元的运动和变形进行模拟。通过超静定梁冲击试验、不规则块体单轴压缩试验和料斗流动“卡阻”试验3个数值模拟算例，论证此法可以有效地捕捉单元的碰撞、分离和变形等空间运动和自身特性以及其细观力学表征。

A deformable spheropolygon-based discrete element method

A deformable spheropolygon-based discrete element method (DSEM) which combines the spheropolygon-based discrete element method (DEM) and the finite element method (FEM) is proposed. In this method, with the rounded discrete elements, the shape of the irregular blocks can be well characterized while the high efficiency advantage of particle discrete element method is also kept. The proposed method can not only eliminate the normal singularity at the corner but also improve the stability and simplify the contact judgment during contact force calculation. Meanwhile, the calculation model of the tangential contact force is also modified to improve the efficiency of contact force calculation. The DSEM breaks through the limitation of the rigid body hypothesis of the spheropolygon. Thus, the interaction between discrete elements with arbitrary shape can be accurately calculated, and the movement and deformation of the elements can also be simulated. Finally, three numerical examples including the dynamic response of statically indeterminate beam, the uniaxial compression test of irregular block, and hopper flow test is simulated using the DSEM to prove that the proposed method can effectively capture both the spatial motion as well as characteristics of elements (such as collision, separation and deformation) and their microscopic mechanical characterization.