A Multi-time-step Discrete Element Method for Bar Structures

doi:10.19596/j.cnki.1001-246x.8427

Abstract

Abstract:

To improve computational efficiency of discrete element method(DEM), referring to domain decomposition method and sub-cycle method in finite element method, a discrete element partition asynchronous time step computing method based on overlapping particles was proposed to deal with continuous medium problems. In the method, the continuum is divided into sub-domains. The velocity-Verlet integral scheme is used to solve the motion equation in sub-domains. Local action regions are formed with overlapping particles in adjacent sub-domains. Interpolation and truncation are not involved in transfer process of boundary data. Numerical examples show that accuracy of the method is high and the computation time is reduced effectively. In practical application, continuous media could be divided into several sub-domains with different particles size, and different time steps are adopted according to particle size characteristics of the sub-domains, with which storage space could be saved and computing efficiency improved greatly.

Key words: discrete element method, linked bar, overlapping particles, asynchronous step, continuous medium

Tong LI, Qian WANG, Xian-long JIN. A Multi-time-step Discrete Element Method for Bar Structures[J]. Chinese Journal of Computational Physics, 2022, 39(4): 395-402.

Figures/Tables 10

Fig.1 Model of linked bar (a) linked bar of spherical particles; (b) equivalent contact area of spherical particles

Fig.2 (a) Particle division with overlapping boundaries and update and (b) transfer of boundary data

Fig.3 Multi-time step calculation flow of different partitions

Fig.4 Update order of boundary particles data

Fig.5 Region division of a uniform cross section rod and interaction between pairs of adjacent particles i and j

Fig.6 Stress-wave propagation through a slender rod calculated with different methods

Fig.7 Axial displacement curves of free end calculated with different methods

Fig.8 A step-cross section rod subjected to axial concentrated load (a) Region division of rod and axial load of point P; (b) Particle partition of elastic rod

Fig.9 Axial displacement response of the free end of a step-cross section rod calculated with different methods

Table 1 Computational times with different time step ratios

计算方法		求解时间/s	时间比率/%
Newmark		216.2	100
同步长		176.4	81.6
异步长	η=3	117.4	54.3
	η=5	62.9	29.1
	η=8	55.6	25.7
	η=10	47.3	21.9
	η=12	12.3	5.7

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