Stress Recovery Procedure for the Bonded Particle Model
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ISSN 1860-2134
Stress Recovery Procedure for the Bonded Particle Model Ruoyu Guan1
Shean Bie1
Canpeng Chen2
1
( State Key Laboratory of Hydraulic Engineering Simulation and Safety, School of Civil Engineering, Tianjin University, Tianjin 300072, China) (2 CCCC-FHDI Engineering Co., Ltd., Guangzhou 510230, China)
Received 14 September 2020; revision received 4 November 2020; Accepted 5 November 2020 c The Chinese Society of Theoretical and Applied Mechanics 2020
ABSTRACT In the simulation of discontinuous block systems, the discrete element method (DEM) has better computational efficiency and convergence than the finite element method (FEM). When several DEM particles are bonded together with parallel bonds (the bonded particle model, BPM), various shapes and block fractures can be simulated. The main aim of the BPM is to simulate a continuous material in which the stress distribution is continuous. Since the existing stress result for a single particle is an average value over the particle’s area, stress results do not exist in the area between particles. In this paper, the stress value for a single two-dimensional DEM particle is deduced. A stress recovery procedure with a linear stress function for a triangular element generated by the centroids of three bonded particles is proposed. In this way, the recovered stress field for the whole mesh composed of all triangular elements is continuous. A stress gradient exists in the whole mesh. This can also provide more accurate stress values for judging a fracture inside a block. Symmetrical and asymmetrical models are simulated by the BPM and FEM. Similar to the FEM results, the recovered stress results for the BPM can describe the stress distribution in the simulated continuous blocks. For the model with the theoretical stress solution, the recovered result and the theoretical solution coincide well.
KEY WORDS Discrete element method, Bonded particle model, Stress recovery procedure, Continuous stress field
1. Introduction The FEM has been widely utilized to simulate a single continuous object. The precision of the results for the stress and displacement obtained by the FEM is quite high. For a discontinuous block system, the contact between blocks leads to a large number of iterations, which leads to poor convergence of the FEM. The DEM was first proposed by Cundall [1] to model discontinuous block systems. The application of the DEM has been extended to many fields [2–4]. The shape of a particle in the DEM can be a polygon or a sphere. When the shape is a polygon, a vertex–vertex type of contact causes the detection of the contact to be quite complicated [5]. However, spherical particles make the detection of contacts over time steps the simplest. In the BPM, parallel bonds are utilized to bond several spherical particles to simulate complicated shapes of blocks [6]. The BPM has been widely applied to model the cracks and fractures inside blocks [7–10]. The behavior observed in experiments and that of the BPM coincided well [11–15].
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