The distance potential function-based finite-discrete element method
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ORIGINAL PAPER
The distance potential function-based finite-discrete element method Xunnan Liu1 · Jia Mao1 · Lanhao Zhao1 · Linyu Shao1 · Tongchun Li1,2 Received: 23 November 2019 / Accepted: 17 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The work is devoted to a coupling method for the finite element method (FEM) and the distance potential discrete element method. In this work, a well-defined distance potential function is developed. Meanwhile, a holonomic and precise algorithm for contact interaction is established, accounting for the influence of the tangential contact force. In addition, the measurement of deformation behaviors of each discrete element is handled by the FEM, where the coupling model and the conversion method of the equivalent nodal force accounting for the influence of contact forces are proposed to generate the corresponding equations of motion. Finally, the velocity verlet algorithm is applied enabling the significant simplification for the calculation of the equations of motion. The proposed approach provides an accurate contact interaction avoiding the influence of the element shape and reflect the movement procedure of multiple deformable bodies precisely. This viewpoint is proved by the classical benchmark cases. Keywords Discrete element method · Finite element method · Distance potential function · Contact force model · Deformation behaviors
1 Introduction The discrete element method (DEM) offers an efficient tool for tracing mechanical behaviors of discontinuous media. Initially, the underlying rigid-body assumption is adopted in the DEM. This assertion shows its rationality for the systems, such as joined rock masses and block collections, since the deformation of such media is mainly caused by the sliding and rotation of blocks and evolution of discontinuous interfaces. However, the system consisted of multiple deformable bodies usually involves with the large displacement and rotation, and investigations conducted in these phenomena gain more popularity in typical applications of the computational mechanics [1, 2]. Accordingly, a model capable of representing the interactions and the deformation properties is extremely indispensable for modeling the complicated behaviors of the discontinuous system.
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Lanhao Zhao [email protected]
1
College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing Xikang Rd., 210098, People’s Republic of China
2
College of Agricultural Engineering, Hohai University, Nanjing 210098, People’s Republic of China
In recent times, an increasing number of models are set up by coupling the DEM with continuous approaches to capture the actual behavior of the system associated with geometric information and contact mechanical properties. A typical simplified model is suggested by Cundall and Strack [3–5]. The main idea refers to the idealized discontinuous mathematical model, that deformable blocks are represented by the triangular elements and joints are modelled as contact surfaces between
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