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General polygon mesh discrete element method for arbitrarily shaped particles and complex structures based on an energy-conserving contact model

基于能量守恒接触模型的任意形态颗粒和复杂结构通用多边形网格离散元方法

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Abstract

Interactions between irregular particles and structures always exist in the natural environment and industrial production process. For the desired simulation into the dynamic behaviors of arbitrarily shaped particles in complex structures, a general polygon mesh discrete element method (DEM) is developed based on the general energy-conserving contact theory. Within this method, a complete normal contact model for a contact pair with a complex contact region is proposed when the elastic strain energy density is utilized to specify a contact energy function. Since the shape of both complex particles and structures are uniformly constructed by polygon meshes, a unified contact detection implementation performed in this method is introduced in detail. This proposed method is characterized by the universal and uniform models of shape construction, contact detection, and contact force calculation for both particle-particle contact pairs and particle-structure contact pairs. To qualitatively demonstrate the conservation and robustness of the method, a set of validations or simulations considering the differently shaped particles, such as convex particles, concave particles, and particles with surface asperities, are applied. It is concluded from these validations or simulations that the general polygon mesh DEM and the corresponding proposed models are valid tools for research into the behavior of granular materials in complex structures.

摘要

非规则颗粒与复杂结构的接触行为在自然环境与工业生产过程中广泛存在, 为对复杂结构中任意形态颗粒的动力过程进行合理仿真, 本文基于能量守恒接触理论发展了一种通用的多边形网格离散元方法. 在该方法中, 将弹性应变能密度用于指定接触能函数的具体形式, 从而得到了考虑接触区域复杂形貌的法向接触力模型. 同时, 针对由多边形网格统一构建的非规则颗粒和复杂结构, 建立了一个统一的接触检测施行方案. 因此, 多边形网格离散元方法针对于颗粒-颗粒和颗粒-结构之间接触行为的模拟在形状构造、接触检测和接触力计算等方面均建立了通用和统一的模型, 避免了因不同接触情形下接触计算模型的不同而导致的数值跳跃. 为了定性地验证该方法的能量守恒性和鲁棒性, 选取了一组考虑到不同形状类型(凸形、凹形和表面粗糙形)的颗粒样本进行了从简单到复杂的系列验证和模拟. 相关验证及模拟结果表明, 本文发展的通用多边形网格离散元方法及其包含的相关模型是研究复杂结构中非规则颗粒材料动力学行为的一种有效工具.

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Acknowledgements

This work was supported by the National Key Research and Development Program of China (Grant Nos. 2021YFA1500302 and 2018YFA0605902), and the National Natural Science Foundation of China (Grant Nos. 11872136, 42176241, and U20A20327).

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116024, China

    Ji Li  (李继), Ting Qiao  (乔婷) & Shunying Ji  (季顺迎)

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  1. Ji Li  (李继)
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  2. Ting Qiao  (乔婷)
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  3. Shunying Ji  (季顺迎)
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Corresponding author

Correspondence to Shunying Ji  (季顺迎).

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Author contributions

Ji Li designed the overall scheme of the general polygon mesh discrete element method proposed in this paper, and completed the initial code construction. Ting Qiao developed an energy-conserving contact model based on elastic strain energy theoretically, and further improved the code implementation of the proposed method. Ji Li and Ting Qiao jointly designed the verification scheme and organized the manuscript. Shunying Ji managed the project, provided research resources, and revised and edited the final version of the manuscript.

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Li, J., Qiao, T. & Ji, S. General polygon mesh discrete element method for arbitrarily shaped particles and complex structures based on an energy-conserving contact model. Acta Mech. Sin. 39, 722245 (2023). https://doi.org/10.1007/s10409-022-22245-x

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