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CG-enriched concurrent multi-scale modeling of dynamic surface interactions between discrete particles and solid continua

粗粒化强化有限-离散元多尺度耦合方法在颗粒-连续体表面动态 作用问题上的应用

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Abstract

The interaction between granular materials and deformable structures is relevant to many industries, such as mining, construction, and powder processing. Surface coupling between the discrete (DEM) and the finite element method (FEM) is commonly used to numerically describe particle-continuum interactions. Using a recently developed “surface-coupling” method, enriched by coarse graining, a micro-macro transition technique to extract continuum fields from discrete particle data, we study the time evolution of linear momenta and energies in various particle-continuum systems and their dependencies on the coarse-graining (CG) width, the support of the smoothing kernel. Via three numerical examples including (1) a dense granular flow impacting on a flexible obstacle, (2) a viscoelastic cube bouncing and resting on a frictional granular bed, and (3) a monolayer of particles flowing on a cantilever, we show that CG-enriched surface coupling not only leads to more accurate predictions but also reduces excess energies numerically generated by the coupling method, and CG is more effective as the particle-structure interaction becomes dynamic. By varying the CG width, we observe stronger attenuation, decreasing the magnitudes of high-frequency oscillations, facilitating stress relaxation in dissipative coupled systems, and that the identification of the optimal CG width is indeed problem-dependent.

摘要

颗粒材料和可变形结构之间的相互作用与采矿、施工、粉末加工等许多工业过程相关. 离散(DEM)和有限元法(FEM)之间的 表面耦合通常用来模拟颗粒材料与连续体介质间的相互作用. 本文使用最新提出“广义表面耦合”方法, 通过粗粒化(CG)强化连续物理 场从离散颗粒尺度数据中的提取, 在离散-连续体接触面实现微观-宏观过渡. 本文着重研究了颗粒-连续耦合系统中动量和能量的时间 演化及其在CG宽度(即平滑内核有效范围)上的依赖性. 通过三个数值算例, 包括(1)密实颗粒流撞击柔性障碍物, (2)粘弹性立方体坠落 并静止于颗粒床, (3)悬臂梁表面受重力作用滑动继而使梁弯曲的颗粒流, 证明了CG强化的FEM-DEM表面耦合可以使数值结果更加准 确, 并减少耦合系统中的多余能量. 通过比较三个计算实例, 本文发现随着颗粒-连续体相互作用从静态到动态过度, CG强化面耦合方 法的优势更加明显. 随着CG宽度增加, 耦合系统中过剩能量的衰减越强, 高频振荡的振幅也越小, 从而促进耦合系统中的应力松弛过 程. 但是最佳CG宽度的选择仍然取决于具体的耦合问题.

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Acknowledgements

Hongyang Cheng acknowledges funding from the Sectorplan Béta & Techniek of the Dutch Government. Thomas Weinhart acknowledges funding from the NWO-TTW project No.16604 Virtual Prototyping of Particulate Processes (ViPr)—Design and Optimisation via Multi-scale Modelling and Rapid Prototyping. This work made use of the Dutch national e-infrastructure with the support of the SURF Cooperative (Grant No. EINF-3381). We thank Anthony R. Thornton for the initial discussions on the implementation of FEM-DEM coupling in oomph-lib and Mercury-DPM and Mohammed. B. A. Hassan for defining the problem of deformable objects impacting granular beds, as part of his EngD project.

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Authors and Affiliations

  1. Chair of Soil MicroMechanics, Department of Civil Engineering, Faculty of Engineering Technology, MESA+, University of Twente, 7500 AE, Enschede, The Netherlands

    Hongyang Cheng  (程宏旸)

  2. Multi-Scale Mechanics Group, Department of Thermal and Fluid Engineering, Faculty of Engineering Technology, MESA+, University of Twente, 7500 AE, Enschede, The Netherlands

    Stefan Luding & Thomas Weinhart

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  1. Hongyang Cheng  (程宏旸)
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Correspondence to Hongyang Cheng  (程宏旸).

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Author contributions

Hongyang Cheng contributed to the conceptualization, data curation, formal analysis, funding acquisition, investigation, methodology, resources, software, validation, visualization, writing of the original draft, and writing-review and editing. Stefan Luding contributed to the conceptualization, methodology, visualization, writing-review and editing. Thomas Weinhart contributed to the conceptualization, methodology, visualization, software, writing-review and editing, project administration, and funding acquisition.

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Cheng, H., Luding, S. & Weinhart, T. CG-enriched concurrent multi-scale modeling of dynamic surface interactions between discrete particles and solid continua. Acta Mech. Sin. 39, 722218 (2023). https://doi.org/10.1007/s10409-022-22218-x

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