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 引用本文: 王嗣强, 季顺迎. 考虑等效曲率的超二次曲面单元非线性接触模型[J]. 力学学报, 2018, 50(5): 1081-1092.
Wang Siqiang, Ji Shunying. NON-LINEAR CONTACT MODEL FOR SUPER-QUADRIC ELEMENT CONSIDERING THE EQUIVALENT RADIUS OF CURVATURE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(5): 1081-1092.
 Citation: Wang Siqiang, Ji Shunying. NON-LINEAR CONTACT MODEL FOR SUPER-QUADRIC ELEMENT CONSIDERING THE EQUIVALENT RADIUS OF CURVATURE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(5): 1081-1092.

## NON-LINEAR CONTACT MODEL FOR SUPER-QUADRIC ELEMENT CONSIDERING THE EQUIVALENT RADIUS OF CURVATURE

• 摘要: 基于连续函数包络的超二次曲面单元可有效地描述自然界和工业生产中的非球体颗粒形态, 并通过非线性迭代方法精确计算单元间的接触力. 对于具有复杂几何形态的超二次曲面单元, 线性接触模型不能准确地计算不同接触模式下的作用力. 考虑超二次曲面单元相互作用时不同颗粒形状及表面曲率的影响, 本文发展了相应的非线性黏弹性接触模型. 该模型将不同接触模式下的法向刚度和黏滞力统一表述为单元间局部接触点处等效曲率半径的函数; 切向接触作用则借鉴基于Mohr-Coulomb摩擦定律的球体单元非线性接触模型的计算方法. 为检验超二次曲面单元接触模型的可靠性, 对球形颗粒间的法向碰撞、椭球体颗粒间的斜冲击过程、圆柱体的静态堆积和椭球体的动态卸料过程进行离散元模拟, 并与有限元数值结果及试验结果进行对比验证. 计算表明, 考虑接触点处等效曲率半径的超二次曲面非线性接触模型可准确地计算单元间的接触碰撞作用, 并合理地反映非球形颗粒体系的运动规律. 在此基础上进一步分析了不同长宽比和表面尖锐度对卸料过程中颗粒流动特性的影响, 为非球形颗粒材料的流动特性分析提供了一种有效的离散元方法.

Abstract: The super-quadric elements based on the continuous function representation can effectively describe the non-spherical particles in nature and industrial applications, and accurately calculate the contact force between the elements through a non-linear iterative method. For the super-quadric elements with complex geometric shapes, the linear contact force model cannot precisely calculate the contact force under various contact patterns. Considering different shapes and surface curvatures between non-spherical elements, a corresponding non-linear viscoelastic contact force model is developed. In this model, the equivalent radius of curvature is introduced to calculate the elastic contact stiffness and viscous force in normal direction. Meanwhile, the elastic force and the viscous force in tangential direction are simplified based on the contact force model of spherical element. To validate the super-quadric algorithms and the contact force model, the normal collision between spherical particles, the oblique contact between ellipsoidal elements, the static packing of cylinders and the dynamic hopper discharge of ellipsoids are simulated with the super-quadric elements. The proposed method is well verified by finite element numerical results and physical experimental data. The non-linear contact force model of super-quadric element with considering the equivalent radius of curvature can accurately calculate the inelastic collision, so as to reasonably reflect the motion law of the non-spherical particle system. Based on the aforementioned method, the effects of aspect ratio and blockiness on the flow characteristics in the discharging process are further analyzed. The results show spherical particles have the fastest flow rate while cube-like particles have the slowest flow rate. Meanwhile, the flow rate of ellipsoids and cylinder-like particles decreases with increasing or decreasing the aspect ratio. In addition, cube-like particles are more likely to form face-face contacts and have a lower flow rate. The super-quadric element with non-linear contact force model can provide an effective numerical approach to simulate the flow characteristics of non-spherical granular materials.

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