基于水平集接触算法的任意形态颗粒材料球谐离散元方法  

A discrete element method with spherical harmonics for irregular granular materials based on the level set contact algorithm

作　　者：王嗣强 乔婷 张林风 季顺迎[1] WANG SiQiang;QIAO Ting;ZHANG LinFeng;JI ShunYing(State Key Laboratory of Structure Analysis of Industrial Equipment,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室,大连116024

出　　处：《中国科学：物理学、力学、天文学》2022年第2期38-53,共16页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家重点研发计划(编号:2018YFA0605902,2016YFC1402706);国家自然科学基金(编号:11872136,11772085)资助项目。

摘　　要：为对自然环境或工业领域中非规则颗粒材料的力学特性进行精确计算,本文采用球谐函数发展了可描述任意几何颗粒形态的球谐离散元方法.考虑球谐单元的凹凸形态及多点接触特性,发展了基于水平集方法的任意形态接触算法,以准确计算单元间的接触方向和重叠量.该算法将不同形态的球谐单元离散为由一系列点组成的零水平集函数和空间离散水平集函数,并将单元间的接触问题转化为两个水平集函数间的求解问题.通过将一系列零水平集点代入邻居单元的空间离散水平集函数中进行三线性插值,可确定两个接触单元间的多接触点及作用力.为检验基于水平集算法的球谐离散元方法的可靠性,对单颗粒与刚性壁面的弹性碰撞、单颗粒自由下落和多颗粒动力堆积过程进行了离散元模拟,研究了颗粒的平动和转动动能随时间的变化规律.计算结果表明,基于水平集算法的球谐离散元方法可准确地计算单元间的接触碰撞作用,并可保证弹性碰撞时颗粒系统的能量守恒及非弹性碰撞时颗粒系统的能量衰减直至动能为零.在此基础之上进一步分析了不同表面凹凸特性对颗粒堆积中体积分数和平均配位数的影响,为任意形态颗粒材料的数值模拟提供了一种有效的离散元方法.To calculate the mechanical properties of irregular granular materials in natural or industrial fields, a discrete element model based on spherical harmonics that can describe arbitrarily shaped particles is developed. Considering the uneven surfaces and multiple contact points of the spherical harmonic elements, a contact model of arbitrary shapes based on the level set algorithm is developed to calculate the contact direction and overlap between the elements. In this model,spherical harmonic elements with different shapes are discretized into a zero level set function and a discrete spatial-level set function composed of a series of points. In addition, the contact detection between elements is transformed into a solution of two level set functions. All zero level set points are brought into the spatial-level set function of the neighboring element, and the multiple contact points and forces between the two neighboring elements are determined via trilinear interpolation. The elastic collision of a single particle with a wall, the free fall of a particle, and the packing process of multiple particles are simulated using the discrete element method, and the evolution of the translational and rotational kinetic energy of particles over time is studied to validate the discrete element model of the spherical harmonic function based on the level set method. The results show that the discrete element model of spherical harmonic functions based on the level set method can be used to calculate the contact forces between elements. Meanwhile, the energy of the granular system remains constant during the elastic collision, and the system energy decays during the inelastic collision until the kinetic energy approaches zero. Based on the aforementioned method, the influence of uneven surfaces on the packing fraction and average coordination number of granular materials is analyzed, and an effective discrete element model is provided for the numerical simulation of irregular granular materials.

关 键 词：离散元方法 任意形态 颗粒材料 球谐函数 水平集算法 多接触点判断 

分 类 号：O341[理学—固体力学]