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基于膨胀颗粒DDA的复杂区域二维颗粒建模方法

A TWO-DIMENSIONAL PARTICLE MODELING METHOD FOR COMPLEX REGIONS BASED ON EXPANDING PARTICLE DDA

  • 摘要: 本文提出一种面向含孔洞及裂隙复杂形貌材料圆单元模型的全新建模方法. 该方法创新性地以非连续变形分析(DDA)方法为力学框架, 通过颗粒初始布置、颗粒膨胀与自协调平衡、均匀密实堆积体获取三个步骤, 不断驱动颗粒系统达到均匀密实状态. 建模时, 先定义填充区域、指定密实度和颗粒粒径分布形式, 再逐步缩小颗粒并无重叠地放置于填充区域内; 随后, 在逐步放大颗粒的同时, 运用圆单元DDA驱动颗粒向平衡位置移动; 最后, 当颗粒的位移增量满足预设收敛标准时, 获取最终圆单元模型. 系统的案例测试表明: 得益于DDA隐式解法的优势, 该方法计算稳定性高, 对复杂内外轮廓和裂隙具有极强适应性; 可同时精准控制颗粒粒径分布形式和密实度, 并保障最终模型的均匀性和随机性; 可兼顾一定的计算效率, 在普通PC上串行运行该建模程序, 含数万颗粒的模型建模耗时为数分钟, 建模效率略高于PFC软件; 模型轮廓及裂隙复杂度不影响单时步计算耗时, 但影响达到收敛所需计算步数. 该建模方法可进一步推动以圆单元为基本单元的非连续数值方法的发展及应用.

     

    Abstract: This paper proposes a novel modeling method for disk-based models of materials with complex geometries containing holes and fractures. This method innovatively adopts the Discontinuous Deformation Analysis (DDA) method as the mechanical framework and achieves a uniformly dense packing state through three steps: initial particle placement, particle expansion and self-coordinated equilibrium, and acquisition of a uniformly dense packing. In the modeling process, the filling region is first defined, and the packing density and particle size distribution are specified. Particles are then gradually reduced in size and placed into the filling region without overlap. Subsequently, while progressively enlarging the particles, the disk DDA is employed to drive the particles toward equilibrium positions. Finally, when the displacement increments of the particles satisfy the preset convergence criteria, the final circular element model is obtained. A series of systematic case studies were carried out, and the results showed that the proposed method exhibits high computational stability and strong adaptability to complex internal and external contours as well as fractures of the filling region. Owing to the advantages of the implicit solution used in DDA method, this modeling approach can simultaneously precisely control both the particle size distribution and packing density while ensuring the uniformity and randomness of the final model. The modeling method also maintains reasonable computational efficiency; when running the modeling program serially on an ordinary PC, models containing tens of thousands of particles can be generated within several minutes, yielding a modeling efficiency slightly higher than that of the PFC (Particle Flow Code) software. The complexity of model contours and fractures does not affect the computation time per time step, but does influence the number of steps required to achieve convergence. This modeling method can further promote the development and application of discontinuous numerical methods that use circular elements as fundamental elements.

     

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