Abstract—A computer model of fracture in heterogeneous materials (including rocks) is proposed to study evolution of the defect structure (cracks) during deformation process. The model is based on the Discrete Element Method (DEM), which, in contrast to the methods relying on continuum mechanics, naturally simulates the formation and evolution of cracks. We used the bonded particle model (BPM), which is widely used in various modifications to study the fracture process. The material is modeled by a set of spherical particles (simulating polycrystalline grains), connected by bonds placed at particle contact points, which simulate grain boundaries. In the BPM model, crack initiation is determined by the breakage of bonds, and its propagation is provided by the coalescence of a numerous set of broken bonds. Computer experiments were performed with different material parameters (different mechanical properties of grains and grain boundaries, different grain sizes) to determine their effect on the local stress patterns, defect formation, and fracture source nucleation and development. The calculations were performed in the open-source DEM simulation software MUSEN. Samples were modeled by cylinders filled with spherical particles of the same or different radii packed up to reaching the void ratio 0.35–0.37. The materials simulating grains and bonds (grain boundaries) were specified with mechanical parameters corresponding to granite, quartz, orthoclase, oligoclase, and glass. The sample was placed in a virtual press in which a bottom plate was fixed and a top plate was moved towards the lower plate at a constant rate until the sample failed. The maximum local stress calculations have shown that homogeneous materials yield more heterogeneous spatial distributions of local stresses and vice versa—material heterogeneity leads to more uniform stress distributions. Comparison with the results of laboratory rock deformation experiments has shown that the proposed model of polycrystalline materials realistically describes some features of fracture in these materials when the main processes occur along the grain boundaries. These features include the brittle type of fracture in homogeneous materials and the presence of nonlinear elasticity (plasticity) revealed for more heterogeneous materials based on the stress-strain diagrams, as well as the time behavior of “acoustic emission rate” (or acoustic activity)—the number of bonds broken per unit time. For heterogeneous materials, the model shows a two-stage pattern of the fracture process with uniform defect accumulation throughout the sample at the first stage and the formation and growth of fracture nucleation sites at the second stage.

摘要—提出了异质材料（包括岩石）断裂的计算机模型，以研究变形过程中缺陷结构（裂纹）的演变。该模型基于离散元法 (DEM)，与依赖连续介质力学的方法相比，它自然地模拟了裂纹的形成和演化。我们使用了广泛用于各种修改的键合粒子模型 (BPM) 来研究断裂过程。该材料由一组球形颗粒（模拟多晶颗粒）建模，这些颗粒通过放置在模拟晶界的颗粒接触点处的键连接。在 BPM 模型中，裂纹的萌生是由键的断裂决定的，而裂纹的传播是由大量断裂键的结合提供的。对不同的材料参数（晶粒和晶界的不同机械性能、不同的晶粒尺寸）进行了计算机实验，以确定它们对局部应力模式、缺陷形成和断裂源成核和发展的影响。计算在开源 DEM 模拟软件 MUSEN 中进行。样品由填充有相同或不同半径的球形颗粒的圆柱体建模，这些颗粒堆积起来达到空隙率 0.35–0.37。模拟晶粒和键（晶界）的材料指定了与花岗岩、石英、正长石、低长石和玻璃相对应的机械参数。将样品放置在虚拟压力机中，其中底板固定，顶板以恒定速率向下板移动，直到样品失效。最大局部应力计算表明，均质材料会产生更不均匀的局部应力空间分布，反之亦然——材料的不均匀性会导致更均匀的应力分布。与实验室岩石变形实验结果的比较表明，当主要过程沿晶界发生时，所提出的多晶材料模型真实地描述了这些材料的一些断裂特征。这些特征包括均质材料中的脆性断裂类型和基于应力-应变图显示更多异质材料的非线性弹性（塑性）的存在，以及“声发射率”（或声活动）的时间行为——单位时间内断裂的键数。对于异质材料，