Granular fracture holds significant implications in material mechanics. However, the previous studies in ordinary state-based peridynamic (OSB-PD) framework often neglect the internal crystalline structure of particles or only consider limited crystal orientation. To address this gap, a novel OSB-PD model for granular fracture within polycrystalline materials is proposed, in which the periodic functions are incorporated in the PD strain energy density, taking into account the inherent random orientation in cubic crystals. By comparing energy density from PD and the classical continuum mechanics, four PD material parameters are defined. Moreover, the corresponding surface correction method in the global coordinate system is also proposed. Several numerical examples including fracture analysis of polycrystalline materials are conducted to validate the effectiveness of the proposed method. The proposed ordinary state-based peridynamic model offers a fresh perspective for investigating granular fracture behaviors within polycrystalline materials.

中文翻译：

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立方晶体中任意取向的多晶材料中粒状断裂的普通基于状态的近场动力学模型

粒状断裂在材料力学中具有重要意义。然而，以往基于普通态的近场动力学（OSB-PD）框架的研究往往忽略粒子的内部晶体结构或仅考虑有限的晶体取向。为了解决这一问题，提出了一种用于多晶材料内粒状断裂的新型 OSB-PD 模型，其中将周期函数纳入 PD 应变能密度中，同时考虑到立方晶体固有的随机取向。通过比较 PD 和经典连续介质力学的能量密度，定义了四个 PD 材料参数。此外，还提出了全局坐标系下相应的曲面校正方法。进行了包括多晶材料断裂分析在内的几个数值算例来验证所提出方法的有效性。所提出的基于普通状态的近场动力学模型为研究多晶材料内的颗粒断裂行为提供了新的视角。