Abstract Mode I opening and mixed-mode I-II fracture experiments were performed with a homogeneous, fine grained sandstone using the three-point bending test. Specimens were notched at various lengths and positions of the beam edge to produce the desired loading condition. A micropolar peridynamic model was used to simulate the fracture initiation and propagation process. The analytical implicit formulation was derived by defining a specific macroelastic energy density function for micropolar non-local lattices, which depends on three deformation parameters: bond stretch, bond shear deformation accounting for the rotational degrees of freedom, and the particle’s relative rotation. The micropolar non-local lattice model is capable of handling a variable Poisson’s ratio, and is suitable for modelling the mechanical behavior of Cauchy isotropic solids subjected to non-homogeneous deformation fields and fracture. A preliminary analysis on a smooth boundary specimen was performed in order to validate the results obtained with the conceived peridynamic model adopting irregular discretizations. The failure process in notched sandstone specimens was simulated numerically in quasi-static conditions. Numerical results were compared with experimental data obtained from electronic speckle pattern interferometry (ESPI) tests, which were used to quantify and detect the fracture phenomena. Due to the intrinsic features of peridynamic theory, realistic crack patterns and crack initiation angles were obtained from the numerical simulations.

中文翻译：

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使用微极近场动力学公式模拟岩石中的断裂

摘要 使用三点弯曲试验对均质细粒砂岩进行了模式 I 打开和混合模式 I-II 断裂实验。试样在梁边缘的不同长度和位置处开槽，以产生所需的加载条件。微极近场动力学模型用于模拟裂缝的萌生和扩展过程。解析隐式公式是通过定义微极非局部晶格的特定宏观弹性能量密度函数得出的，该函数取决于三个变形参数：键拉伸、键剪切变形占旋转自由度，以及粒子的相对旋转。微极非局部晶格模型能够处理可变泊松比，适用于模拟受到非均匀变形场和断裂的柯西各向同性固体的力学行为。为了验证采用不规则离散化的近场动力学模型所获得的结果，对光滑边界试样进行了初步分析。在准静态条件下对缺口砂岩试样的破坏过程进行了数值模拟。将数值结果与从电子散斑干涉测量 (ESPI) 测试中获得的实验数据进行比较，这些数据用于量化和检测断裂现象。由于近场动力学理论的内在特征，从数值模拟中获得了真实的裂纹模式和裂纹萌生角。为了验证采用不规则离散化的近场动力学模型所获得的结果，对光滑边界试样进行了初步分析。在准静态条件下对缺口砂岩试样的破坏过程进行了数值模拟。将数值结果与从电子散斑干涉测量 (ESPI) 测试中获得的实验数据进行比较，这些数据用于量化和检测断裂现象。由于近场动力学理论的内在特征，从数值模拟中获得了真实的裂纹模式和裂纹萌生角。为了验证采用不规则离散化的近场动力学模型所获得的结果，对光滑边界试样进行了初步分析。在准静态条件下对缺口砂岩试样的破坏过程进行了数值模拟。将数值结果与从电子散斑干涉测量 (ESPI) 测试中获得的实验数据进行比较，这些数据用于量化和检测断裂现象。由于近场动力学理论的内在特征，从数值模拟中获得了真实的裂纹模式和裂纹萌生角。在准静态条件下对缺口砂岩试样的破坏过程进行了数值模拟。将数值结果与从电子散斑干涉测量 (ESPI) 测试中获得的实验数据进行比较，这些数据用于量化和检测断裂现象。由于近场动力学理论的内在特征，从数值模拟中获得了真实的裂纹模式和裂纹萌生角。在准静态条件下对缺口砂岩试样的破坏过程进行了数值模拟。将数值结果与从电子散斑干涉测量 (ESPI) 测试中获得的实验数据进行比较，这些数据用于量化和检测断裂现象。由于近场动力学理论的内在特征，从数值模拟中获得了真实的裂纹模式和裂纹萌生角。