Contact problems are ubiquitous in engineering systems. Establishing contact models to predict the crack propagation and fracture is significant. Therefore, the present study proposes two peridynamic contact models for two-dimensional (2D) and three-dimensional (3D) contact problems based on the micro-beam bond and the Hertz theory, using the relative position of particles and the contact micromoduli to calculate the contact forces. Firstly, the strain is generated on the contact surface when two bodies come into contact. Simultaneously, the contact stiffness is obtained by the Hertz theory, and the contact forces are calculated according to the relationship between the strain of contact surface and the contact stiffness. Next, based on the peridynamic theory, the contact horizon and contact micromoduli are defined for the calculation of contact forces. Finally, the contact micromoduli for 2D and 3D contact problems are derived by equating the contact forces obtained from both theories. Additionally, this study defines the correction coefficients to reduce the calculation error of the proposed models and investigates the influence of different contact horizons on the calculation of contact forces. To validate the effectiveness of the proposed contact models, three numerical examples are compared with the results from the finite element method or experiments. It is demonstrated that the proposed contact models accurately calculate the contact forces and predict the crack propagation.

中文翻译：

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基于微梁粘结的断裂分析近场动力学接触模型


接触问题在工程系统中普遍存在。建立接触模型来预测裂纹扩展和断裂具有重要意义。因此，本研究提出了基于微梁键合和赫兹理论的二维（2D）和三维（3D）接触问题的两种近场动力学接触模型，利用粒子的相对位置和接触微模量来计算接触力。首先，当两个物体接触时，接触表面上会产生应变。同时，通过赫兹理论得到接触刚度，并根据接触面应变与接触刚度之间的关系计算接触力。接下来，基于近场动力学理论，定义接触层和接触微模量来计算接触力。最后，通过使从两种理论获得的接触力相等，得出 2D 和 3D 接触问题的接触微模量。此外，本研究定义了修正系数以减少所提出模型的计算误差，并研究了不同接触层位对接触力计算的影响。为了验证所提出的接触模型的有效性，将三个数值例子与有限元方法或实验的结果进行了比较。结果表明，所提出的接触模型可以准确计算接触力并预测裂纹扩展。