Abstract A micropolar peridynamic model is presented for characterizing crack propagation in isotropic and orthotropic brittle materials. The analytical formulation of the two-dimensional model is based on the definition of a micropotential energy function that accounts for the four independent elastic constants that define orthotropy and that in the limit can be reduced to isotropy. A distinctive feature of the model is that the bonds’ elastic parameters are continuous functions of orientation with respect to principal material axes. By defining three deformation parameters that quantify bond stretch, bond shear deformation and particles relative rotation, the first continuum bond-based peridynamic model is obtained for two-dimensional Cauchy orthotropic materials characterized by four independent material moduli that is suitable for describing fracture as well as homogeneous and non-homogeneous deformations. The accuracy of the computational model as applied to crack-tip analyses is assessed by comparing the displacement and stress fields within the boundary layer that develops in the immediate vicinity of a crack with the analytical asymptotic results for an orthotropic continuum. The extension of such cracks when they are subjected to mixed-mode loading is simulated under the assumption of illustrative crack extension criteria, and the predictions are compared to those of the maximum hoop stress intensity factor criterion (HSIF-criterion) and the maximum energy release rate criterion (G-criterion).

中文翻译：

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各向同性和各向异性微极常动态固体中的裂纹扭结

摘要 提出了一种用于表征各向同性和正交各向异性脆性材料中裂纹扩展的微极近场动力学模型。二维模型的解析公式基于微势能函数的定义，该函数解释了定义正交各向异性的四个独立弹性常数，并且在极限情况下可以简化为各向同性。该模型的一个显着特点是键的弹性参数是相对于主材料轴的连续取向函数。通过定义量化键拉伸、键剪切变形和颗粒相对旋转的三个变形参数，第一个基于连续键的近场动力学模型是针对二维柯西正交各向异性材料获得的，其特征是四个独立的材料模量，适用于描述断裂以及均匀和非均匀变形。应用于裂纹尖端分析的计算模型的准确性是通过比较在裂纹附近形成的边界层内的位移和应力场与正交各向异性连续体的分析渐近结果来评估的。在说明性裂纹扩展标准的假设下，模拟这些裂纹在受到混合模式加载时的扩展，