广义微极近场动力学模型及三维断裂行为模拟

A Generalized Micropolar Peridynamic Model and Its Simulation of Three-Dimensional Fracture Behaviors

摘要:

固体断裂破坏是一类非常复杂的现象，一直以来都是工程学科的经典难题。针对准脆性材料的三维断裂问题，提出一种广义微极近场动力学（GMPD）模型。首先，采用Timoshenko梁模拟物质点间的相互作用并建立了相应的控制方程，充分考虑三维条件下键的轴向变形、切向变形和相对转角；其次，引入分别对应键拉伸、剪切和转动刚度的键参数，保证复杂加载条件下近场动力学和传统连续介质力学的能量一致性；同时提出基于能量的新型断裂准则，推导出键轴向变形、切向变形以及相对转角的临界值，可以实现准脆性材料的破坏过程模拟；最后基于所提出的GMPD模型，对轴向压缩条件下准脆性材料的三维断裂过程进行模拟，通过将分析结果与试验结果进行对比，有效验证了本模型的正确性和精度，可以准确描述复杂加载条件下翼型裂纹、反翼型裂纹和次生裂纹等不同类型裂纹的萌生和扩展过程。

Abstract:

The fracture of solid is still a long-standing problem in engineering and computational mechanics， which is an extremely complex phenomenon. A generalized micropolar peridynamic （GMPD） model is proposed for the three-dimensional fracture problem of quasi-brittle materials. First， the governing equations of the bonds are established by employing the Timoshenko beam theory to simulate the interaction between material points， which considers axial deformation， tangential deformation， and the relative rotational angle of bonds. Then， three kinds of peridynamic parameters， corresponding to the tensile， the shear， and the bending stiffness of the bond， are introduced to keep the consistence of the strain energy obtained from the proposed peridynamic model and from the continuum mechanics under complex loading conditions. Moreover， a novel energy-based failure criterion， involving the maximum stretch， the shear strain， and the rotation angle limits of the bond， is proposed to describe the dynamic failure for quasi-brittle materials. Finally， the three-dimensional fracture processes of the quasi-brittle materials under axial compression loads are simulated by the proposed model. The proposed model is verified by comparisons of its results and those from experimental observations， which can accurately simulate the initiation and propagation processes of different types of cracks， such as wing crack， anti-wing crack， and secondary crack.