基于近场动力学的薄板弯曲大变形及断裂分析

薄板结构仅在较小的荷载下就能产生较大的位移、旋转,甚至引发结构产生裂纹并扩展,进而发生结构整体断裂,因此,建立薄板结构在大变形过程中的裂纹扩展及断裂仿真模型,具有重要的工程实际意义.文章建立了用于薄板结构几何大变形和断裂分析的近场动力学(PD)和连续介质力学(CCM)耦合模型.首先基于冯·卡门假设,采用更新的拉格朗日法得到薄板在几何大变形增量步下的虚应变能密度增量公式,并利用虚功原理和均质化假设求出几何大变形微梁键的本构模型参数;接着分别建立几何大变形薄板PD模型与CCM模型的虚应变能密度增量,并建立了薄板几何大变形PD-CCM耦合模型;最后模拟了薄板结构在横向变形作用下的渐进断裂过程,得到与实验结果高度一致的仿真结果,验证了所提出的几何非线性PD-CCM耦合模型的精度.结果表明:本文所提出的薄板PD-CCM耦合模型具有简单高效,无需考虑材料参数限制和边界效应的特点,可以很好地用于预测薄板结构在几何大变形过程中的局部损伤和结构断裂,有利于薄板结构的断裂安全评价和理论发展.

LARGE DEFORMATION AND FRACTURE ANALYSIS OF THIN PLATE BENDING BASED ON PERIDYNAMICS

Thin plate structures are widely used in the fields of automobiles, ships, and aerospace because of their excellent load-bearing performance, light weight and easy processing. However, in practical applications, thin plate structures often produce large displacement, rotation and even cause crack initiation and growth under small loads, and then the overall structure fractures. Therefore, it is of great engineering practical significance to establish a crack growth and fracture simulation model of thin plate structures in the process of large deformation. In this paper, a peridynamic (PD) and classical continuum mechanics (CCM) coupling model for geometrically nonlinear deformation and fracture analysis of thin plate structures is established. First of all, the updated Lagrangian formula is used to obtain the expression of virtual strain energy density increment of thin plates at each increment step in large deformation analysis under von Karman's hypothesis. Then, the PD constitutive parameters of geometrically nonlinear micro-beam bond are obtained by using the virtual work principle and homogenization hypothesis. After that, the virtual strain energy density increments of the PD model and CCM model for geometrically large deformation thin plate were respectively established, and the geometrically large deformation PD-CCM coupling model of the thin plate was established. Finally, the progressive fracture process of the thin plate structure under the action of lateral deformation is simulated, and the simulation results are highly consistent with the experimental results, which verifies the accuracy of the proposed geometrically nonlinear PD-CCM coupling model. It is shown that the proposed geometrically nonlinear PD-CCM coupling model is simple and efficient without restriction on material parameters and consideration of boundary effects, and can be well used to predict local damage and structural fracture of thin plate structures during geometrically large deformations. It is beneficial to the fracture safety evaluation and theoretical development of thin plate structures.