三维实体和壳体中裂纹任意扩展与分叉的扩展有限元研究

The project aims to develop the theoretical model, calculation method and programs for the Extended Finite Element Method (XFEM), which is used to simulate and study the phenomena of crack propagation and branching in the three-dimensional(3D) solids and curved shells. The simulation of crack branching in the process of dynamic crack propagation is carried out by establishing the level set function and shape function in branching elements，two-dimensional crack branching criterion and developing XFEM programs. The 3D solid element-based XEEM formula is established in order to calculate the stress intensity factor and energy release rate for 3D crack. The crack propagation and branching criteria are set up, thus the crack arbitrary propagation and branching in 3D solid can be simulated. The XFEM method based on continuum-based (CB) shell elements is developed for the analysis and simulation of crack propagation in bi-material curved shells. The mechanism is investigated for the equilibrium crack propagation in the shell. Then, the influences of material modulus, load condition, geometric scale, constraint and position of the hole are studied. By establishing and developing the theoretical model, calculation method and finite element program, we will simulate the crack arbitrary propagation and branching in 3D solid structures and curved shells. The simulation of crack propagation is following its natural selection, which is reproduced the original failure behavior.

本项目旨在发展扩展有限元的理论模型、计算方法和程序，研究三维实体和曲面壳体中的裂纹扩展和分叉机理。建立含分叉单元的水平集函数和扩充形函数，提出平面二维裂纹分叉准则，发展二维扩展有限元算法和计算程序，模拟动态裂纹扩展过程中的分叉现象；建立基于三维实体单元的扩展有限元计算格式，实现对三维应力强度因子和能量释放率的计算，引入三维裂纹扩展和分叉准则，模拟三维实体中裂纹沿任意路径扩展或发生分叉的过程；将基于连续体壳单元的扩展有限元算法应用于双材料壳体，模拟在曲面壳体中双材料亚界面裂纹扩展的机理，确立材料模量、载荷条件、几何尺度、约束条件和开孔位置等因素对裂纹扩展的影响规律。通过建立理论模型和计算方法，编写计算程序，发展模拟裂纹在三维实体和曲面壳体中的任意扩展和分叉行为，真实地实现裂纹扩展的自然选择。

时至今日，壳体结构中三维裂纹沿曲线或不规则路径扩展的问题，仍是棘手的力学难题。在大变形框架下，提出针对壳体结构断裂力学的理论模型和计算方法，尤其在壳体上要使裂纹任意扩展，不受单元网格分布限制，是计算固体力学领域的前沿问题，极具挑战性。. 本基金项目在国际上首次提出基于大变形连续体壳的曲面壳体断裂扩展有限元的理论模型与计算方法，该方法具有以下特点：一是连续体壳（CB壳）单元的变形建立在三维实体单元基础上，可以考虑壳体厚度改变，同时适用于薄壳与中厚壳，实现了壳体断裂理论与数值模型的统一；二是允许裂纹在单元内部或穿过单元，可以在规则网格上计算路径复杂的裂纹，无需预先给定扩展路径，可实现裂纹任意扩展，且在扩展过程中无需重新划分单元网格；三是可以处理裂纹面不垂直于中面的情况；四是通过扩充形函数的特性捕捉裂纹尖端奇异场，可在较稀疏的网格分布下得到较高精度的计算结果。