分布粘聚元的系统理论研究  

RESEARCH ON DISTRIBUTED COHESIVE ELEMENT METHOD

作　　者：辛克贵[1] 何铭华[1] 

机构地区：[1]清华大学土木工程系,土木工程安全与耐久教育部重点实验室,北京100084

出　　处：《工程力学》2011年第A02期109-128,共20页Engineering Mechanics

基　　金：国家自然科学基金项目(50878117),国家自然科学基金重点项目(51038006);清华大学自主科研计划项目(2010081766)

摘　　要：该文扼要地阐述了一种新型计算方法分布粘聚元的研究意义、理论体系和部分研究进展。粘聚元法通过释放传统有限元的刚性粘聚,将连续体离散为满足连续介质条件的体单元以及位于单元边界处的粘聚元相结合的增广体系。基于分区混合广义变分原理建立了分布粘聚元增广体系的分区广义势能泛函,建立了分布粘聚元的控制方程列式。从动量定理入手建立了分布粘聚元的动力平衡控制方程,考虑惯性影响,以满足分析动态裂纹拓展的需求。从离散的角度建立了多键氛围叠加法BAS;在BAS的基础上,结合EAM理论推导建立了多尺度的嵌入原子超弹性本构EAH,在纳观尺度上给出了多尺度应力计算的封闭解。从算例的角度给出了不同加载速率下带预制裂纹的试件的任意裂纹拓展结果,验证了分布粘聚元在断裂分析以及多尺度分析的有效性。The research significance, theory foundation and some advances of a distributited cohesive element method, as a new numerical method, is reported briefly. By releasing the rigid cohesive constraint of conventional finite element methods, the continuum is discretized as an augmented system consisting of bulk elements and distributed cohesive elements. Based on a generalized sub-region mixed variational principle, the generalized sub-region mixed potential functional of the augmented system and the governing equations of the distributed cohesive element method are derived. Considering the inertia effect during dynamic fracture, the equation of motion for the distributed cohesive element method is derived, based on linear momentum balance. To establish a discrete constitutive model, a multi-Bond Atmosphere Superposition （BAS） model is proposed. By combining EAM and BAS, a multiscale Embedded Atom Hyperelastic （EAH） model is established and it is the closed-form solution for nanoscale stress calculation. Two numerical examples are presented to demonstrate the capacity of the distributed cohesive element method in an arbitrary crack propagation simulation.

关 键 词：广义协调元 分布粘聚元 多键氛围叠加法 嵌入原子超弹性(EAH)分区混合势能泛函 多尺度分析 EEB估计 无网格法 离散单元法 裂纹长度偏差 裂纹相似度偏差 裂纹Hausdorff距离 

分 类 号：O241[理学—计算数学] O346[理学—数学]