高速运动裂纹扩展和分叉现象的近场动力学数值模拟  

Numerical Simulation of High-Speed Crack Propagating and Branching Phenomena Based on Peridynamics

作　　者：谷新保[1,2] 周小平[1] 徐潇[1] 

机构地区：[1]重庆大学土木工程学院,重庆400045 [2]四川工学院土木工程学院.四川自贡643000

出　　处：《应用数学和力学》2016年第7期729-739,共11页Applied Mathematics and Mechanics

基　　金：国家重点基础研究发展计划(973计划)(2014CB046903);国家自然科学基金(51325903,51279218);重庆市自然科学基金(院士专项)(cstc2013jcyjys30002);教育部博士点专项基金(20130191110037);四川省科技厅资助项目(2016GFW0137)~~

摘　　要：首先介绍了近场动力学的基本理论,然后以两个实例分析了高速运动裂纹的扩展及分叉现象.分析了近场动力学参数(邻域半径、相邻节点距)及外部参数(材料的弹性模量、密度、温度改变量)等对裂纹分叉的速度和角度的影响并进行了对比分析,数值结果表明:随着邻域半径的增大,裂纹传播速度逐渐减少而裂纹分叉角度逐渐增加;随着相邻节点间距的增加,裂纹的传播速度逐渐减少而裂纹分叉角度也逐渐减少;裂纹分叉长度偏向于弹性模量小和密度大的材料;裂纹传播速度随着弹性模量差值的增大而增大,随着密度差值的减小而增大,同时随着外界温度改变量的增大而减少.近场动力学能自发地模拟裂纹扩展和分叉,不需要借助任何外部准则,不需要预先设置裂纹扩展路径,因此它具有天然的优势.The peridynamic theory was first introduced,then 2 examples of high-speed crack propagating and branching phenomena were given and investigated. The effects of peridynamic parameters including the neighbourhood radius and the grid spacing,and such external parameters as the material elastic modulus,the material density and the temperature difference,on the crack propagating velocity and the crack branching angle were analyzed. It is found from the numerical results that the crack propagating velocity decreases and the crack branching angle increases with the neighbourhood radius; both the crack propagating velocity and the crack branching angle decrease with the grid spacing; the crack branching length in the material of a smaller elastic modulus and a larger density is longer; the crack propagating velocity increases with the elastic modulus difference; the crack propagating velocity increases as the materials＇ density difference decreases,and decreases with the temperature difference. Moreover,the crack propagating and branching process can be simulated with the peridynamic method spontaneously,without any outer criterion and preset crack propagating paths. Therefore,peridynamics has natural advantages in the simulation of high-speed crack propagating and branching phenomena.

关 键 词：近场动力学理论 高速运动裂纹 扩展和分叉现象 数值模拟 

分 类 号：O317[理学—一般力学与力学基础] V214.9[理学—力学]