裂纹扩展和连接过程的近场动力学数值模拟  

Numerical simulation of propagation and coalescence of cracks using peridynamic theory

作　　者：谷新保[1,2] 周小平[1] GU Xin-bao ZHOU Xiao-ping(College of Civil Engineering, Chongqing University, Chongqing 400015, China School of Civil Engineering, Sichuan University of Science ＆ Engineering, Zigong, Sichuan 643000, China)

机构地区：[1]重庆大学土木工程学院,重庆400015 [2]四川理工学院土木工程学院,四川自贡643000

出　　处：《岩土力学》2017年第2期610-616,共7页Rock and Soil Mechanics

基　　金：国家重点基础研究发展计划项目(973计划)(No.2014CB046903);国家自然科学基金资助项目(No.51325903;No.51279218);重庆市自然科学基金院士专项(No.cstc2013jcyjys30002);四川理工学院人才引进项目(No.2016RCL19);桥梁无损检测与工程计算四川省高校重点实验室2016年度开放基金项目(No.2016QYJ02)~~

摘　　要：利用传统应变能密度与近场动力学的应变能密度相等以及近场动力学的基本方程,推导了以状态为基础的近场动力学基本方程。引入损伤理论,对以状态为基础的近场动力学基本方程进行离散化,编制了近场动力学数值分析程序。利用近场动力学理论对经典的带孔单侧拉伸板破裂过程及双向拉伸状态下岩石裂纹扩展和连接过程进行了数值模拟,并与RFPA2D数值结果进行了对比分析。结果表明,以状态为基础的近场动力学理论不仅突破了以键为基础的近场动力学理论恒定泊松比的限制,而且不需要借助任何外部断裂准则就能很好地模拟裂纹的扩展和连接过程,相对于其他的数值模拟方法具有很大的优势,同时也给裂纹的扩展和连接的数值模拟提供了更好的思路。A fundamental equation of state-based peridynamic theory is derived firstly from equating the traditional strain energy density to peridynamic ones and using the peridynamic fundamental equation. This paper introduces the damage theory to the fundamental equation of state-based peridynamic theory, and discretizes the fundamental equation, and then develops a corresponding peridynamic numerical program. Then classical fracture process of a single side tensional plate with a circle hole and the propagation and coalescence of cracks in rock under biaxial tensile stress are simulated using the theory. Numerical results from state-based peridynamic theory are in good agreement with those from RFPA2 D. The results indicate that the state-based peridynamic theory not only breaks through the limitation of constant Poisson＇s ratio on bond-based peridynamic theory, but also efficiently simulates the propagation and coalescence of cracks without any external fracture criterion. Therefore, the state-based peridynamic theory has great advantage over other numerical methods, and it can also provide a better understanding of propagation and coalescence of cracks.

关 键 词：近场动力学理论 裂纹扩展和连接 数值模拟 

分 类 号：TU457[建筑科学—岩土工程]