摘要
在线性断裂力学的理论中,路径无关积分发挥着重要作用,然而,对于M积分的物理意义的解释上还有一些问题,需要进一步研究。本文从理论上研究了三维裂纹损伤脆性固体中M积分与总势能变化关系,通过一个理论的推导方法得到了在三维问题中M积分与总势能变化(CTPE)之间隐含的关系,即M=3CTPE。从这个关系当中得到如下结论:对于事先存在的裂纹引起的系统的能量变化,M积分提供的能量释放的物理解释比能量释放率更加自然、合理。本结论可以进一步被深化研究到所有脆性固体材料的损伤和断裂的描述中去,如混凝土、岩石等。
Within the framework of linear fracture mechanics, it is well known that the M-integral plays an important role in the fracture analysis. However, there still exist some questions in its physical interpretation, so the M-integral is still necessary to be investigated further. Here, the relation between the M-integral and the Change of Total Potential Energy （CTPE） is studied theoretically in brittle solids with three dimensional crack damage. The implicit relation between the M-integral and CTPE for three-dimensional solids, i.e. M = 3CTPE, is obtained by a theoretical derivation procedure, from which it is concluded that the M-integral may provide a more natural description obout the potential energy release due to the formation of the pre-existing microcracks, rather than the description about the release rute of total potential energy release rate. This conclusion can be further extended to the description about either damage or fracture behaviors for all brittle solids such as concrete, rocks, etc.
出处
《水利与建筑工程学报》
2009年第1期36-38,共3页
Journal of Water Resources and Architectural Engineering
基金
西安理工大学博士启动基金项目(106-220602)
关键词
三维固体
断裂
裂纹
路径无关积分
M积分
总势能
three-dimensional solid
fracture
crack
path-independent integral
M-integral
total potential energy
