中文摘要：

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。

英文摘要：

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.