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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。
Based on the fact that the equivalent strain energy density of near strain and near-field dynamics and the basic equations of near-field dynamics derive the state-based basic dynamics of near-field dynamics. The damage theory is introduced to discretize the basic state-based near-field dynamics equations and a numerical program for near-field dynamics is developed. The near-field dynamics theory is used to simulate the crack propagation process and the crack propagation and connection process under the condition of biaxial tensile test. The numerical simulation results are compared with those of RFPA2D. The results show that the state-based near-field dynamics theory not only breaks the limit of the constant-Poisson ratio of the near-field kinetic theory based on the bond, but also simulates the crack propagation well without any external fracture criterion Compared with other numerical simulation methods, this method has great advantages and provides a better idea for crack propagation and numerical simulation of connection.