近场动力学法频散特性及其在岩石层裂分析中应用

Dispersion characteristics of peridynamics method and its application to spalling analysis of rock

摘要:

为了解近场动力学方法（peridynamics，PD）的计算精度，考察该法用于岩石层裂破坏模拟的效果，对PD进行了频散分析和算法验证.首先由频散分析后发现：当空间步长不变时，随影响域变大PD法频散愈严重；而空间步长减小时，影响域节点数不变，其频散会变弱；当影响域大小不变时，内部划分节点越密集，频散越弱.其次，通过该方法与传统有限差分法的比较表明PD离散方程可看作一系列差分方程的组合，其截断误差为影响域半径δ的二阶无穷小；当δ为Δx时，PD算法与中心差分法是等价的，且此时计算精度最高.最后，通过PD法应用于岩杆一维层裂模拟分析，探讨了其空间步长、影响域尺寸对计算结果的影响，得出层裂时间、层裂位置及损伤分布情况，并与层裂试验进行对比分析.PD可用于岩石层裂破坏分析，将FDM和PD法两者结合进行层裂模拟时，计算时间少、优势明显.

Abstract:

The dispersion characteristics of PD is carried out to figure out the accuracy of peridynamics method (PD) and its simulation effects on rock spalling. Firstly, based on the dispersion analyses of the PD discrete equations, it is found that the numerical dispersion is more apparent with increasing the domain size if the space step is fixed; with the number of nodes in the domain fixed, the numerical dispersion becomes weaker when the space step decreases; the numerical dispersion also gets weaker with the increase of the nodes at a fixed domain. Subsequently, by comparing it to the traditional finite difference method, it is pointed out that the PD discrete equations can be written as the combination of a series of differential equations, whose truncation error is the second order infinitesimal of the domain radius (δ); when δ is set as the space step, PD method is equivalent to the central difference method, owning the highest calculational accuracy. Finally, the PD method is used to explore the one-dimensional spalling phenomenon of rock bar. The effects of space step and domain size on computing results are discussed, and the spalling time, spalling locations and damage distribution are further given. The effectiveness of PD method is also verified by contrast with the spalling test. It is shown that PD can be used for rock spalling analysis and high-precision results can be obtained by PD method coupled with FDM, costing less time and owning a clear advantage.