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 引用本文: 刘造保, 田锋, 周金鑫. 岩石脆性破坏全过程的准态基近场动力学方法. 力学学报, 2024, 56(5): 1395-1410.
Liu Zaobao, Tian Feng, Zhou Jinxin. Quasi-state-based peridynamics method for the whole process of rock brittle failure. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(5): 1395-1410.
 Citation: Liu Zaobao, Tian Feng, Zhou Jinxin. Quasi-state-based peridynamics method for the whole process of rock brittle failure. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(5): 1395-1410.

## QUASI-STATE-BASED PERIDYNAMICS METHOD FOR THE WHOLE PROCESS OF ROCK BRITTLE FAILURE

• 摘要: 近场动力学(peridynamics, PD)作为一种新兴方法, 正展现出成为一种分析复杂岩体力学响应方法的巨大潜力. 然而, 键基近场动力学与连续介质力学联系薄弱, 缺乏对岩石多类型断裂模式和峰后行为的处理能力, 而且接触-摩擦模型严重简化. 为此, 提出了一种准态基近场动力学方法. 首先, 通过基于键型区分的力密度计算方法, 实现了键的应力张量计算, 加深了其与连续介质力学的联系; 然后, 提出了一种通用式的断裂准则引入思路, 推导了一种适于当前理论的单直线型虚拟裂缝模型, 实现了对岩石多类型脆性破坏的全过程模拟; 最后, 通过粒子网格孪生算法, 实现了不同介质状态的物质点和孪生网格的同步处理, 通过势函数和库伦摩擦定律, 实现了对各类接触情形和接触程度的准确判断和表征, 并增加了考虑摩擦系数的摩擦力密度计算. 已有算例表明, 模拟结果与实验结果的吻合程度很高. 这使得完善后的近场动力学的近场动力学处理非连续介质形成-演化过程的能力得到了有效提升, 扩充了原有的理论框架和适用范围.

Abstract: Peridynamics (PD), as an emerging methodology, is demonstrating substantial potential as a means to analyze the mechanical responses of complex rock formations. However, the bond-based peridynamics method exhibits weak connections with continuum mechanics (CM). It cannot handle multiple fracture modes and post-peak behavior in rocks and significantly oversimplifies the contact-friction model. The calculation system of state-based peridynamics is more complex and less stable. Therefore, this paper proposed a quasi-state-based peridynamics method. This paper first achieves a simultaneous calculation of bond force density and stress tensor by employing a force density calculation method that distinguishes based on bond types, thereby deepening its association with continuum mechanics. Subsequently, a general criterion introduction approach (e.g., maximum tensile stress criterion and Mohr-Coulomb criterion) is provided, leading to the derivation of a single linear fictitious crack model suitable for the current theoretical framework. This enables a comprehensive simulation of multiple types of brittle failure in rock materials. Finally, using a particle mesh twin algorithm, binding fracture criterion and the discretization process of twin meshes, simultaneous calculations of material points and twin meshes in different medium states are accomplished. Through potential function and Coulomb's friction law, accurate assessments and characterizations of contact situations and degrees are achieved, incorporating friction force density calculations considering the friction coefficient. Case studies demonstrate a good agreement between simulation results and experimental outcomes. This signifies a significantly improved capability of the refined peridynamics in handling the formation-evolution processes of discontinuous media, thereby substantially broadening its original theoretical framework and applicability.

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