求解三维固体结构裂纹扩展的有限质点法  

The Finite Particle Method for Solving Crack Propagation of Three-Dimensional Solids

作　　者：杨超[1,2] 张鹏飞 汪伟 罗尧治[1] Chao Yang;Pengfei Zhang;Wei Wang;Yaozhi Luo(College of Civil Engineering and Architecture,Zhejiang University,Hangzhou,310058;Innovation Center of Yangtze River Delta,Zhejiang University,Jiaxing,314100;MCC Huatian Engineering Technology Co.Ltd.,Nanjing,210019)

机构地区：[1]浙江大学建筑工程学院,杭州310058 [2]浙江大学长三角智慧绿洲创新中心,嘉兴314100 [3]中冶华天南京工程技术有限公司,南京210019

出　　处：《固体力学学报》2025年第1期39-53,共15页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金项目(52238001,52008366);国家重点研发计划资助项目(2021YFF0501000)资助.

摘　　要：对三维固体裂纹扩展的数值模拟一直是较为复杂的过程,裂纹路径的不可预知性使其计算求解相当繁琐且耗时.有限质点法是以向量力学为基础的一种结构复杂行为分析的新方法,本文将它与粘聚力模型相结合用于三维固体动态断裂问题的分析.该方法将固体域离散为质点群,允许通过自由增减质点实现从连续到非连续变形过程的模拟,处理裂纹扩展问题有独特优势.本文基于外加粘聚力模型构建有限质点法三维固体断裂的判别准则和粘聚元自动嵌入的断裂分析模式,提出一种基于遍历搜索的质点拓扑更新的通用处理方法,利用CUDA开发工具包编制三维固体断裂计算的GPU并行求解程序,并通过若干算例探讨方法和程序的有效性和正确性.Simulating three-dimensional(3D)crack propagation in solid structures poses significant challenges due to the unpredictability of crack paths,complicating both computation and solution strategies.Traditional methods often face difficulties in accurately capturing arbitrary crack propagation during large deformations.The finite particle method(FPM),based on vector mechanics,offers a novel numerical approach for analyzing complex behaviors in solid mechanics.Different from conventional continuumbased methods,FPM discretizes the solid domain into a collection of finite particles,each governed by Newton's second law of motion.This particle-based formulation enables seamless transitions between continuum and non-continuum behaviors by dynamically adding or removing particles,providing significant advantages for crack propagation analysis in both static and dynamic scenarios.In this study,the FPM is extended to address the dynamic fracture in 3D solids,focusing on the challenges related to crack initiation,propagation,and branching.The FPM is combined with an extrinsic cohesive zone model(CZM)to capture the complex behaviors of fractures,avoiding the need to pre-define crack paths and effectively managing discontinuities caused by crack propagation.A discriminant criterion is developed to identify the onset of crack initiation,and an automated embedding process for cohesive elements is implemented to enable real-time simulation of fracture surfaces.To manage the evolving topologies that arise from crack propagation,we propose a general strategy based on an ergodic search algorithm,which updates the connectivity of the discretized solid model dynamically as cracks evolve.In addition,we develop a GPU-based parallel solver using the CUDA toolkit to significantly accelerate fracture computations.The accuracy and applicability of the proposed method are validated through several numerical examples,including fracture simulations of plates and beams subjected to dynamic loading.The results demonstrate the capability of the me

关 键 词：三维固体 有限质点法 粘聚力模型 裂纹扩展 并行计算 

分 类 号：O346.1[理学—固体力学]