岩土体大变形分析的Cosserat-粒子有限元法  

Cosserat-particle finite element method for large deformation analysis of rock and soil

作　　者：唐洪祥[1] 崔家铭 张雪 张磊[1] 刘乐天 TANG Hongxiang;CUI Jiaming;ZHANG Xue;ZHANG Lei;LIU Letian(Dalian University of Technology,State Key Laboratory of Coastal and Offshore Engineering,Dalian 116024,China;Northwest Survey,Design and Research Institute,Power Construction Corporation of China,Xi'an 710100,China;Department of Civil Engineering and Industrial Design,University of Liverpool,Liverpool,L693BX,UK;Dalian Wanda Sports Culture Tourism Development Company,Dalian 116000,China)

机构地区：[1]大连理工大学海岸和近海工程国家重点实验室,辽宁大连116024 [2]中国电建集团西北勘测设计研究院有限公司,陕西西安710100 [3]利物浦大学土木工程与工业设计系,利物浦L693BX [4]连万达体育文化旅游开发有限公司,辽宁大连116000

出　　处：《岩土工程学报》2023年第3期495-502,共8页Chinese Journal of Geotechnical Engineering

基　　金：国家自然科学基金项目(51890912,51979025)。

摘　　要：粒子有限元法(PFEM)既继承了有限元法坚实的数学基础,又具有模拟大变形、复杂边界问题的能力,在流固耦合、岩土工程领域有广泛的应用。但另一方面,岩土体在大变形过程中往往具有应变软化特性和应变局部化现象,为保持问题求解的适定性,需要在本构方程中引入正则化机制,采用Cosserat连续体理论是引入正则化机制有效方法之一。将PFEM计算方法与Cosserat连续体理论结合,发展了Cosserat-PFEM方法。与传统PFEM中使用三角形单元不同,提出的新方法将边界识别、网格划分相互独立进行,使得四边形等单元的使用成为可能,以提高数值求解的精度与克服三角形单元对应变局部化问题模拟的倾向性。算例表明,本文发展的Cosserat-PFEM方法及基于ABAQUS软件开发的程序是可靠和有效的,拓展了PFEM的应用范围,具有模拟大变形问题并保持问题适定性的能力,适用于大变形渐进破坏问题的模拟。The particle finite element method(PFEM) inherits the solid mathematical foundation of the finite element method and possesses the capability of modeling the problems with large deformation and complex boundary, so it has been widely used in the fields of fluid-structure coupling and geotechnical engineering. While in the process of large deformation of rock and soil, strain softening and strain localization often occur. In order to keep the well-posedness for the large deformation problem, it is necessary to introduce the regularization mechanism into the constitutive equation. The Cosserat continuum theory is one of the effective methods to introduce the regularization mechanism. Combining the PFEM with the Cosserat continuum theory, the Cosserat-PFEM method is developed. Besides, unlike the traditional PFEM using triangular elements, in the Cosserat-PFEM method the boundary recognition and the mesh generation are carried out independently, which makes it possible to use quadrilateral elements, so as to improve the numerical accuracy and overcome the tendency of triangular elements to simulate the strain localization. The examples show that the developed Cosserat-PFEM method and the programme explored based on the ABAQUS software are reliable and efficient, and expand the application scope of the PFEM. It is also demonstrated that the Cosserat-PFEM has the capability to simulate large deformation problems and keep the well-posedness of the problems, and is suitable for the simulation of large deformation and progressive failure problems.

关 键 词：粒子有限元 Cosserat连续体 边界识别 大变形 四边形单元 

分 类 号：TU435[建筑科学—岩土工程]