本征边界积分方程法模拟含流体粒子固体的性能

doi:10.12066/j.issn.1007-2861.2090

上海大学学报(自然科学版) ›› 2020, Vol. 26 ›› Issue (5): 790-801.doi: 10.12066/j.issn.1007-2861.2090

本征边界积分方程法模拟含流体粒子固体的性能

周吉成¹, 和东宏¹, 马杭²()

1.上海大学上海市应用数学和力学研究所, 上海 200072
2.上海大学理学院, 上海 200444

收稿日期:2018-08-14 出版日期:2020-10-30 发布日期:2020-11-06
通讯作者: 马杭 E-mail:hangma@staff.shu.edu.cn
基金资助:
国家自然科学基金资助项目(11672173);国家自然科学基金资助项目(11272195)

Modelling solids with fluid-filled pores using eigenstrain formulation of boundary integral equations

ZHOU Jicheng¹, HE Donghong¹, MA Hang²()

1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
2. College of Sciences, Shanghai University, Shanghai 200444, China

Received:2018-08-14 Online:2020-10-30 Published:2020-11-06
Contact: MA Hang E-mail:hangma@staff.shu.edu.cn

摘要/Abstract

摘要：

针对含流体粒子固体问题, 将 Eshelby 的本征应变和等效夹杂理论引入边界积分方程中, 提出含大量流体粒子固体的本征应变边界积分方程的计算模型及迭代算法. 通过全空间中多粒子近场群的定义, 在本征应变边界积分方程中引入局部 Eshelby 矩阵, 以解决粒子间相互作用的问题, 从而保证了迭代计算的收敛性. 通过数值算例的比较, 验证了计算模型的正确性和计算方法的可行性, 其中对于全空间单个圆形粒子的情况采用了解析解作为比较基准, 其他情况则采用子域边界积分方程法的结果作为比较基准. 采用代表性体积单元(representative volume element, RVE)模拟了含流体粒子固体材料的整体力学性能, 对含有 1 000 多个流体粒子的 RVE 在粒子规则分布和随机分布的条件下进行了计算, 验证了本计算模型和算法的可行性和高效率.

关键词: 流体粒子, 本征应变, Eshelby 张量, 等效夹杂, 局部 Eshelby 矩阵

Abstract:

In view of the fact that elastic solids contain fluid-filled pores, Eshelby's idea of eigenstrain and equivalent inclusion has been incorporated into the boundary integral equations (BIE), and as a result, the computational model of eigenstrain boundary integral equations and the corresponding iterative solution procedures are presented in the paper for the numerical simulation of solids with fluid-filled pores in great number. In order to guarantee the convergence of iteration sufficiently, the local Eshelby matrix has been proposed and constructed from the BIE combined with Eshelby's idea. The feasibility and effectiveness of the proposed computational model are verified in comparison with the results of the analytical solution in the case of a single circular fluid-filled pore in full space and of the subdomain BIE in other cases. The overall mechanical properties of solids are computed using a representative volume element (RVE) with more than one thousand fluid-filled pores distributed either regularly or randomly with the proposed computational model, showing the feasibility and high efficiency of the present model and the solution procedures.

Key words: fluid-filled pores, eigenstrain, Eshelby tensor, equivalent inclusion, local Eshelby matrix

中图分类号:

O241

周吉成, 和东宏, 马杭. 本征边界积分方程法模拟含流体粒子固体的性能[J]. 上海大学学报(自然科学版), 2020, 26(5): 790-801.

ZHOU Jicheng, HE Donghong, MA Hang. Modelling solids with fluid-filled pores using eigenstrain formulation of boundary integral equations[J]. Journal of Shanghai University（Natural Science Edition）, 2020, 26(5): 790-801.

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本征边界积分方程法模拟含流体粒子固体的性能

Modelling solids with fluid-filled pores using eigenstrain formulation of boundary integral equations

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