椭球粒子的本征应变边界积分方程与局部Eshelby 矩阵

doi:10.3969/j.issn.1007-2861.2014.01.039

上海大学学报(自然科学版) ›› 2015, Vol. 21 ›› Issue (03): 344-355.doi: 10.3969/j.issn.1007-2861.2014.01.039

椭球粒子的本征应变边界积分方程与局部Eshelby 矩阵

马杭^1, 方静波²

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

收稿日期:2013-12-24 出版日期:2015-06-22 发布日期:2015-06-22
通讯作者: 马杭(1951—), 男, 教授, 博士生导师, 研究方向为计算固体力学. E-mail: hangma@staff.shu.edu.cn E-mail:hangma@staff.shu.edu.cn
作者简介:马杭(1951—), 男, 教授, 博士生导师, 研究方向为计算固体力学. E-mail: hangma@staff.shu.edu.cn
基金资助:
国家自然科学基金资助项目(11272195, 11332005)

Eigenstrain boundary integral equation with local Eshelby matrix for ellipsoidal particles

MA Hang¹, FANG Jing-bo²

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

Received:2013-12-24 Online:2015-06-22 Published:2015-06-22

摘要/Abstract

摘要： 针对粒子增强材料的大规模数值模拟问题, 将局部Eshelby 矩阵的概念引入到本征应变边界积分方程计算模型中, 以解决粒子间的相互作用问题. 局部Eshelby 矩阵可以看作Eshelby 张量和等效夹杂物的概念在数值方面的一种拓广. 以全空间边界元子域法为参照, 利用计算模型对无限域中的若干椭球粒子进行了三维应力分析. 数值算例不仅验证了模型的正确性和方法的可行性, 也表现出较高的计算效率, 说明该计算模型和方法具有对粒子增强材料进行大规模数值分析的能力.

关键词: Eshelby 张量, 本征应变, 等效夹杂物, 近场粒子, 局部Eshelby矩阵

Abstract: Aiming at large scale numerical simulation of particle reinforced materials, a concept of local Eshelby matrix is introduced into a computational model of the eigenstrain boundary integral equation to solve the problem of interactions among particles. The local Eshelby matrix can be considered as an extension of Eshelby tensor and an equivalent inclusion in a numerical form. Taking the sub-domain boundary element method as the control, three-dimensional stress analyses are carried out for some ellipsoidal particles in infinite media with the proposed computational model. Numerical examples verify correctness, feasibility and high efficiency of the present model with the corresponding solution procedure, showing potential of solving large scale numerical simulations for particle reinforced materials.

Key words: eigenstrain, equivalent inclusion, Eshelby tensor, local Eshelby matrix, near field particle

中图分类号:

O 241

马杭1, 方静波2. 椭球粒子的本征应变边界积分方程与局部Eshelby 矩阵[J]. 上海大学学报(自然科学版), 2015, 21(03): 344-355.

MA Hang-1, FANG Jing-Be-2. Eigenstrain boundary integral equation with local Eshelby matrix for ellipsoidal particles[J]. Journal of Shanghai University（Natural Science Edition）, 2015, 21(03): 344-355.

参考文献

[1] Eshelby J D. The determination of the elastic field of an ellipsoidal inclusion and related problems [J]. Proceedings of the Royal Society of London Series A: Mathematical and Physical

Sciences, 1957, A241(1226): 376-396.

[2] Mura T, Shodja H M, Hirose Y. Inclusion problems (part 2) [J]. Applied Mechanics Review,1996, 49(10): S118-S127.

[3] Kiris A, Inan E. Eshelby tensors for a spherical inclusion in microelongated elastic fields [J]. International Journal of Engineering Science, 2005, 43: 49-58.
[4] Mercier S, Jacques N, Molinari A. Validation of an interaction law for the Eshelby inclusion problem in elasto-viscoplasticity [J]. International Journal of Solids and Structures, 2005, 42:

1923-1941.

[5] Shen L X, Yi S. An effective inclusion model for effective moluli of heterogeneous materials with ellipsoidal inhomogeneities [J]. International Journal of Solids and Structures, 2001, 38:

5789-5805.

[6] Pan E. Elastic or piezoelastic fields around a quantum dot: fully coupled or semicoupled model? [J] Journal of Applied Physics, 2002, 91(6): 3785-3796.

[7] Ma H, Deng H L. Nondestructive determination of welding residual stresses by boundary element method [J]. Advances in Engineering Software, 1998, 29: 89-95.

[8] Ma H, Guo Z, Dhanasekar M, et al. Efficient solution of multiple cracks in great number using eigen COD boundary integral equations with iteration procedure [J]. Engineering Analysis

with Boundary Elements, 2013, 37(3): 487-500.

[9] Kakavas P A, Kontoni D N. Numerical investigation of the stress field of particulate reinforced polymeric composites subjected to tension [J]. International Journal for Numerical Methods in Engineering, 2006, 65: 1145-1164.

[10] Lee J, Choi S, Mal A. Stress analysis of an unbounded elastic solid with orthotropic inclusions and voids using a new integral equation technique [J]. International Journal of Solids and

Structures, 2001, 38: 2789-2802.

[11] Dong C Y, Cheung Y K, Lo S H. A regularized domain integral formulation for inclusion problems of various shapes by equivalent inclusion method [J]. Computer Methods in Applied

Mechanics and Engineering, 2002, 191(31): 3411-3421.

[12] Nakasone Y, Nishiyama H, Nojiri T. Numerical equivalent inclusion method: a new computational method for analyzing stress fields in and around inclusions of various shapes [J].

Materials Science and Engineering, 2000, A285: 229-238.

[13] Greengard L F, Rokhlin V. A fast algorithm for particle simulations [J]. Journal of Computational Physics, 1987, 73: 325-48.

[14] Liu Y J, Nishimura N, Tanahashi T, et al. A fast boundary element method for the analysis of fiber-reinforced composites based on a rigid-inclusion model [J]. ASME Journal of Applied

Mechanics, 2005, 72: 115-128.

[15] Ma H, Yan C, Qin Q H. Eigenstrain formulation of boundary integral equations for modeling particle-reinforced composites [J]. Engineering Analysis with Boundary Elements, 2009, 33(3): 410-419.

[16] Ma H, Xia L W, Qin Q H. Computational model for short-fiber composites with eigen-strain formulation of boundary integral equations [J]. Applied Mathematics and Mechanics, 2008,

29(6): 757-767.

[17] Ma H, Fang J B, Qin Q H. Simulation of ellipsoidal particle-reinforced materials with eigenstrain formulation of 3D BIE [J]. Advances in Engineering Software, 2011, 42(10): 750-759.

[18] Chen Y Z. Boundary integral equation method for two dissimilar elastic inclusions in an infinite plate [J]. Engineering Analysis with Boundary Elements, 2012, 36(1): 137-146.

椭球粒子的本征应变边界积分方程与局部Eshelby 矩阵

Eigenstrain boundary integral equation with local Eshelby matrix for ellipsoidal particles

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