This paper introduces the inclusion based boundary element method (iBEM) to calculate the elastic fields and effective modulus of a composite containing particles for both three dimensional (3D) and two dimensional (2D) cases. Considering a finite bounded domain containing many inclusions, the isotropic Green’s function has been used to obtain the elastic field caused by source fields on inclusion domains and applied loads on the boundary. Based on Eshelby’s equivalent inclusion method (EIM), the material mismatch between the particle and matrix phases is simulated with a continuously distributed source field, namely eigenstrain, on particles. Because explicit integrals can be obtained for ellipsoidal particles, no mesh is needed for those particles, which enables virtual experiments of a composite containing a large number of particles. The classic Eshelby’s tensor is extended from a constant eigenstrain for the single particle in the infinite domain to a form of a Taylor series for particle-boundary interaction and particle-particle interactions. Using the Hadamard regularization, the 2D formulation is derived from the 3D case by the integral of the elastic solution in the third direction together with an analytical circular harmonic potential integral scheme. The iBEM is particularly suitable to conduct virtual experiments for studying the local elastic field with the integrals of all sources and calculating the effective material properties by the volume average of local fields. A parametric study of accuracy on stress field for uniform, linear, quadratic eigenstrain fields was performed and case studies have been presented to demonstrate the capability of the iBEM for virtual experiments of composites. Some interesting discoveries of microstructure-dependent material behavior are reported with the aid of virtual experiments.

本文介绍了基于夹杂物的边界元方法（iBEM），以计算三维（3D）和二维（2D）情况下包含颗​​粒的复合材料的弹性场和有效模量。考虑到包含许多夹杂物的有限有界域，各向同性格林函数已用于获得由包含物域上的源场和边界上施加的载荷引起的弹性场。基于Eshelby的等效包含法（EIM），使用连续分布的源场（即特征应变）对粒子进行模拟，以模拟粒子相与基质相之间的材料失配。因为可以为椭圆形粒子获得显式积分，所以这些粒子不需要网格，从而可以对包含大量粒子的复合物进行虚拟实验。经典的Eshelby张量从无限域中单个粒子的恒定本征应变扩展为泰勒级数形式，用于粒子边界相互作用和粒子-粒子相互作用。使用Hadamard正则化，通过3维情况下的3D情况，通过弹性解在第三方向上的积分以及解析的圆形谐波势积分方案，可以得出2D公式。iBEM特别适合进行虚拟实验，以研究具有所有来源积分的局部弹性场，并通过局部场的体积平均值计算有效材料性能。对应力场的均匀性，线性，进行了二次特征应变场分析，并进行了案例研究，以证明iBEM在复合材料虚拟实验中的能力。在虚拟实验的帮助下，报告了一些与微观结构有关的材料行为的有趣发现。