Solutions of the elastic fields in a half-plane region containing multiple inhomogeneities with the equivalent inclusion method and the applications to properties of composites

2019 ◽  
Vol 230 (5) ◽  
pp. 1529-1547 ◽  
Author(s):  
Xiangxin Dang ◽  
Yingjie Liu ◽  
Linjuan Wang ◽  
Jianxiang Wang
Keyword(s):  
Half Plane ◽  
Plane Region ◽  
Elastic Fields ◽  
Equivalent Inclusion Method ◽  
Inclusion Method ◽  
Equivalent Inclusion ◽  
Properties Of Composites

Elastic Fields of Interacting Elliptical Inhomogeneities for Two-Dimensional Problems Based on the Equivalent Inclusion Method

2014 ◽  
Vol 501-504 ◽  
pp. 2515-2519
Author(s):  
Jiong Zhang ◽  
Qi Qing Huang ◽  
Zhan Qu
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Two Dimensional ◽  
Element Analysis ◽  
Numerical Examples ◽  
Elastic Fields ◽  
Equivalent Inclusion Method ◽  
Inclusion Method ◽  
Equivalent Inclusion ◽  
The Finite Element Analysis

In this paper, the equivalent inclusion method is used to calculate the elastic fields of a two-dimensional plate containing any number of ellipitical inhomogeneities. Both the interior and the exterior Eshelbys tensors are used in this method. Numerical examples are given to assess the performance of the presented method. The solutions obtained with this method have been checked and confirmed by the finite element analysis results.

Eshelby Equivalent Inclusion Method for Composites with Interface Effects

2006 ◽  
Vol 312 ◽  
pp. 161-166 ◽  
Author(s):  
H.L. Duan ◽  
Xin Yi ◽  
Zhu Ping Huang ◽  
J. Wang
Keyword(s):  
Effective Properties ◽  
Stress Fields ◽  
Hydrostatic Loading ◽  
Equivalent Inclusion Method ◽  
Inclusion Method ◽  
Equivalent Inclusion ◽  
Linear Spring ◽  
Eshelby Equivalent Inclusion Method ◽  
Interface Effects ◽  
Properties Of Composites

The Eshelby equivalent inclusion method is generalized to calculate the stress fields related to spherical inhomogeneities with two interface conditions depicted by the interface stress model and the linear-spring model. It is found that the method gives the exact results for the hydrostatic loading and very accurate results for a deviatoric loading. The method can be used to predict the effective properties of composites with the interface effects.

A Method to Evaluate the Elastic Properties of Ceramics-Enhanced Composites Undertaking Interfacial Delamination

2007 ◽  
Vol 336-338 ◽  
pp. 2513-2516
Author(s):  
Hua Jian Chang ◽  
Shu Wen Zhan
Keyword(s):  
Composite Materials ◽  
Present Method ◽  
Present Model ◽  
Constitutive Law ◽  
Layer Model ◽  
Interfacial Delamination ◽  
Equivalent Inclusion Method ◽  
Equivalent Inclusion ◽  
Micromechanical Approach ◽  
Properties Of Composites

A micromechanical approach is developed to investigate the behavior of composite materials, which undergo interfacial delamination. The main objective of this approach is to build a bridge between the intricate theories and the engineering applications. On the basis of the spring-layer model, which is useful to treat the interfacial debonding and sliding, the present paper proposes a convenient method to assess the effects of delamination on the overall properties of composites. By applying the Equivalent Inclusion Method (EIM), two fundamental tensors are derived in the present model, the modified Eshelby tensor, and the compliance tensor (or stiffness tensor) of the weakened inclusions. Both of them are the fundamental tensors for constructing the overall constitutive law of composite materials. By simply substituting these tensors into an existing constitutive model, for instance, the Mori-Tanaka model, one can easily evaluate the effects of interfacial delamination on the overall properties of composite materials. Therefore, the present method offers a pretty convenient tool. Some numerical results are carried out in order to demonstrate the performance of this model.

Elastic Fields in Double Inhomogeneity by the Equivalent Inclusion Method

2000 ◽  
Vol 68 (1) ◽  
pp. 3-10 ◽  
Author(s):  
H. M. Shodja ◽  
A. S. Sarvestani
Keyword(s):  
Elastic Constants ◽  
Present Method ◽  
Present Theory ◽  
Actual Distribution ◽  
Equivalent Inclusion Method ◽  
Inclusion Method ◽  
Ellipsoidal Inhomogeneity ◽  
Equivalent Inclusion ◽  
Comparison Results ◽  
Special Cases

Consider a double-inhomogeneity system whose microstructural configuration is composed of an ellipsoidal inhomogeneity of arbitrary elastic constants, size, and orientation encapsulated in another ellipsoidal inhomogeneity, which in turn is surrounded by an infinite medium. Each of these three constituents in general possesses elastic constants different from one another. The double-inhomogeneity system under consideration is subjected to far-field strain (stress). Using the equivalent inclusion method (EIM), the double inhomogeneity is replaced by an equivalent double-inclusion (EDI) problem with proper polynomial eigenstrains. The double inclusion is subsequently broken down to single-inclusion problems by means of superposition. The present theory is the first to obtain the actual distribution rather than the averages of the field quantities over the double inhomogeneity using Eshelby’s EIM. The present method is precise and is valid for thin as well as thick layers of coatings, and accommodates eccentric heterogeneity of arbitrary size and orientation. To establish the accuracy and robustness of the present method and for the sake of comparison, results on some of the previously reported problems, which are special cases encompassed by the present theory, will be re-examined. The formulations are easily extended to treat multi-inhomogeneity cases, where an inhomogeneity is surrounded by many layers of coatings. Employing an averaging scheme to the present theory, the average consistency conditions reported by Hori and Nemat-Nasser for the evaluation of average strains and stresses are recovered.

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