Micromechanical investigation of thermal stresses of a finite plane containing multiple elliptical inclusions based on the equivalent inclusion method and distributed dislocation method

2021 ◽  
Vol 35 (1) ◽  
pp. 247-256
Author(s):  
Jiong Zhang ◽  
Yunhai Huang ◽  
Weidong Liu ◽  
Liankun Wang ◽  
Chao Yang ◽  
...  
Keyword(s):  
Thermal Stresses ◽  
Finite Plane ◽  
Equivalent Inclusion Method ◽  
Inclusion Method ◽  
Equivalent Inclusion ◽  
Distributed Dislocation

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.

Semi-Analytic Solution of Multiple Inhomogeneous Inclusions and Cracks in an Infinite Space

2015 ◽  
Vol 12 (01) ◽  
pp. 1550002 ◽  
Author(s):  
Kun Zhou ◽  
Rongbing Wei ◽  
Guijun Bi ◽  
Xu Wang ◽  
Bin Song ◽  
...  
Keyword(s):  
Analytic Solution ◽  
The Finite Element Method ◽  
Infinite Space ◽  
Equivalent Inclusion Method ◽  
Equivalent Inclusion ◽  
Dislocation Densities ◽  
Distributed Dislocation ◽  
Potential Applications ◽  
Novel Method ◽  
Dislocation Technique

This work develops a semi-analytic solution for multiple inhomogeneous inclusions of arbitrary shape and cracks in an isotropic infinite space. The solution is capable of fully taking into account the interactions among any number of inhomogeneous inclusions and cracks which no reported analytic or semi-analytic solution can handle. In the solution development, a novel method combining the equivalent inclusion method (EIM) and the distributed dislocation technique (DDT) is proposed. Each inhomogeneous inclusion is modeled as a homogenous inclusion with initial eigenstrain plus unknown equivalent eigenstrain using the EIM, and each crack of mixed modes I and II is modeled as a distribution of edge climb and glide dislocations with unknown densities. All the unknown equivalent eigenstrains and dislocation densities are solved simultaneously by means of iteration using the conjugate gradient method (CGM). The fast Fourier transform algorithm is also employed to greatly improve computational efficiency. The solution is verified by the finite element method (FEM) and its capability and generality are demonstrated through the study of a few sample cases. This work has potential applications in reliability analysis of heterogeneous materials.

Numerical Implementation of the Equivalent Inclusion Method for 2D Arbitrarily Shaped Inhomogeneities

2014 ◽  
Vol 118 (1) ◽  
pp. 39-61 ◽  
Author(s):  
Qinghua Zhou ◽  
Xiaoqing Jin ◽  
Zhanjiang Wang ◽  
Jiaxu Wang ◽  
Leon M. Keer ◽  
...  
Keyword(s):  
Numerical Implementation ◽  
Equivalent Inclusion Method ◽  
Inclusion Method ◽  
Equivalent Inclusion
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