Equivalent Inclusion Method-Based Virtual Experiments of Magnetic Particle Alignment in a Viscous Fluid

2019 ◽  
Author(s):  
Gan Song ◽  
Sung-Hwan Jang ◽  
Liang-Liang Zhang ◽  
Hui-Ming Yin
Keyword(s):  
Viscous Fluid ◽  
Magnetic Particle ◽  
Virtual Experiments ◽  
Equivalent Inclusion Method ◽  
Inclusion Method ◽  
Equivalent Inclusion ◽  
Particle Alignment

Equivalent Inclusion Method for the Stokes Flow of Drops Moving in a Viscous Fluid

2014 ◽  
Vol 81 (7) ◽  
Author(s):  
H. M. Yin ◽  
P.-H. Lee ◽  
Y. J. Liu
Keyword(s):  
Viscous Fluid ◽  
Stokes Flow ◽  
The Body ◽  
Function Technique ◽  
Elongation Ratio ◽  
Spherical Drop ◽  
Equivalent Inclusion Method ◽  
Inclusion Method ◽  
Equivalent Inclusion ◽  
The Matrix

The equivalent inclusion method is presented to derive the Stokes flow of multiple drops moving in a viscous fluid at a small Reynolds number. The drops are replaced by inclusions with the same viscosity as the fluid, but an eigenstrain rate field that is a fictitious nonmechanical strain rate field is introduced to represent the viscosity mismatch between each drop and the matrix fluid. The velocity and pressure fields can be solved by considering the body force and eigenstrain rate on the inclusions with the Green's function technique. When one spherical drop is considered, the solution recovers the closed-form classic solution. This method is versatile and can be used in the simulation of a many-body system with different drop size, elongation ratio, and viscosity. Numerical examples demonstrate the capability and accuracy of the proposed formulation and illustrate particles' rotation and motion caused by particle interactions.

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.

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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