Multiple ellipsoidal/elliptical inhomogeneities embedded in infinite matrix by equivalent inhomogeneous inclusion method

2021 ◽  
pp. 108128652110071
Author(s):  
Xiu-wei Yu ◽  
Zhong-wei Wang ◽  
Hao Wang
Keyword(s):  
Separation Distance ◽  
Stress And Strain ◽  
Infinite Matrix ◽  
The Finite Element Method ◽  
Stress Concentrations ◽  
Strain Fields ◽  
Equivalent Inclusion Method ◽  
Inclusion Method ◽  
Equivalent Inclusion ◽  
Small Separation

Traditional equivalent inclusion method provides unreliable predictions of the stress concentrations of two spherical inhomogeneities with small separation distance. This paper determines the stress and strain fields of multiple ellipsoidal/elliptical inhomogeneities by equivalent inhomogeneous inclusion method. Equivalent inhomogeneous inclusion method is an inverse of equivalent inclusion method and substitutes the subdomains of matrix with known strains by equivalent inhomogeneous inclusions. The stress and strain fields of multiple inhomogeneities are decomposed into the superposition of matrix under applied load and each solitary inhomogeneous inclusion with polynomial eigenstrains by the iteration of equivalent inhomogeneous inclusion method. Multiple circular and spherical inhomogeneities are respectively used as examples and examined by the finite element method. The stress concentrations of multiple inhomogeneities with small separation distances are well predicted by equivalent inhomogeneous inclusion method and the accuracies improve with the increase of eigenstrain orders. Equivalent inhomogeneous inclusion method gives more accurate stress predictions than equivalent inclusion method in the problem of two spherical inhomogeneities.

Two-Ellipsoidal Inhomogeneities by the Equivalent Inclusion Method

1975 ◽  
Vol 42 (4) ◽  
pp. 847-852 ◽  
Author(s):  
Z. A. Moschovidis ◽  
T. Mura
Keyword(s):  
Computer Program ◽  
Strain Field ◽  
Applied Strain ◽  
Stress And Strain ◽  
Isotropic Matrix ◽  
Equivalent Inclusion Method ◽  
Inclusion Method ◽  
Equivalent Inclusion ◽  
The Matrix ◽  
Final Stress

The problem of two ellipsoidal inhomogeneities in an infinitely extended isotropic matrix is treated by the equivalent inclusion method. The matrix is subjected to an applied strain field in the form of a polynomial of degree M in the position coordinates xi. The final stress and strain states are calculated for two isotropic ellipsoidal inhomogeneities both in the interior and the exterior (in the matrix) by using a computer program developed. The method can be extended to more than two inhomogeneities.

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.

Large Deformation Modeling Applied to the Sheet Metal Electromagnetic Forming

2008 ◽  
Author(s):  
C. Dumitras ◽  
I. Cozminca
Keyword(s):  
Finite Element ◽  
Deformation Process ◽  
Electromagnetic Forming ◽  
Stress And Strain ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Strain Fields ◽  
The Finite Element Analysis ◽  
History Of ◽  
Free Bulging

The electromagnetic forming has the advantage of a minimum forming time, but this is a major obstacle in determining the process’s history of the forming workpiece. Both experimental and theoretical known analysis methods for this process give a discret array of data (only for the displacements). One considers it is more adequate to use the finite element method in studying this process. The main advantage of the finite element analysis is given by the fact that it shows the stress and strain fields in a continuous way during the deformation process. Also, it offers a model from which one can predict the final shape of the part and the possible crack zones. One present a compared study of the experimental and the simulated results achieved of the free bulging aluminum specimens by electromagnetic impulses.

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