Eshelby’s tensor for cubic piezoelectric crystals and its application to cavity problems

2016 ◽  
Vol 155 ◽  
pp. 119-129 ◽  
Author(s):  
Chun-Ron Chiang
Keyword(s):  
Piezoelectric Crystals ◽  
Eshelby’S Tensor

Phonon focusing in piezoelectric crystals

1987 ◽  
Vol 36 (3) ◽  
pp. 1432-1447 ◽  
Author(s):  
A. G. Every ◽  
A. K. McCurdy
Keyword(s):  
Piezoelectric Crystals ◽  
Phonon Focusing

Detection of odorants using an array of piezoelectric crystals and neural-network pattern recognition

1991 ◽  
Vol 249 (2) ◽  
pp. 323-329 ◽  
Author(s):  
S.-M. Chang ◽  
Y. Iwasaki ◽  
M. Suzuki ◽  
E. Tamiya ◽  
I. Karube ◽  
...  
Keyword(s):  
Neural Network ◽  
Pattern Recognition ◽  
Piezoelectric Crystals ◽  
Network Pattern

Elastic solution of a polyhedral particle with a polynomial eigenstrain and particle discretization

2021 ◽  
pp. 1-35
Author(s):  
Chunlin Wu ◽  
Liangliang Zhang ◽  
Huiming Yin
Keyword(s):  
Taylor Series ◽  
Three Dimensional ◽  
Stress Singularity ◽  
Elastic Field ◽  
Analytical Form ◽  
Tetrahedral Elements ◽  
Equivalent Inclusion Method ◽  
Equivalent Inclusion ◽  
Eshelby’S Tensor ◽  
Domain Discretization

Abstract The paper extends the recent work (JAM, 88, 061002, 2021) of the Eshelby's tensors for polynomial eigenstrains from a two dimensional (2D) to three dimensional (3D) domain, which provides the solution to the elastic field with continuously distributed eigenstrain on a polyhedral inclusion approximated by the Taylor series of polynomials. Similarly, the polynomial eigenstrain is expanded at the centroid of the polyhedral inclusion with uniform, linear and quadratic order terms, which provides tailorable accuracy of the elastic solutions of polyhedral inhomogeneity by using Eshelby's equivalent inclusion method. However, for both 2D and 3D cases, the stress distribution in the inhomogeneity exhibits a certain discrepancy from the finite element results at the neighborhood of the vertices due to the singularity of Eshelby's tensors, which makes it inaccurate to use the Taylor series of polynomials at the centroid to catch the eigenstrain at the vertices. This paper formulates the domain discretization with tetrahedral elements to accurately solve for eigenstrain distribution and predict the stress field. With the eigenstrain determined at each node, the elastic field can be predicted with the closed-form domain integral of Green's function. The parametric analysis shows the performance difference between the polynomial eigenstrain by the Taylor expansion at the centroid and the 𝐶0 continuous eigenstrain by particle discretization. Because the stress singularity is evaluated by the analytical form of the Eshelby's tensor, the elastic analysis is robust, stable and efficient.

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