Three-dimensional crack problems for the isotropic or transversely isotropic infinite solid

2003 ◽  
pp. 77-129
Author(s):  
Mark Kachanov ◽  
Boris Shafiro ◽  
Igor Tsukrov
Keyword(s):  
Three Dimensional ◽  
Transversely Isotropic ◽  
Crack Problems

THREE-DIMENSIONAL ANALYSIS OF ARBITRARY-SHAPED CRACKS IN PIEZOELECTRIC SOLIDS UNDER SHEAR LOADING

2006 ◽  
Vol 03 (03) ◽  
pp. 321-336
Author(s):  
HE-GEN YU ◽  
MENG-CHENG CHEN
Keyword(s):  
Electric Displacement ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Shear Loading ◽  
Elastic Fields ◽  
Uniform Shear ◽  
Closed Type ◽  
Ellipsoidal Coordinates ◽  
Crack Problems ◽  
Planar Crack

This paper is a sequel of the author's previous work [Chen (2004)]. It deals with some basic linear electro-elastic fracture problems for an arbitrary-shaped planar crack in a three-dimensional infinite transversely isotropic piezoelectric material subjected to shear loading that is antisymmetric with respect to the crack. The finite-part integral concept is used to derive hypersingular integral equations for the crack from available solutions of the point force and charge for an infinite transversely isotropic piezoelectric solid. Closed-type solutions for the full electro-elastic fields, for the stress and electric displacement K-fields and the energy release rate G are obtained. In particular, under uniform shear loading, exact expressions for an elliptical crack are derived with introducing the ellipsoidal coordinates. Finally, numerical examples for some typical crack problems are also demonstrated in table and graphic forms.

Indentation of a Transversely Isotropic Thermoporoelastic Half-Space by a Rigid Circular Cylindrical Punch

2017 ◽  
Vol 84 (11) ◽  
Author(s):  
Yilan Huang ◽  
Guozhan Xia ◽  
Weiqiu Chen ◽  
Xiangyu Li
Keyword(s):  
Half Space ◽  
Original Problem ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
The Finite Element Method ◽  
Thermal Fields ◽  
Cylindrical Punch ◽  
The One ◽  
Physical Quantities ◽  
Potential Theory Method

Exact solutions to the three-dimensional (3D) contact problem of a rigid flat-ended circular cylindrical indenter punching onto a transversely isotropic thermoporoelastic half-space are presented. The couplings among the elastic, hydrostatic, and thermal fields are considered, and two different sets of boundary conditions are formulated for two different cases. We use a concise general solution to represent all the field variables in terms of potential functions and transform the original problem to the one that is mathematically expressed by integral (or integro-differential) equations. The potential theory method is extended and applied to exactly solve these integral equations. As a consequence, all the physical quantities of the coupling fields are derived analytically. To validate the analytical solutions, we also simulate the contact behavior by using the finite element method (FEM). An excellent agreement between the analytical predictions and the numerical simulations is obtained. Further attention is also paid to the discussion on the obtained results. The present solutions can be used as a theoretical reference when practically applying microscale image formation techniques such as thermal scanning probe microscopy (SPM) and electrochemical strain microscopy (ESM).

Complete solutions of three-dimensional problems in transversely isotropic media

2018 ◽  
Vol 32 (3) ◽  
pp. 775-802 ◽  
Author(s):  
Francesco Marmo ◽  
Salvatore Sessa ◽  
Nicoló Vaiana ◽  
Daniela De Gregorio ◽  
Luciano Rosati
Keyword(s):  
Three Dimensional ◽  
Transversely Isotropic ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Complete Solutions
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