On transversely isotropic, orthotropic and relative isotropic functions of symmetric tensors, skew-symmetric tensors and vectors. Part IV: The representations for three dimensional orthotropic functions

1993 ◽  
Vol 31 (10) ◽  
pp. 1435-1443
Author(s):  
Q.-S. Zheng
Keyword(s):  
Three Dimensional ◽  
Transversely Isotropic ◽  
Symmetric Tensors ◽  
Isotropic Functions

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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