Elastic fields due to defects in transversely isotropic bimaterials

1995 ◽  
Vol 449 (1935) ◽  
pp. 1-30 ◽  
Keyword(s):  
Point Defects ◽  
Analytic Solution ◽  
Transversely Isotropic ◽  
Planar Interface ◽  
Dislocation Loops ◽  
Elastic Fields ◽  
Closed Form Solutions ◽  
Transversely Isotropic Solids ◽  
Isotropic Solids ◽  
Plane Of Isotropy

A method for obtaining the analytic solution of the elastic fields due to defects such as inclusions, dislocations, disclinations, and point defects in transversely isotropic bimaterials is presented. The bimaterial consists of two semi-infinite transversely isotropic solids either perfectly bonded together or in frictionless contact with each other at a planar interface which is parallel to the plane of isotropy of both solids. The elastic solution is expressed in terms of the hexagonal stress vectors for the double force and the double force with moment. Closed form solutions for inclusions with pure dilatational eigenstrain, straight dislocation and disclination lines, circular, dislocation loops, and point defects are presented.

Near-Tip Fields for Penny-Shaped Cracks in Magnetoelectroelastic Media

2006 ◽  
Vol 312 ◽  
pp. 41-46 ◽  
Author(s):  
Bao Lin Wang ◽  
Yiu Wing Mai
Keyword(s):  
Closed Form ◽  
Transversely Isotropic ◽  
Crack Plane ◽  
Axially Symmetric ◽  
Crack Configuration ◽  
Penny Shaped Crack ◽  
Electric And Magnetic Fields ◽  
Shaped Crack ◽  
Transversely Isotropic Solids ◽  
Isotropic Solids

This paper solves the penny-shaped crack configuration in transversely isotropic solids with coupled magneto-electro-elastic properties. The crack plane is coincident with the plane of symmetry such that the resulting elastic, electric and magnetic fields are axially symmetric. The mechanical, electrical and magnetical loads are considered separately. Closed-form expressions for the stresses, electric displacements, and magnetic inductions near the crack frontier are given.

True bounds on Poisson's ratios for transversely isotropic solids

1992 ◽  
Vol 27 (1) ◽  
pp. 43-44 ◽  
Author(s):  
P S Theocaris ◽  
T P Philippidis
Keyword(s):  
Energy Density ◽  
Basic Principle ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Elastic Solid ◽  
Transversely Isotropic ◽  
Linear Elastic ◽  
Positive Strain ◽  
Transversely Isotropic Solids ◽  
Isotropic Solids

The basic principle of positive strain energy density of an anisotropic linear or non-linear elastic solid imposes bounds on the values of the stiffness and compliance tensor components. Although rational mathematical structuring of valid intervals for these components is possible and relatively simple, there are mathematical procedures less strictly followed by previous authors, which led to an overestimation of the bounds and misinterpretation of experimental results.

Green’s Functions for Two-Phase Transversely Isotropic Materials

1979 ◽  
Vol 46 (3) ◽  
pp. 551-556 ◽  
Author(s):  
Y.-C. Pan ◽  
T.-W. Chou
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Elastic Constants ◽  
Transversely Isotropic ◽  
Two Phase ◽  
Closed Form Solutions ◽  
Isotropic Materials ◽  
Function Solution ◽  
Present Solution ◽  
Plane Of Isotropy

Closed-form solutions are obtained for the Green’s function problems of point forces applied in the interior of a two-phase material consisting of two semi-infinite transversely isotropic elastic media bonded along a plane interface. The interface is parallel to the plane of isotropy of both media. The solutions are applicable to all combinations of elastic constants. The present solution reduces to Sueklo’s expression when the point force is normal to the plane of isotropy and (C11C33)1/2 ≠ C13 + 2C44 for both phases. When the elastic constants of one of the phases are set to zero, the solution can be reduced to the Green’s function for semi-infinite media obtained by Michell, Lekhnitzki, Hu, Shield, and Pan and Chou. The Green’s function solution of Pan and Chou for an infinite transversely isotropic solid can be reproduced from the present expression by setting the elastic constants of both phases to be equal. Finally, the Green’s function for isotropic materials can also be obtained from the present solution by suitable substitution of elastic constants.

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