Green's Function for Transversely Isotropic Thermoelastic Diffusion Bimaterials

2014 ◽  
Vol 37 (10) ◽  
pp. 1201-1229 ◽  
Author(s):  
Rajneesh Kumar ◽  
Vandana Gupta
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Transversely Isotropic ◽  
Thermoelastic Diffusion

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.

An Improved Technique for Elastodynamic Green's Function Computation for Transversely Isotropic Solids

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Samaneh Fooladi ◽  
Tribikram Kundu
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Composite Structures ◽  
Transversely Isotropic ◽  
Computational Effort ◽  
Computational Time ◽  
Function Computation ◽  
Time Harmonic ◽  
Transversely Isotropic Solids ◽  
Isotropic Solids

Elastodynamic Green's function for anisotropic solids is required for wave propagation modeling in composites. Such modeling is needed for the interpretation of experimental results generated by ultrasonic excitation or mechanical vibration-based nondestructive evaluation tests of composite structures. For isotropic materials, the elastodynamic Green’s function can be obtained analytically. However, for anisotropic solids, numerical integration is required for the elastodynamic Green's function computation. It can be expressed as a summation of two integrals—a singular integral and a nonsingular (or regular) integral. The regular integral over the surface of a unit hemisphere needs to be evaluated numerically and is responsible for the majority of the computational time for the elastodynamic Green's function calculation. In this paper, it is shown that for transversely isotropic solids, which form a major portion of anisotropic materials, the integration domain of the regular part of the elastodynamic time-harmonic Green's function can be reduced from a hemisphere to a quarter-sphere. The analysis is performed in the frequency domain by considering time-harmonic Green's function. This improvement is then applied to a numerical example where it is shown that it nearly halves the computational time. This reduction in computational effort is important for a boundary element method and a distributed point source method whose computational efficiencies heavily depend on Green's function computational time.

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