Lattice Statics Green's Function for Modeling of Dislocations in Crystals

1998 ◽  
Vol 529 ◽  
Author(s):  
V.K. Tewary
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Edge Dislocation ◽  
Transform Method ◽  
Lattice Statics ◽  
Simple Cubic ◽  
Cubic Model ◽  
Translation Symmetry ◽  
Matrix Partitioning ◽  
End Space

AbstractA lattice statics Green's function method is described for modeling an edge dislocation in a crystal lattice. The edge dislocation is created by introducing a half plane of vacancies as in Volterra's construction. The defect space is decomposed into a part that has translation symmetry and a localized end space. The Dyson's equation for the defect Green's function is solved by using a defect space Fourier transform method for the translational part and matrix partitioning for the localized part. Preliminary results for a simple cubic model are presented.

Lattice statics Green's function method for calculation of atomistic structure of grain boundary interfaces in solids: Part II. Anharmonic theory

1989 ◽  
Vol 4 (2) ◽  
pp. 320-326 ◽  
Author(s):  
V. K. Tewary ◽  
E. R. Fuller
Keyword(s):  
Grain Boundary ◽  
Green’S Function ◽  
Green's Function ◽  
Function Method ◽  
Nonlinear Matrix Equation ◽  
Green’S Function Method ◽  
Lattice Statics ◽  
Nonlinear Matrix ◽  
Atomistic Structure ◽  
Anharmonic Force

The lattice statics Green's function method for calculation of the atomistic structure of grain boundary interfaces in solids as described in Part I is extended to include anharmonic effects. It is shown that the ‘anharmonic’ response of a solid to ‘anharmonic’ forces can be represented in terms of the ‘harmonic’ response of the solid to an effective anharmonic force. The Green's function method then requires solving a finite order nonlinear matrix equation, which is done by using standard numerical methods. For the purpose of illustration, the method is applied to calculate the atomistic structure of a ∑5 tilt boundary in fec copper.

A Green’s Function Formulation of Anticracks and Their Interaction With Load-Induced Singularities

1989 ◽  
Vol 56 (3) ◽  
pp. 550-555 ◽  
Author(s):  
John Dundurs ◽  
Xanthippi Markenscoff
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Edge Dislocation ◽  
Weight Functions ◽  
Bimaterial Interface ◽  
Elastic Fields ◽  
Function Formulation ◽  
Concentrated Forces ◽  
Concentrated Couple ◽  
Working Out

This paper provides a Green’s function formulation of anticracks (rigid lamellar inclusions of negligible thickness that are bonded to the surrounding elastic material). Apart from systematizing several previously known solutions, the article gives the pertinent fields for concentrated forces, dislocations, and a concentrated couple applied on the line of the anticrack. There is a reason for working out these results: In contrast to concentrated forces, a concentrated couple approaching the tip of an anticrack makes the elastic fields explode. Finite limits can be achieved, however, by appropriately diminishing the magnitude of the couple, which then leads to fields that are intimately connected with the weight functions for the anticrack. An edge dislocation going to the tip of an anticrack puts a net force on the lamellar inclusion, which is shown to be related to a previously known feature of dislocations near a bimaterial interface.

Lattice statics of interfaces and interfacial cracks in bimaterial solids

1992 ◽  
Vol 7 (4) ◽  
pp. 1018-1028 ◽  
Author(s):  
V.K. Tewary ◽  
Robb Thomson
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Displacement Field ◽  
Nearest Neighbor ◽  
Interfacial Crack ◽  
Continuum Theory ◽  
Two Phase ◽  
Lattice Statics ◽  
Interfacial Cracks

A method for calculating lattice statics Green's function is described for a bimaterial lattice or a bicrystal containing a plane interface. The method involves creation of two half space lattices containing free surfaces and then joining them to form a bicrystal. The two half space lattices may have different structures as in a two-phase bicrystal or may be of the same type but joined at different orientations to form a grain boundary interface. The method is quite general but, in this paper, has been applied only to a simple model bicrystal formed by two simple cubic lattices with nearest neighbor interactions. The bimaterial Green's function is modified to account for an interfacial crack that is used to calculate the displacement field due to an applied external force. It is found that the displacement field, as calculated by using the lattice theory, does not have the unphysical oscillations predicted by the continuum theory.

Resistance calculation of the decorated centered cubic networks: Applications of the Green's function

2014 ◽  
Vol 28 (32) ◽  
pp. 1450252 ◽  
Author(s):  
M. Q. Owaidat ◽  
J. H. Asad ◽  
J. M. Khalifeh
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Function Method ◽  
Three Dimensional ◽  
Numerical Results ◽  
Effective Resistance ◽  
Cubic Lattice ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
Simple Cubic Lattice

The effective resistance between any pair of vertices (sites) on the three-dimensional decorated centered cubic lattices is determined by using lattice Green's function method. Numerical results are presented for infinite decorated centered cubic networks. A mapping between the resistance of the edge-centered cubic lattice and that of the simple cubic lattice is shown.

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