The two-dimensional stress fields induced by a set of infinitely many parallel edge dislocations are difficult to estimate as those of individual dislocations decay slowly. A simple numerical metho...

The stress field of an infinite set of discrete dislocations

Order-N method for force calculation in many-dislocation systems.

It is known that in two-dimensional periodic arrays of dislocations the summation of the periodic image fields is conditionally convergent. This is due to the long-range character of the elastic fields of dislocations. As a result, the stress field obtained for a doubly periodic array of dislocation dipoles may contain a spurious constant stress that depends on the adopted summation scheme. In the present work, we provide, based on micromechanical considerations, a simple physical explanation of the origin of the conditional convergence of lattice sums of image interactions. In this context, the spurious stresses are found in a closed form for an arbitrary elastic anisotropy, and this is achieved without using the stress field of an individual dislocation. An alternative procedure is also developed where the macroscopic spurious stresses are determined using the solution of the Eshelby's inclusion problem.

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The stress field of an infinite set of discrete dislocations

References

Order-N method for force calculation in many-dislocation systems.

Macroscopic stress and strain in a doubly periodic array of dislocation dipoles.

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