In this paper, the interaction between a screw dislocation and an arbitrary shaped elastic inhomogeneity with different material properties than the surrounding matrix is investigated. The exact solution to this problem is derived by means of complex variable methods and Faber series expansion. Specifically, the conformal mapping function maps the matrix region surrounding the inhomogeneity onto the outside of a unit circle in the image plane, while the analytic function defined in the elastic inhomogeneity is expressed in terms of a Faber series expansion. Once the series form solution is obtained, the stress fields due to the screw dislocation can be obtained. Also the image force on the screw dislocation due to its interaction with the elastic inhomogeneity is derived. Three examples of a screw dislocation interacting with (1) an equilateral triangular inhomogeneity, (2) a square inhomogeneity, and (3) a five-pointed star-shaped inhomogeneity are presented to illustrate how the stiffness of the triangular, square or five-pointed star-shaped inhomogeneity can influence the mobility of the screw dislocation.

1.
Dundurs
,
J.
, and
Mura
,
T.
, 1964, “
Interaction Between an Edge Dislocation and a Circular Inclusion
,”
J. Mech. Phys. Solids
0022-5096
12
, pp.
177
189
.
2.
Dundurs
,
J.
, 1967, “
On the Interaction of a Screw Dislocation With Inhomogeneities
,”
Recent Adv. Eng. Sci.
,
2
, pp.
223
233
.
3.
Sendeckyj
,
G. P.
, 1970, “
Fundamental Aspects of Dislocation Theory
”.
J. A.
Summons
,
Wit R.
De
, and
R.
Bulouch
, eds.,
National Bureau of Standards (U.S.)
, Special Publication 317, Vol.
I
, p.
57
.
4.
Stagni
,
L.
, and
Lizzio
,
R.
, 1983, “
Shape Effects in the Interaction Between an Edge Dislocation and an Elliptical Inhomogeneity
,”
Appl. Phys. A: Solids Surf.
0721-7250
A30
, pp.
217
221
.
5.
Chen
,
D. H.
, 1994, “
Interference Between an Elliptical Inclusion and Point Force or Dislocation
,”
J. Jpn. Soci. Mech. Engi.
,
60
, pp.
2796
2801
.
6.
Wu
,
K. C.
, 1992, “
Interaction of a Dislocation With an Elliptic Hole or Rigid Inclusion in an Anisotropic Material
,”
J. Appl. Phys.
0021-8979
72
, pp.
2156
2163
.
7.
Santare
,
M. H.
, and
Keer
,
L. M.
, 1986, “
Interaction Between an Edge Dislocation and a Rigid Elliptic Inclusion
,”
ASME J. Appl. Mech.
0021-8936
53
, pp.
382
385
.
8.
Tsukrov
,
I.
, and
Novak
,
J.
, 2004, “
Effective Elastic Properties of Solids With Two-dimensional Inclusions of Irregular Shapes
,”
Int. J. Solids Struct.
0020-7683
41
, pp.
6905
6924
.
9.
Ru
,
C. Q.
, 1999, “
Analytic Solution for Eshelby’s Problem of an Inclusion of Arbitrary Shape in a Plane or Half-plane
,”
ASME J. Appl. Mech.
0021-8936
66
, pp.
315
322
.
10.
Ru
,
C. Q.
, 2003, “
Eshelby Inclusion of Arbitrary Shape in an Anisotropic Plane or Half-plane
,”
Acta Mech.
0001-5970
160
, pp.
219
234
.
11.
Curtiss
,
J. H.
, 1971, “
Faber Polynomials and Faber Series
,”
Am. Math. Monthly
78
, pp.
577
596
.
12.
Gao
,
C. F.
, and
Noda
,
N.
, 2004, “
Faber Series Method for Two-dimensional Problems of Arbitrarily Shaped Inclusion in Piezoelectric Materials
,”
Acta Mech.
0001-5970
171
, pp.
1
13
.
13.
Chen
,
T.
, and
Chiang
,
S. C.
, 1997, “
Electroelastic Fields and Effective Moduli of a Medium Containing Cavities or Rigid Inclusions of Arbitrary Shape Under Anti-plane Mechanical and In-plane Electric Fields
,”
Acta Mech.
0001-5970
121
, pp.
79
96
.
14.
Thorpe
,
M. F.
, 1992, “
The Conductivity of a Sheet Containing a few Polygonal Holes or Superconducting Inclusions
,”
Proc. R. Soc. London, Ser. A
1364-5021
437
, pp.
215
227
.
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